Introductory Chemistry

Some Basic Definitions

🧭 Overview

🧠 One-sentence thesis

Chemistry studies matter and energy interactions by describing matter through physical and chemical properties, classifying it into elements, compounds, and mixtures, and distinguishing physical changes from chemical changes.

📌 Key points (3–5)

What chemistry studies: the interactions of matter with other matter and with energy.
Two ways to describe matter: physical properties (characteristics as it exists) vs. chemical properties (how it changes form with other matter).
Two types of change: physical change (alters physical properties without changing chemical composition) vs. chemical change (creates new matter with new properties).
Common confusion: pure substances (elements and compounds) vs. mixtures (physical combinations); homogeneous mixtures (solutions) look uniform, heterogeneous mixtures show distinct components.
Classifying elements: metals (shiny, conductive, malleable) vs. nonmetals (brittle, poor conductors) vs. semimetals (properties of both).

🧱 What matter is and how to describe it

🧱 Defining matter

Matter: anything that has mass and takes up space.

Books, computers, food, dirt, and even air are all matter.
Air is easy to overlook because it is thin, but it still has mass and occupies space.
Things that are not matter: thoughts, ideas, emotions, hopes—these have no mass and take no space.
Example: A hot dog is matter (has mass, takes up space); love is not matter (it is an emotion).

🔍 Physical properties

Physical properties: characteristics that describe matter as it exists.

Examples: shape, color, size, temperature.
An important physical property is the phase (or state) of matter.
The three fundamental phases: solid, liquid, gas.
Physical properties tell you what matter looks like or feels like right now, without changing what it is chemically.

⚗️ Chemical properties

Chemical properties: characteristics that describe how matter changes form in the presence of other matter.

Examples: Does it burn? Does it react violently with water?
Chemical properties reveal what matter can do when it interacts with other substances.
Example: The fact that a match burns is a chemical property.
Don't confuse: physical properties describe matter as-is; chemical properties describe how matter transforms.

🔄 Physical vs. chemical changes

🔄 Physical change

Physical change: when a sample of matter changes one or more of its physical properties.

The chemical composition stays the same.
Examples: solid ice melts into liquid water; alcohol in a thermometer expands or contracts with temperature.
Example: Water in the air turns into snow—this is a physical change (gas phase → solid phase).
Example: A person's hair is cut—this is a physical change (shortening length, no chemical reaction).

🔥 Chemical change

Chemical change: the process of demonstrating a chemical property.

The chemical composition changes; new forms of matter with new physical properties are created.
Example: Bread dough becomes fresh bread in an oven—chemical changes occur due to heat.
Note: chemical changes are often accompanied by physical changes, because the new matter will have different physical properties.
Example: A fire in a fireplace is a chemical change (burning); warming water for coffee is a physical change (temperature increase only).

🧪 Substances: elements and compounds

🧪 What a substance is

Substance: a sample of matter that has the same physical and chemical properties throughout.

Sometimes called a "pure substance," but "pure" is not needed in the strict chemical definition.
Chemistry has a specific definition for "substance" that differs from everyday vague usage.
There are two types of substances: elements and compounds.

⚛️ Elements

Element: the simplest type of chemical substance; it cannot be broken down into simpler chemical substances by ordinary chemical means.

About 115 elements are known; 80 are stable (the rest are radioactive).
Each element has its own unique set of physical and chemical properties.
Examples: iron, carbon, gold.

🧬 Compounds

Compound: a combination of more than one element.

The physical and chemical properties of a compound are different from those of its constituent elements.
A compound behaves as a completely different substance.
Over 50 million compounds are known, with more discovered daily.
Examples: water, penicillin, sodium chloride (table salt).

🥤 Mixtures: heterogeneous and homogeneous

🥤 What mixtures are

Mixtures: physical combinations of more than one substance.

Mixtures are not pure substances; they contain multiple elements or compounds physically combined.
There are two types: heterogeneous and homogeneous.

🌰 Heterogeneous mixtures

Heterogeneous mixture: a mixture composed of two or more substances where it is easy to tell that more than one substance is present.

Sometimes visible to the naked eye.
Example: A combination of salt crystals and steel wool—you can see which particles are salt and which are steel wool.
Example: A mixture of iron metal filings and sulfur powder (assuming they are simply mixed together).

💧 Homogeneous mixtures (solutions)

Homogeneous mixture: a combination of two or more substances that is so intimately mixed that the mixture behaves as a single substance.

Another word for homogeneous mixture is solution.
Very difficult to tell that more than one substance is present, even with a powerful microscope.
Example: Salt crystals dissolved in water—the mixture looks uniform.
Example: Soda water (carbon dioxide dissolved in water); an amalgam (metals dissolved in mercury).
Don't confuse: the human body is a heterogeneous mixture (you can distinguish organs, tissues, etc.); an amalgam is a homogeneous mixture (uniform throughout).

🪙 Classifying elements: metals, nonmetals, semimetals

🪙 Metals

Metal: an element that is solid at room temperature (with mercury as a well-known exception), is shiny and silvery, conducts electricity and heat well, can be pounded into thin sheets (malleability), and can be drawn into thin wires (ductility).

Example: Iron is a metal because it is solid, shiny, and conducts electricity and heat well.
Mercury is the only metal that is liquid at room temperature but has all other expected metal properties.

🌫️ Nonmetals

Nonmetal: an element that is brittle when solid, does not conduct electricity or heat very well, and cannot be made into thin sheets or wires.

Nonmetals exist in a variety of phases and colors at room temperature.
Example: Elemental sulfur is a yellow nonmetal, usually found as a powder.
Example: Oxygen is a nonmetal (it is a gas at room temperature, does not conduct well).

⚙️ Semimetals (metalloids)

Semimetals (or metalloids): elements that have properties of both metals and nonmetals.

Example: Elemental carbon conducts heat and electricity well (metal-like) but is black, brittle, and cannot be made into sheets or wires (nonmetal-like).
Example: Pure silicon is shiny and silvery (metal-like) but does not conduct electricity or heat well (nonmetal-like).

Category	Key properties	Examples
Metals	Shiny, conductive, malleable, ductile	Iron, mercury
Nonmetals	Brittle, poor conductors, various colors/phases	Sulfur, oxygen
Semimetals	Mix of metal and nonmetal properties	Carbon, silicon

🌍 Chemistry in everyday life

🌍 Morning routine examples

The excerpt provides a "Chemistry Is Everywhere: In the Morning" sidebar with everyday examples:

Shower/bath: Soap and shampoo contain chemicals that interact with oil and dirt to remove them; fragrances make you smell good.
Brushing teeth: Toothpaste contains abrasives (tiny hard particles that physically scrub) and fluoride (chemically interacts with tooth surfaces to prevent cavities).
Vitamins and medicines: Vitamins and supplements provide chemicals your body needs; medicines are chemicals that combat disease.
Cooking eggs: Frying eggs involves heating them so a chemical reaction occurs to cook them.
Digestion: Food in the stomach is chemically reacted so the body can absorb nutrients.
Driving: Vehicles burn gasoline (a chemical change) to provide energy.

These examples show that chemistry is not abstract—it is present in personal hygiene, food preparation, health, and transportation.

Chemistry as a Science

🧭 Overview

🧠 One-sentence thesis

Science is a process of learning about the natural universe through observation and experiment, evolving over 350+ years into humanity's best method for understanding the world around us.

📌 Key points (3–5)

What science is: a process of knowing about the natural universe through observation and experiment, not just thinking.
How the scientific method works: hypothesis → experiment → refine (though real science builds on existing knowledge, not starting fresh daily).
Hierarchy of scientific knowledge: hypothesis (educated guess) → theory (general principle from collected evidence) → law (statement thought never violated).
Common confusion: "theory" in everyday speech means "guess," but in science it means a powerful, well-supported explanation; "law" in everyday life is breakable, but scientific laws are thought inviolate.
What counts as science: only studies of the natural universe (stars, planets, life, matter)—not contrived human constructs like language or ethics.

🔬 The scientific process

🔬 What makes something science

Science is the process of knowing about the natural universe through observation and experiment.

Science focuses exclusively on the natural universe—things that occur naturally around us (stars, planets, how matter functions, life on earth).
It is not the only way of knowing; the ancient Greeks simply sat and thought, but science has proven more effective over 350+ years.
Science is concerned only with what occurs naturally, not with human-made constructs.

🧪 How hypotheses and experiments work

A hypothesis is an educated guess about how the natural universe works.

A good hypothesis is grounded in previously understood knowledge and represents a testable extension.
Example from the excerpt: "If I mix one part hydrogen with one part oxygen, I can make a substance that contains both elements."
Scientists then devise experiments—tests of the natural universe to see if the guess is correct.

Why experiments are necessary:

The natural universe is not always obvious.
Example: It's obvious a dropped object falls (explained by gravity), but it's not obvious that the entire universe is composed of only ~115 fundamental elements.
The concept of the element is only ~200 years old; it took decades of tests and millions of experiments to establish what elements actually are.

🏗️ Building blocks of scientific knowledge

Level	Definition	Strength	Example from excerpt
Hypothesis	Educated guess designed to test if the universe works in a new way	Testable extension of known knowledge	Mixing hydrogen and oxygen
Theory	General statement explaining a large number of observations	Very powerful; "overwhelming amount of evidence"	"All matter is composed of atoms"
Law	Specific statement thought never violated by the entire natural universe	Highest understanding; thought inviolate	Law of gravitation (all matter attracts all other matter)

Don't confuse:

Theory in science vs. everyday usage: In common speech, "theory" often means hypothesis ("I have a theory…"), but in science it indicates overwhelming evidence.
Law in science vs. everyday usage: Everyday laws are arbitrary limits that can be broken with consequences (speed limits); scientific laws are thought to be never violated.

🌍 What counts as science vs. non-science

🌍 The natural universe criterion

Science deals only with the natural universe. Other fields may be worth knowing but are not science if they study contrived or human-made systems.

Examples from the excerpt:

Field	Is it science?	Why or why not
Geology (study of the earth)	Yes	Earth is a natural object
Biology (study of living organisms)	Yes	Living organisms are part of the natural universe
Ethics (study of morality)	No	Deals with right and wrong—useful concepts but not natural phenomena
Political science	No	All governments are created by humans (despite "science" in the name)
English language	No	Ultimately contrived/made up; we agreed b-l-u-e represents a color, but could have used any word

🎨 The language example

The word "blue" represents a certain color because everyone agreed.
We could use "hardnrf" instead—as long as everyone agreed.
Anyone learning a second language wonders why a certain word describes a certain concept; ultimately, speakers agreed (it was contrived).
Language is very important in society but is not science.

🔢 Qualitative vs. quantitative science

🔢 Two ways to describe the universe

Qualitative implies a description of the quality of an object.

Quantitative description represents the specific amount of something; it means knowing how much is present, usually by counting or measuring it.

Science can be either qualitative or quantitative—both are important in chemistry.

📊 Examples from the excerpt

Statement	Type	Why
"Sulfur is yellow"	Qualitative	Describes a physical property/quality
"Gold metal is yellow"	Qualitative	Describes how it is
"25 students in a class"	Quantitative	Specific amount by counting
"A ream of paper has 500 sheets"	Quantitative	Specific amount
"The weather outside is snowy"	Qualitative	Description of how the day is
"The temperature outside is 24 degrees Fahrenheit"	Quantitative	Specific quantity (temperature)
"Roses are red, and violets are blue"	Qualitative	Color descriptions
"Four score and seven years ago"	Quantitative	Specific amount of time (87 years)

🧬 Fields within science

🧬 How science is organized

Science has become so large that it is separated into more specific fields:

Mathematics: the language of science; all scientific fields use it (some more than others).
Physics and astronomy: concerned with fundamental interactions between matter and energy.
Chemistry: the study of interactions of matter with other matter and with energy.
Biology: the study of living organisms.
Geology: the study of the earth.

Important note: These fields are not always completely separate; boundaries are not always readily apparent.

Example: A scientist may be labeled a biochemist if studying the chemistry of biological organisms.

Expressing Numbers

🧭 Overview

🧠 One-sentence thesis

Scientific notation provides a compact and clear way to express very large or very small numbers by using powers of 10, avoiding the cumbersome zeros required in standard notation.

📌 Key points (3–5)

What scientific notation is: expressing a number as a coefficient (between 1 and 10) multiplied by a power of 10.
When to use it: for very large numbers (e.g., 306,000,000) or very small numbers (e.g., 0.000000419) where standard notation becomes cumbersome.
How exponents work: positive exponents for numbers greater than 1; negative exponents for numbers between 0 and 1; the exponent value equals the number of zeros.
Common confusion: the sign of the exponent—positive means "large number," negative means "small decimal number less than one."
Practical shortcut: count how many places you move the decimal point to get a value between 1 and 10; that count is the exponent (positive if moving left, negative if moving right).

🔢 Standard vs. scientific notation

🔢 What standard notation is

Standard notation: the straightforward expression of a number.

Numbers like 17, 101.5, and 0.00446 are written in standard notation.
Fine for relatively small numbers, but becomes cumbersome for very large or very small numbers due to the many zeros needed.
Example: 306,000,000 requires eight digits, most of which are zeros; 0.000000419 requires many leading zeros to place the nonzero digits correctly.

🔬 What scientific notation is

Scientific notation: an expression of a number using powers of 10.

The number is written as a coefficient (the first nonzero digit, a decimal point, then the rest of the digits) multiplied by a power of 10.
The coefficient is the part multiplied by the power of 10.
Example: 79,345 becomes 7.9345 × 10⁴ because 79,345 = 7.9345 × 10,000 and 10,000 = 10⁴.
Extra zeros at the end or beginning are typically omitted.

⚡ Powers of 10 and exponents

⚡ Positive exponents for large numbers

Exponent: the raised number to the right of the 10 indicating the number of factors of 10 in the original number.

Powers of 10 with positive exponents represent large numbers:
- 10¹ = 10
- 10² = 100 = 10 × 10
- 10³ = 1,000 = 10 × 10 × 10
- 10⁴ = 10,000 = 10 × 10 × 10 × 10
The exponent's value equals the number of zeros in the number expressed in standard notation.
Example: 306,000 = 3.06 × 100,000 = 3.06 × 10⁵.

⚡ Negative exponents for small numbers

Powers of 10 with negative exponents represent small decimal numbers:
- 10⁻¹ = 0.1 = 1/10
- 10⁻² = 0.01 = 1/100
- 10⁻³ = 0.001 = 1/1,000
- 10⁻⁴ = 0.0001 = 1/10,000
A negative exponent implies a decimal number less than one.
The exponent's value equals the number of zeros in the denominator of the associated fraction.
Example: 0.00884 = 8.84 × 0.001 = 8.84 × 10⁻³.

🔍 Don't confuse the sign of the exponent

Positive exponent: the original number is greater than 1 (a large number).
Negative exponent: the original number is between 0 and 1 (a small decimal).
The sign does not indicate whether the number itself is positive or negative; it indicates size relative to 1.

🛠️ How to convert to scientific notation

🛠️ Step-by-step method

Write the first nonzero digit.
Add a decimal point.
Write the rest of the digits (omitting trailing or leading zeros).
Determine the power of 10 needed to turn this coefficient back into the original number.
Multiply the coefficient by that power of 10.

Example from the excerpt:

79,345 → 7.9345 (coefficient) × 10,000 (which is 10⁴) → 7.9345 × 10⁴.
0.000000559 → 5.59 (coefficient) × 0.0000001 (which is 10⁻⁷) → 5.59 × 10⁻⁷.

📏 Counting decimal places shortcut

Count the number of places you move the decimal point to get a numerical value between 1 and 10.
The number of places equals the power of 10.
Direction matters:
- Move decimal to the left → positive exponent (original number was large).
- Move decimal to the right → negative exponent (original number was small).
Example: 2,760,000 → move decimal 6 places left → 2.76 × 10⁶.
Example: 0.0009706 → move decimal 4 places right → 9.706 × 10⁻⁴.

🧮 Using scientific notation in practice

🧮 Entering into calculators

Many chemistry quantities are expressed in scientific notation.
Different calculator models require different actions to enter scientific notation correctly.
The excerpt advises: if in doubt, consult your instructor immediately.
Some calculators display only the coefficient and the power of 10 separately (e.g., showing "3.84951" and "18" to represent 3.84951 × 10¹⁸).

📋 Key takeaways from the excerpt

Notation type	What it is	When to use
Standard notation	Straightforward expression of a number	For relatively small numbers
Scientific notation	Coefficient times a power of 10	For very large or very small numbers
Positive exponent	Power of 10 is positive	Numbers greater than 1
Negative exponent	Power of 10 is negative	Numbers between 0 and 1

Significant Figures

🧭 Overview

🧠 One-sentence thesis

Significant figures limit measurements and calculations to only the digits we can reliably know or estimate, preventing false precision in reported values.

📌 Key points (3–5)

What significant figures represent: the limits of what values in a measurement or calculation we are sure of, including all known values plus the first estimated value.
Why we need them: starting with measurements of limited precision (e.g., three digits) should not produce answers with many more digits (e.g., twelve), which would be presumptuous.
Rules for identifying significant figures: nonzero digits are always significant; embedded zeros are significant; trailing zeros without a decimal point are not significant; leading zeros in decimals are not significant.
Common confusion: zeros can be significant or not depending on their position—scientific notation removes ambiguity by including only significant zeros in the coefficient.
Different rules for different operations: addition/subtraction limit by rightmost common column; multiplication/division limit by the data value with the fewest significant figures.

📏 Understanding measurements and estimation

📏 The measurement process

When measuring with a ruler, you can read certain digits with certainty (by counting tick marks) and must estimate one additional digit.
Example: An object is past the 1.3 cm mark but before 1.4 cm; with a practiced eye, you estimate it as about six-tenths of the way between, giving 1.36 cm.
The hundredths place (6) is an estimate, so reporting a thousandths place would be meaningless—you cannot estimate beyond what you can reasonably see.

🎯 The convention for reporting

Significant figures (sometimes called significant digits) represent the limits of what values of a measurement or a calculation we are sure of.

The quantity reported should include all known values and the first estimated value.
This prevents claiming more precision than the measurement method allows.

🔢 Rules for identifying significant figures

✅ What counts as significant

Rule	Description	Example
Nonzero digits	Any nonzero digit is always significant	36.7 has three significant figures
Embedded zeros	Zeros between nonzero digits are significant	2,002 has four significant figures
Trailing zeros with decimal	Zeros at the end of a number with a decimal point are significant	765,890.0 has seven significant figures

❌ What does not count as significant

Rule	Description	Example
Trailing zeros without decimal	Zeros at the end without a decimal point are not significant	306,490,000 has five significant figures (the trailing zeros only position the other digits)
Leading zeros	Zeros at the beginning of a decimal number are not significant	0.006606 has four significant figures (the first three zeros only position the digits)

🔬 Using scientific notation to clarify

Scientific notation removes ambiguity about zeros: it includes zeros in the coefficient only if they are significant.
Example: 8.666 × 10⁶ has four significant figures; 8.6660 × 10⁶ has five significant figures (the last zero is significant because it appears in the coefficient).

➕ Calculations with significant figures

➕ Addition and subtraction rule

Limit the reported answer to the rightmost column that all numbers have significant figures in common.

Look at where each number's significant figures end (which decimal place).
The answer cannot be more precise than the least precise measurement.
Example: Adding 1.2 (stops at tenths) and 4.41 (stops at hundredths) gives 5.61, but report only 5.6 (limited to tenths column).

✖️ Multiplication and division rule

Limit the answer to the number of significant figures that the data value with the least number of significant figures has.

Count significant figures in each value.
The final answer uses the smallest count.
Example: Dividing 23 (two significant figures) by 448 (three significant figures) gives 0.051339286…, but report only 0.051 (two significant figures).

🔄 Rounding convention

Round up if the first dropped digit is 5 or greater.
Round down if the first dropped digit is less than 5.
Example: 119.902 limited to tenths becomes 119.9 (the dropped 02 starts with 0, which is less than 5).
Example: 201.867 limited to hundredths becomes 201.87 (the dropped 7 is greater than 5, so round up).

⚠️ Don't confuse the two rules

Addition/subtraction: focus on decimal place position (rightmost common column).
Multiplication/division: focus on total count of significant figures (fewest in any value).
Calculators do not understand significant figures—you must apply these rules manually to limit the final answer appropriately.

Converting Units

🧭 Overview

🧠 One-sentence thesis

Unit conversion is a formal algebraic technique that uses conversion factors (fractions equal to 1) to systematically replace one unit with another while preserving the quantity's value.

📌 Key points (3–5)

Conversion factors equal 1: they have the same quantity in numerator and denominator, just expressed in different units (e.g., 3 ft / 1 yd = 1).
Cancellation is key: place the unit you want to remove where it will cancel—if it's in the numerator, put it in the denominator of the conversion factor.
Derived units need multiple factors: converting m² to cm² requires two conversion factors (one for each meter); m³ requires three.
Common confusion: when converting units in the denominator (e.g., m/min to m/s), the unit to remove must go in the numerator of the conversion factor.
Exact numbers don't affect significant figures: defined relationships like "1 km = 1,000 m" involve exact numbers that don't limit precision.

🔧 The conversion factor method

🔧 What is a conversion factor

A conversion factor is an expression equal to 1, constructed from an equality between two units, used to formally change one unit into another.

Start with a known equality, e.g., 1 yd = 3 ft.
Divide both sides by one of the quantities to create a fraction that equals 1.
Two possible conversion factors arise: (3 ft / 1 yd) or (1 yd / 3 ft).
Both equal 1 because numerator and denominator represent the same quantity.

🎯 Choosing the right conversion factor

The rule: pick the conversion factor that puts the unit you want to eliminate in a position where it will cancel.
If your original unit is in the numerator, choose the factor with that unit in the denominator.
If your original unit is in the denominator, choose the factor with that unit in the numerator.
Example: Converting 4 yd to feet—use (3 ft / 1 yd) so "yd" cancels, leaving "ft".

✖️ Multiplying by 1 preserves value

Multiplying any quantity by 1 doesn't change its value.
Writing 1 as a conversion factor lets you change units without changing the quantity.
The process: (original quantity) × (conversion factor) = (same quantity in new units).

📏 Converting simple units

📏 Single-unit conversions

The excerpt demonstrates converting meters to millimeters:

Start with the definition: 1 mm = (1/1,000) m, or 1,000 mm = 1 m.
Construct the conversion factor: (1,000 mm / 1 m).
Apply: 14.66 m × (1,000 mm / 1 m) = 14,660 mm.
The "m" units cancel, leaving "mm".

🔢 Prefix-to-prefix conversions

When converting between two prefixed units (e.g., kilograms to milligrams):

Two-step method: convert to the base unit first, then to the target unit.
Example: 2.77 kg → grams → milligrams.
Step 1: 2.77 kg × (1,000 g / 1 kg) = 2,770 g.
Step 2: 2,770 g × (1,000 mg / 1 g) = 2,770,000 mg.
One-step method: chain both conversion factors in a single expression.

🧊 Converting derived units

🧊 Squared and cubed units

Derived units with exponents (m², m³) contain multiple instances of the base unit and require multiple conversion factors.

m² means m × m, so you need two conversion factors.
m³ means m × m × m, so you need three conversion factors.
Example: Converting 17.6 m² to cm²:
- Use (100 cm / 1 m) twice: 17.6 m² × (100 cm / 1 m) × (100 cm / 1 m) = 176,000 cm².
Example: Converting 0.883 m³ to cm³:
- Use (100 cm / 1 m) three times to get 883,000 cm³.

⬇️ Units in the denominator

When the unit to convert is in the denominator (e.g., m/min):

The unit you want to remove must appear in the numerator of the conversion factor.
This cancels the original denominator unit and introduces the new unit in the denominator.
Example: Converting 88.4 m/min to m/s:
- Use (1 min / 60 s) so "min" cancels: 88.4 m/min × (1 min / 60 s) = 1.47 m/s.
Don't confuse: if you put the unit in the wrong position, it won't cancel correctly.

🔢 Significant figures and exact numbers

🔢 Exact numbers in conversions

Exact numbers come from defined relationships (not measurements) and do not limit the number of significant figures in the final answer.

Prefix definitions are exact: "kilo-" means exactly 1,000, not approximately.
In the conversion factor (1,000 m / 1 km), neither 1,000 nor 1 affects significant figures.
These numbers can be thought of as having infinite significant figures.
Only the measured quantity determines the precision of the final answer.

📐 Applying significant figures

When performing conversions, apply significant figure rules to the original measured value.
The conversion factors themselves (being exact) don't reduce precision.
Example: If you start with 14.66 m (four significant figures), your answer should also have four significant figures after conversion.

Other Units: Temperature and Density

🧭 Overview

🧠 One-sentence thesis

Unit conversion is a critical mathematical technique in chemistry that requires constructing conversion factors from equalities, applying them in single or multistep processes, and recognizing that exact numbers from defined relationships do not affect significant figure determination.

📌 Key points (3–5)

Core conversion strategy: Convert to the base unit (no prefix) first, then to the desired unit with a different prefix, or combine both steps algebraically.
Exact numbers vs measured numbers: Numbers from defined relationships (e.g., "kilo-" means exactly 1,000) have infinite significant figures and do not limit the precision of a final answer.
Multistep conversions: Complex conversions (e.g., area, volume, or rates) require converting units in both numerator and denominator.
Common confusion: Distinguishing between exact numbers (from definitions like prefixes) and measured numbers (which determine significant figures).
Real-world stakes: Unit confusion can have serious consequences, as illustrated by the Gimli Glider incident where pounds were mistaken for kilograms.

🔄 Conversion strategies

🔄 Two-step vs one-step method

The excerpt presents two equivalent approaches for converting between units with different numerical prefixes:

Two-step method: First convert to the base unit (no prefix), then convert to the target unit.
One-step method: Combine both conversions into a single algebraic expression.

Example from the excerpt: Converting 2.77 kg to milligrams can be done either way and yields the same answer.

The excerpt states: "You can do the conversion in two separate steps or as one long algebraic step."

Why this matters: The two-step method is easier to understand and less error-prone for beginners; the one-step method is more efficient once you're comfortable with the process.

🧮 How to construct conversion factors

Start with an equality that relates two units (e.g., 1 km = 1,000 m).
Build a fraction that cancels the unwanted unit and leaves the desired unit.
The excerpt emphasizes that conversion factors come from "equalities that relate two different units."

Example from the excerpt: To convert microseconds to nanoseconds, first convert to the base unit (seconds) using the definition of "micro-", then convert to nanoseconds using the definition of "nano-".

🔢 Handling prefix conversions

When converting between prefixes (e.g., kilo- to milli-):

Do not memorize all prefix-to-prefix conversions.
Do use the base unit as an intermediate step.
Each prefix has a defined relationship to the base unit (e.g., kilo- = 1,000, milli- = 0.001).

The excerpt explicitly recommends: "go the easier route: first convert the quantity to the base unit...using the definition of the original prefix. Then convert the quantity in the base unit to the desired unit using the definition of the second prefix."

🎯 Exact numbers and significant figures

🎯 What makes a number "exact"

Exact number: a number from a defined relationship, not a measured one.

Numbers that come from definitions (like prefix meanings) are exact.
Numbers that come from measurements are not exact and have limited significant figures.

Example from the excerpt: The prefix "kilo-" means exactly 1,000—"no more or no less." This 1,000 can be thought of as having an infinite number of significant figures.

🎯 Why exact numbers don't limit precision

When calculating with both exact and measured numbers:

Only the measured numbers determine the significant figures in the final answer.
Exact numbers "do not impact the number of significant figures in a final answer."

Example from the excerpt: In converting a garden plot's area from square centimeters to square meters, "The 1 and 100 in the conversion factors do not affect the determination of significant figures because they are exact numbers, defined by the centi- prefix."

Don't confuse: A large number like 1,000 might look imprecise, but if it comes from a definition (like "kilo- = 1,000"), it is exact and does not limit your answer's precision.

📐 Applying this to area and volume

The excerpt provides an example with a rectangular garden plot (36.7 cm × 128.8 cm):

The dimensions are measured (3 significant figures each).
The conversion factors (1 cm = 0.01 m, or 100 cm = 1 m) are exact.
The final answer is limited to 3 significant figures by the measurements, not by the conversion factors.

🚨 Real-world consequences: The Gimli Glider

✈️ What happened

On July 23, 1983, an Air Canada Boeing 767 ran out of fuel mid-flight and had to glide to an emergency landing at Gimli, Manitoba.

The cause: Confusion between pounds and kilograms during fueling.
The context: Canada was transitioning from the English system to the metric system; the 767's gauges were calibrated in kilograms, but the ground crew fueled the plane with 22,300 pounds instead of 22,300 kilograms.
The result: The plane received "just less than half of the fuel needed," causing engines to quit halfway to Ottawa.

✈️ Why units matter

The excerpt emphasizes: "an incident that would not have occurred if people were watching their units."

No loss of life occurred, only minor injuries during evacuation.
The pilots' skill (Captain Pearson was an experienced glider pilot) saved 61 passengers and 8 crew members.
The aircraft was nicknamed "the Gimli Glider" for the rest of its operational life (retired in 2008).

Lesson: Unit conversion is not just an academic exercise; it is a "powerful mathematical technique in chemistry that must be mastered" with real-world safety implications.

🧩 Complex conversions

🧩 Multidimensional units (area, volume)

When converting area or volume:

Convert each dimension separately.
Square or cube the conversion factor as needed.

Example from the excerpt: Converting 9.44 m² to square centimeters requires recognizing that 1 m = 100 cm, so 1 m² = (100 cm)² = 10,000 cm².

🧩 Rates and compound units

When converting rates (e.g., meters per second to kilometers per hour):

Convert the numerator and denominator separately.
The excerpt notes: "you will have to convert units in both the numerator and the denominator."

Example from the excerpt: A garden snail moves at 0.2 m/min, which converts to about 0.003 m/s, which is 3 mm/s.

🧩 Inappropriate conversions

The excerpt includes exercises that ask why certain conversions are inappropriate:

Square centimeters to cubic meters: "One is a unit of area, and the other is a unit of volume"—they measure different dimensions and cannot be directly converted.
Cubic meters to cubic seconds: Meters measure length/volume; seconds measure time—they are fundamentally different quantities.

Don't confuse: Only units that measure the same type of quantity (length, time, mass, etc.) can be converted into one another.

📋 Key takeaways from the excerpt

The excerpt concludes with these essential points:

Takeaway	Explanation
Units can be converted using proper conversion factors	Conversion factors are ratios constructed from equalities
Conversion factors come from equalities	Two different units related by a defined or measured relationship
Conversions can be single or multistep	Choose the method that minimizes errors
Unit conversion must be mastered	It is a "powerful mathematical technique in chemistry"
Exact numbers don't affect significant figures	Only measured values limit precision

Expressing Units

🧭 Overview

🧠 One-sentence thesis

Chemistry requires combining numbers with appropriate SI units and prefixes to communicate quantities clearly, and these units can be multiplied or divided to create derived units for complex measurements.

📌 Key points (3–5)

Numbers need units: A number tells "how much," but the unit tells "of what"—both are essential for meaningful communication.
SI fundamental units: Chemistry uses the International System with fundamental units like the metre (m) for length, kilogram (kg) for mass, and second (s) for time.
Prefixes scale units: Numerical prefixes (kilo-, milli-, micro-, etc.) represent multiples or fractions of fundamental units, making them conveniently sized for specific quantities.
Derived units from combinations: Units can be multiplied (e.g., m² for area) or divided (e.g., m/s for velocity) to express more complex quantities.
Common confusion: Choosing appropriate unit size—a human hair width makes more sense in micrometres than metres; large volumes work better in kilolitres than litres.

📏 Fundamental SI units

📏 The three basic units introduced

The excerpt focuses on three fundamental SI units:

Quantity	Unit	Abbreviation	Comparison
Length	metre	m	A little longer than a yard
Mass	kilogram	kg	About 2.2 pounds
Time	second	s	Standard time unit

Fundamental units: SI-specified base units for various quantities, upon which other measurements are built.

These form the foundation for all other measurements in chemistry.
To express any quantity, you must combine a number with a unit (e.g., 2.4 m or 1.5 × 10⁴ s).

🌍 Why SI matters

SI stands for "le Système International d'unités" (International System of Units).
Chemistry, like most sciences, uses SI to ensure consistent communication worldwide.
Without units, numbers are meaningless—"six" could mean six miles, six inches, or six city blocks.

🔢 Numerical prefixes

🔢 How prefixes work

Numerical prefixes: Multipliers that combine with fundamental units to make them conveniently sized for specific quantities.

Prefixes represent powers of 10—either multiples (larger) or fractions (smaller) of the base unit.
Each prefix has a standard abbreviation that combines with the unit abbreviation.
Example: kilometre (km) = 1,000 × metre = 1,000 m; so 5 km = 5,000 m.

📊 Common prefixes table

Prefix	Abbreviation	Multiplier	Type
giga-	G	1,000,000,000 ×	Multiple
mega-	M	1,000,000 ×	Multiple
kilo-	k	1,000 ×	Multiple
deci-	d	1/10 ×	Fraction
centi-	c	1/100 ×	Fraction
milli-	m	1/1,000 ×	Fraction
micro-	μ	1/1,000,000 ×	Fraction
nano-	n	1/1,000,000,000 ×	Fraction
pico-	p	1/1,000,000,000,000 ×	Fraction

🎯 Choosing appropriate prefixes

The goal is to make units conveniently sized for the quantity being measured.
A human hair width is very small—expressing it as 0.00006 m is awkward; 60 μm is clearer.
Example from the excerpt: 6.0 × 10⁻⁵ m = 60 × 10⁻⁶ m = 60 μm (micrometres).
Don't confuse: The kilogram already contains a prefix (kilo-) as part of the fundamental unit name.

🧮 Derived units

🧮 Creating units through multiplication

Derived units: Units based on fundamental units, created by multiplying or dividing them.

Area example:

Area = width × height
Both width and height are lengths (metres)
Therefore: area = metre × metre = m² ("square metres")
Prefixes work here too: cm², mm², km² are all valid area units

Volume example:

Volume = length × width × height
All three dimensions are lengths
Therefore: volume = metre × metre × metre = m³ ("cubic metres")

🥤 The litre as a derived unit

A cubic metre (m³) is rather large for everyday use.
The litre (L) is defined as one one-thousandth of a cubic metre.
A litre is slightly larger than 1 quart in volume.
Prefixes apply: millilitre (mL) = 1/1,000 L; kilolitre (kL) = 1,000 L

Important relationship:

One litre = one-tenth of a metre cubed
One-tenth of a metre = 10 cm
Therefore: 1 L = 1,000 cm³
Since 1 L = 1,000 mL, then 1 mL = 1 cm³ (these units are interchangeable)

➗ Creating units through division

Units can be divided to express rates or ratios.
The word "per" implies division.

Velocity example:

Velocity = distance ÷ time
If you travel 1 metre for every 1 second: velocity = 1 metre/second = 1 m/s
Other velocity units: km/h (kilometres per hour), μm/ns (micrometres per nanosecond)
Example calculation: 25 m in 5.0 s → velocity = 25 m ÷ 5.0 s = 5.0 m/s

Don't confuse: When dividing units, you're creating a new derived unit (like m/s), not converting between units.

🎓 Practical application

🎓 Expressing quantities properly

Every quantity needs both components:

A number (tells "how much")
A unit (tells "of what")

Without both, communication is incomplete—asking "how close to the lake?" and hearing "six" doesn't help without knowing if it's six miles, inches, or blocks.

🔄 Converting to appropriate units

Large numbers or very small numbers suggest using a different prefix.
Example: 2,500,000 L is better expressed as 2.5 ML (megalitres)
Example: 0.000066 m/s could be 66 μm/s (considering only the numerator unit)
The goal is clarity and convenience in communication.

Acids

🧭 Overview

🧠 One-sentence thesis

Acids are compounds of the H⁺ ion dissolved in water that share distinctive chemical properties including sour taste, reaction with metals, and effects on plant pigments, and they follow systematic naming rules based on their composition.

📌 Key points (3–5)

What acids are: compounds of the H⁺ ion dissolved in water with their own naming system.
Naming rules: binary acids use "hydro- + stem + -ic acid"; acids derived from anions use "stem of anion + -ic acid" (or -ous for lower oxidation states).
Common properties: sour taste, react with metals to form metal ions and hydrogen, change plant pigment colors.
Common confusion: binary vs. oxoacid naming—binary acids (like HBr) get the "hydro-" prefix, while acids from polyatomic ions (like H₂SO₄) use the anion stem.
Real-world presence: acids are prevalent in foods (citric acid in citrus, oxalic acid in spinach), household products (hydrochloric acid cleaners), and the human body (stomach acid).

🏷️ Naming acids

🏷️ Binary acid naming

Binary acids contain hydrogen and one other element.
Naming pattern: hydro- + stem name of the element + -ic acid
Example: HBr becomes hydrobromic acid (hydro- + brom- + -ic acid); HCl becomes hydrochloric acid.

🏷️ Oxoacid naming (from anions)

These acids are derived from polyatomic ions (anions containing oxygen).
Naming pattern: stem of the anion name + -ic acid (or -ous for lower oxidation state)
Example: H₂SO₄ is derived from the sulfate ion, so it becomes sulfuric acid.
Example: HNO₂ (from nitrite) becomes nitrous acid, while HNO₃ (from nitrate) becomes nitric acid.
Don't confuse: the -ate ending in the anion becomes -ic in the acid name; the -ite ending becomes -ous.

🧪 Chemical properties of acids

👅 Sensory and color properties

Sour taste: acids have a characteristic sour taste.
The sourness in citrus fruits and vinegar comes from acids present in these foods.
Plant pigment effects: acids make certain plant pigments change colors.
The ripening of some fruits and vegetables is caused by formation or destruction of excess acid in the plant.

⚗️ Reactivity with metals

Many acids react with metallic elements.
Products: the reaction forms metal ions and elemental hydrogen.
This is one of the distinguishing chemical behaviors that sets acids apart from other compounds.

🌍 Acids in everyday life

🍋 Food acids

Acid	Formula	Where found
Citric acid	H₃C₆H₅O₇	Citrus fruits
Oxalic acid	H₂C₂O₄	Spinach and green leafy vegetables
Phosphoric acid	H₃PO₄	Some soft drinks

🏠 Household and body acids

Hydrochloric acid: found in stomach acid (digestive system) and sold in hardware stores as a cleaner for concrete and masonry.
Acids are very prevalent in the world around us, appearing in natural, biological, and commercial contexts.

Ions and Ionic Compounds

🧭 Overview

🧠 One-sentence thesis

Ions form when atoms gain or lose electrons, and ionic compounds are built by combining positive cations and negative anions in ratios that balance the total charge.

📌 Key points (3–5)

How ions form: electrons move from one atom to another (protons never move); atoms that lose electrons become cations (+), atoms that gain electrons become anions (−).
Characteristic charges: most atoms form ions with a single, predictable charge; metals tend to form cations, nonmetals tend to form anions.
Writing ionic formulas: the total positive charge must balance the total negative charge, using the lowest ratio of ions.
Common confusion: the subscript in an ionic formula (e.g., the 2 in MgCl₂) tells you how many ions are needed to balance charge—it does not mean the element is diatomic or neutral.
Polyatomic ions: groups of atoms with an overall charge (mostly anions containing oxygen) that act as a single unit in ionic compounds.

⚡ What ions are and how they form

⚡ Definition and formation

Ions: species with overall electric charges, formed when electrons move from one atom to another.

Electrically neutral atoms have equal numbers of protons and electrons.
When electrons move, the balance is disrupted and the atom becomes charged.
Key rule: only electrons move; a proton never moves from one atom to another.

➕ Cations vs anions

Cations: species with overall positive charges.
Anions: species with overall negative charges.

Losing electrons → fewer negative charges → cation (positive).
Gaining electrons → more negative charges → anion (negative).
Example: a sodium atom loses one electron → Na⁺ cation; a chlorine atom gains one electron → Cl⁻ anion.

🔢 Monatomic ions

Monatomic ions: ions formed from individual atoms that gain or lose electrons.

Most atoms form ions with a characteristic charge (always the same charge when they ionize).
Example: sodium always forms 1+ (Na⁺), never 2+ or 3+; oxygen always forms 2− (O²⁻).
Pattern: metals (except hydrogen) form cations; nonmetals form anions.
A few metals (iron, cobalt, lead, tin, gold) can form more than one possible charge—these must be memorized.

🏗️ Building and writing ionic compounds

🏗️ What ionic compounds are

Ionic compounds: compounds formed from positive and negative ions.

An ionic compound is never formed between two cations only or two anions only.
It must contain at least one cation and one anion.
Example: NaCl (sodium chloride) is formed from Na⁺ and Cl⁻.

⚖️ Balancing charges in formulas

Ionic formulas: chemical formulas for ionic compounds that show the ratio of cations to anions.

Core principle: the total positive charge must balance the total negative charge.

Use the lowest ratio of ions needed to balance.
Write the cation first, then the anion.
Do not write the charges in the final formula.

Example ions	Charge balance	Formula	Explanation
Na⁺ and Cl⁻	1+ and 1−	NaCl	One of each balances
Mg²⁺ and O²⁻	2+ and 2−	MgO	One of each balances
Mg²⁺ and Cl⁻	2+ and 1−	MgCl₂	Need two Cl⁻ to balance one Mg²⁺
Al³⁺ and O²⁻	3+ and 2−	Al₂O₃	Least common multiple is 6: two Al³⁺ (6+) and three O²⁻ (6−)

Don't confuse: the subscript 2 in MgCl₂ means "two chloride ions," not "one Cl₂ molecule." The chlorine is in ionic form (Cl⁻), not elemental form (Cl₂).

📝 Naming ions and ionic compounds

For cations:

Use the element name + "ion" (or "cation").
Example: Na⁺ is the sodium ion; Ca²⁺ is the calcium ion.
If the metal can have more than one charge, specify the charge with a Roman numeral in parentheses.
Example: Fe²⁺ is iron(II) or the iron two ion; Fe³⁺ is iron(III) or the iron three ion.

For monatomic anions:

Use the stem of the element name + suffix "-ide" + "ion."
Example: Cl⁻ is the chloride ion; N³⁻ is the nitride ion; O²⁻ is the oxide ion.

For ionic compounds:

Combine the cation name and the anion name (omit the word "ion").
Do not use numerical prefixes (like "di-" or "tri-").
Example: NaCl is sodium chloride (not sodium monochloride); MgCl₂ is magnesium chloride (not magnesium dichloride).
Example: FeS is iron(II) sulfide; Fe₂S₃ is iron(III) sulfide.

Don't confuse: the number of ions in the formula is dictated by charge balance, not by naming prefixes.

🧪 Polyatomic ions

🧪 What polyatomic ions are

Polyatomic ions: ions that contain more than one atom, acting as a single charged unit.

Most polyatomic ions are anions (negatively charged).
Only one common polyatomic cation: ammonium (NH₄⁺).
Many contain oxygen atoms, so they are sometimes called oxyanions.

🔤 Common polyatomic ions and naming patterns

Key examples:

Ammonium: NH₄⁺
Nitrate: NO₃⁻ vs nitrite: NO₂⁻
Sulfate: SO₄²⁻ vs sulfite: SO₃²⁻
Carbonate: CO₃²⁻
Phosphate: PO₄³⁻
Hydroxide: OH⁻
Acetate: C₂H₃O₂⁻ (or CH₃COO⁻)

Pattern to remember: the "-ite" ion has one less oxygen atom than the "-ate" ion, but the same charge.

Example: nitrate (NO₃⁻) has three oxygens; nitrite (NO₂⁻) has two oxygens; both have 1− charge.

✍️ Writing formulas with polyatomic ions

If more than one polyatomic ion is needed to balance the charge, enclose the polyatomic ion formula in parentheses and write the subscript outside.
Example: calcium (Ca²⁺) and nitrate (NO₃⁻) → need two nitrate ions → Ca(NO₃)₂ (not CaNO₃₂ or CaN₂O₆).
If only one polyatomic ion is needed, no parentheses are required.
Example: aluminum (Al³⁺) and phosphate (PO₄³⁻) → AlPO₄.

Naming: combine the cation name and the polyatomic ion name (omit "ion").

Example: Ca(NO₃)₂ is calcium nitrate; (NH₄)₂S is ammonium sulfide.
Exception: if the polyatomic ion name itself contains a numerical prefix (like dichromate or triiodide), keep it.

🔍 Distinguishing molecular vs ionic compounds

🔍 How to tell them apart

Type	Formed between	Example
Molecular compounds	Nonmetal + nonmetal	CO₂, H₂O
Ionic compounds	Metal + nonmetal	NaCl, MgO

Use the periodic table to identify metals and nonmetals.
Molecular formulas use prefixes (mono-, di-, tri-); ionic formulas do not (except in polyatomic ion names).

Don't confuse: SO₃ (sulfur trioxide) is a molecular compound (nonmetal + nonmetal); SO₃²⁻ (sulfite ion) is a polyatomic anion used in ionic compounds.

🍽️ Sodium in food (application)

🍽️ Why sodium compounds are common in food

Sodium (as Na⁺) is a necessary nutrient; the human body is about 0.15% sodium.
Ionic sodium compounds are inexpensive and dissolve easily, so they distribute evenly in food mixtures.
Common examples: sodium chloride (table salt, NaCl), sodium nitrite (NaNO₂, in cured meats), sodium benzoate (preservative).

⚠️ Health considerations

The average person needs only about 500 mg of sodium per day.
Most people consume much more—up to 10 times the necessary amount—from processed and packaged foods.
Some studies link high sodium intake to high blood pressure (though newer studies question the link).
Recommendations: avoid processed foods, read labels, don't oversalt, use other herbs and spices.

Key Takeaways (from the excerpt):

Ions form when atoms lose or gain electrons.
Ionic compounds have positive ions and negative ions.
Ionic formulas balance the total positive and negative charges.
Ionic compounds have a simple system of naming.
Groups of atoms can have an overall charge and make ionic compounds.

Masses of Atoms and Molecules

🧭 Overview

🧠 One-sentence thesis

Atoms and molecules have measurable masses expressed in atomic mass units, where an element's atomic mass is a weighted average of its isotopes and a molecule's mass is the sum of its constituent atomic masses.

📌 Key points (3–5)

Why a special unit is needed: individual atoms and molecules are too small for grams or kilograms, so the atomic mass unit (u) is used instead.
How atomic mass unit is defined: one-twelfth the mass of a carbon-12 atom (an isotope with six protons and six neutrons).
Atomic mass vs mass number: atomic mass is a weighted average of all isotopes of an element, not just the whole-number count of protons and neutrons.
Common confusion: no single atom may have the atomic mass value—it's an average weighted by isotope abundance, not the mass of any particular atom.
Molecular mass calculation: sum the atomic masses of all atoms in the molecular formula, counting each type of atom correctly.

⚖️ The atomic mass unit scale

⚖️ Why atoms need their own mass unit

Individual atoms and molecules are extremely small, so their masses are also very small.
Grams and kilograms are "much too big to comfortably describe" these tiny masses.
A different scale was created specifically for atomic and molecular measurements.

📏 Definition of the atomic mass unit

Atomic mass unit (u): one-twelfth of the mass of a carbon-12 atom.

Carbon-12 is the reference isotope (six protons and six neutrons).
By this scale:
- Proton mass: 1.00728 u
- Neutron mass: 1.00866 u
- Electron mass: 0.000549 u
Quick estimation: you can approximate an atom's mass by counting protons plus neutrons (the mass number) and ignoring electrons with little error.
Example: carbon-12 is about 12 u, oxygen-16 is about 16 u, uranium-238 is about 238 u (exact: 238.050788 u).

🧮 Atomic mass of elements

🧮 Why elements are more complicated

Most elements exist as a mixture of isotopes, each with its own mass.
You cannot simply use one isotope's mass; you must account for the isotopic mixture.

📊 Weighted average calculation

Atomic mass of an element: a weighted average of the masses of the isotopes that compose an element.

How to calculate:

Multiply each isotope's mass by its fractional occurrence (as a decimal).
Add all the products together.
The sum is the atomic mass.

Example from the excerpt (hypothetical element):

50% isotope with mass 10 u and 50% with mass 11 u
Calculation: (0.50 × 10 u) + (0.50 × 11 u) = 10.5 u
Important: no single atom has mass 10.5 u; this is the average.

🔬 Real example: boron

Boron exists as about 20% boron-10 (five protons, five neutrons) and 80% boron-11 (five protons, six neutrons).
Calculation: (0.20 × 10 u) + (0.80 × 11 u) = 10.8 u
This 10.8 u is the atomic mass used for boron.

🌐 Why atomic masses are not whole numbers

Virtually all elements exist as isotope mixtures, so atomic masses often vary significantly from whole numbers.
Larger atoms tend to have more isotopes (tin holds the record with 10 isotopes).
The excerpt includes a table of selected atomic masses to three decimal places where possible.

🧪 Molecular mass

🧪 Extending the concept to molecules

Molecular mass: the sum of the masses of the atoms in a molecule.

This is a straightforward extension, but you must count the number of each type of atom correctly in the molecular formula.
Use the atomic mass (weighted average) for each atom, not a specific isotope mass.

🔢 Calculation method

Example from the excerpt: dinitrogen trioxide (N₂O₃)

Add the atomic mass of nitrogen two times plus the atomic mass of oxygen three times.
Calculation: (2 × 14.007 u) + (3 × 15.999 u) = 28.014 u + 47.997 u = 76.011 u
The excerpt notes you would not be far off limiting to one or two decimal places.

💡 Practice examples from the excerpt

Substance	Calculation	Molecular mass
NBr₃	1 nitrogen + 3 bromine	Sum of atomic masses
C₂H₆ (ethane)	2 carbon + 6 hydrogen	Sum of atomic masses
SO₂	1 sulfur + 2 oxygen	64.063 u
PF₃	1 phosphorus + 3 fluorine	87.968 u

Don't confuse: molecular mass requires counting each atom type in the formula—missing or miscounting atoms leads to wrong results.

🔑 Key takeaways from the excerpt

The excerpt explicitly lists these takeaways:

The atomic mass unit (u) is a unit that describes the masses of individual atoms and molecules.
The atomic mass is the weighted average of the masses of all isotopes of an element.
The molecular mass is the sum of the masses of the atoms in a molecule.

Molecules and Chemical Nomenclature

🧭 Overview

🧠 One-sentence thesis

Chemical nomenclature provides a systematic set of rules that assigns every compound a unique name and every name a unique formula, enabling precise identification of molecules composed of multiple atoms.

📌 Key points (3–5)

What molecules are: the smallest part of a substance that retains its physical and chemical properties, composed of two or more atoms connected together.
Diatomic elements: some elements naturally exist as two-atom molecules (H₂, O₂, N₂, F₂, Cl₂, Br₂, I₂) and must be written with subscript 2.
Binary compound naming rules: use numerical prefixes (di-, tri-, tetra-, etc.) to indicate atom counts, combine the first element name with the second element's stem plus "-ide."
Common confusion: distinguishing compounds with the same elements but different atom counts (e.g., SO₂ vs SO₃)—the nomenclature system ensures each has a unique name.
Bidirectional system: the rules work both ways—you can derive a formula from a name and a name from a formula.

🧬 What molecules are

🧬 Definition and nature

A molecule is the smallest part of a substance that has the physical and chemical properties of that substance.

Molecules are substances that exist as two or more atoms connected so strongly they behave as a single particle.
Similar to atoms in some respects, but composed of more than one atom.
The connection between atoms in a molecule is called a chemical bond (represented visually as a cylindrical line connecting ball-shaped atoms).

🔬 Molecular formulas

A molecular formula is a formal listing of what and how many atoms are in a molecule.

Shows which elements are present and how many atoms of each.
Subscript numbers indicate atom count (e.g., H₂ means two hydrogen atoms).
If no subscript appears, only one atom of that element is present (subscript 1 is implied but not written).
Example: O₂ has two oxygen atoms; S₈ has eight sulfur atoms.

⚛️ Elements that exist as molecules

⚛️ Diatomic elements

Seven elements naturally exist as two-atom molecules:

Element	Formula
Hydrogen	H₂
Oxygen	O₂
Nitrogen	N₂
Fluorine	F₂
Chlorine	Cl₂
Bromine	Br₂
Iodine	I₂

These must always be written with subscript 2 when referring to the elemental form.
Don't confuse: elemental oxygen (O₂) vs. a single oxygen atom in a compound.

🔢 Other molecular elements

Sulfur normally exists as an eight-atom molecule: S₈
Phosphorus exists as a four-atom molecule: P₄
Most other elements are assumed to exist as individual atoms rather than molecules.

📝 Naming binary compounds

📝 The four-step naming process

Step 1: Identify the elements in the molecule from its formula.

Step 2: Begin with the first element's name.

Use a numerical prefix (Table 3.6) if there is more than one atom.
Do not use "mono-" for the first element.

Step 3: Name the second element using three pieces:

Numerical prefix indicating atom count
The stem of the element name (e.g., "ox" for oxygen, "chlor" for chlorine)
The suffix "-ide"

Step 4: Combine the two words with a space between them.

🔢 Numerical prefixes

Number of atoms	Prefix
1	mono-
2	di-
3	tri-
4	tetra-
5	penta-
6	hexa-
7	hepta-
8	octa-
9	nona-
10	deca-

Special rule: When a prefix ends in "a" or "o" and the element name begins with "o," drop the "a" or "o" from the prefix.

Example: "monoxide" not "monooxide"; "pentoxide" not "pentaoxide"

🎯 Worked example: SO₂

Step 1: One sulfur atom, two oxygen atoms
Step 2: Start with "sulfur" (no "mono-" prefix for first element)
Step 3: "di-" + "ox" + "-ide" = "dioxide"
Step 4: sulfur dioxide

⚠️ Why precision matters

Different compounds of the same elements have different properties.
SO₂ (sulfur dioxide) and SO₃ (sulfur trioxide) are completely different compounds.
The nomenclature system gives each compound its own unique name to distinguish them.

🔄 Converting between names and formulas

🔄 From name to formula

The system works in reverse: from a compound name, you can determine its molecular formula.

List element symbols in the order given in the name.
Add numerical subscripts based on the prefixes (no subscript if only one atom; 1 is implied).

Examples:

"nitrogen trichloride" → NCl₃
"diphosphorus pentoxide" → P₂O₅ (note the prefix on the first element indicates more than one atom)
"carbon tetrachloride" → CCl₄

🔄 From formula to name

Follow the four-step process described above.

Examples:

PF₃ → phosphorus trifluoride
Se₂Br₂ → diselenium dibromide
CO → carbon monoxide (not "carbon monooxide")

🏷️ Special cases and exceptions

🏷️ Common names

Some simple molecules have common names used as part of the formal nomenclature system:

Formula	Common name	Not called
H₂O	water	dihydrogen monoxide
NH₃	ammonia	nitrogen trihydride
CH₄	methane	carbon tetrahydride

These common names are accepted exceptions to the systematic naming rules.
The excerpt notes that other molecules with common names will be pointed out as they occur.

🏷️ Compounds vs. elements

Don't confuse:

CO (carbon monoxide) = a compound of carbon and oxygen
Co (cobalt) = the element cobalt
Capitalization and subscripts matter for correct identification.

Atomic Theory

🧭 Overview

🧠 One-sentence thesis

Atoms are the fundamental building blocks of all matter, composed of protons, neutrons, and electrons arranged in a nuclear model, with each element defined by its unique atomic number.

📌 Key points (3–5)

Modern atomic theory: All matter is composed of atoms; atoms of the same element are identical; atoms combine in whole-number ratios to form compounds.
Subatomic structure: Atoms contain protons (positive) and neutrons (neutral) in the nucleus, with electrons (negative) orbiting outside.
Atomic number defines elements: The number of protons in the nucleus determines the element's identity and is called the atomic number.
Isotopes are variations: Atoms of the same element can have different numbers of neutrons, creating isotopes with different mass numbers.
Common confusion: Mass number vs. atomic number—mass number is protons plus neutrons; atomic number is protons only.

⚛️ What atoms are and how small they are

🔬 Definition and scale

Atom: The smallest piece of an element that maintains the identity of that element.

Atoms are extremely small: about 50 million atoms in a row would make a 1 cm line.
A printed period contains several million atoms.
Despite their tiny size, all matter is made from atoms.

📜 The three parts of modern atomic theory

The modern atomic theory, first stated by John Dalton in 1808, consists of three parts:

All matter is composed of atoms
Atoms of the same element are the same; atoms of different elements are different
Atoms combine in whole-number ratios to form compounds

These concepts form the basis of chemistry.

🧩 Subatomic particles

⚡ The three types of particles

Although "atom" comes from a Greek word meaning "indivisible," atoms are actually composed of smaller subatomic particles:

Particle	Symbol	Mass (approx.)	Charge
Proton	p⁺	1.6 × 10⁻²⁷ kg	1+
Neutron	n or n⁰	1.6 × 10⁻²⁷ kg	none
Electron	e⁻	9.1 × 10⁻³¹ kg	1−

🔍 Key characteristics

Electron: Discovered first; tiny subatomic particle with negative charge.
Proton: More massive than electron; positive charge.
Neutron: About the same mass as a proton but no charge.
All atoms of all elements are composed of these three particles (with one exception for neutrons).

🏗️ Nuclear model of the atom

🎯 How particles are arranged

Experiments by Ernest Rutherford in the 1910s led to the nuclear model:

Nucleus: The center of an atom where the relatively massive protons and neutrons are collected.

Protons and neutrons are in the nucleus at the center.
Electrons orbit in space outside the nucleus.
Particles are not arranged randomly.

⚖️ Neutral atoms

Neutral atoms have the same number of electrons as protons.
This gives them an overall charge of zero.
However, this will not always be the case (as discussed later in the text).

🔢 Atomic number and what makes elements different

🆔 Atomic number definition

Atomic number: The number of protons in an atom's nucleus.

The fundamental characteristic that all atoms of the same element share is the number of protons.
Each element has its own characteristic atomic number.
Examples:
- Hydrogen: atomic number 1 (one proton)
- Iron: atomic number 26 (26 protons)
- Uranium: atomic number 92 (92 protons)

🧬 What makes elements different

The atomic number (number of protons) is so important that it defines the element's identity. Atoms of different elements have different numbers of protons.

🔄 Isotopes and mass number

🌡️ Isotopes explained

Isotopes: Atoms of the same element (same number of protons) with different numbers of neutrons.

Atoms of the same element can have different numbers of neutrons.
Most naturally occurring elements exist as isotopes.

📊 Hydrogen isotopes example

Example: Hydrogen has three isotopes:

Most hydrogen atoms: 1 proton, 0 neutrons
Deuterium: 1 proton, 1 neutron (about one in a million hydrogen atoms)
Tritium: 1 proton, 2 neutrons (very rare)

➕ Mass number definition

Mass number: The sum of the number of protons and neutrons in the nucleus.

Don't confuse: Mass number vs. atomic number

Atomic number = protons only
Mass number = protons + neutrons

Example calculation: Carbon with 6 protons and 6 neutrons has atomic number 6 and mass number 12.

🏷️ Atomic symbols and notation

🔤 Element symbols

Atomic symbol: A one- or two-letter abbreviation of the name of the element.

Conventions:

First letter is always capitalized
Second letter (if present) is lowercase
Most symbols come from English names
Some come from Latin names (e.g., Na for sodium from "natrium")

Examples: H (hydrogen), Na (sodium), Ni (nickel)

📝 Isotope notation

There is an easy way to represent isotopes using atomic symbols:

Format: The element symbol with mass number (A) as superscript and atomic number (Z) as subscript on the left.

Example: Carbon-12 is written with C as the symbol, 6 as the atomic number, and 12 as the mass number.

Alternative notation: State the mass number after the element name

Carbon-12: 6 protons and 6 neutrons
Uranium-238: 92 protons and 146 neutrons

📋 The periodic table

🗂️ Organization of elements

Periodic table: A special chart that groups all the elements together.

Elements are listed in order of ascending atomic number.
The table has a special shape that relates to electron organization.
One immediate use: helps identify metals and nonmetals.

🔧 Metals vs. nonmetals

Nonmetals: Upper right corner, on one side of a heavy line splitting the right-hand part of the chart.
Metals: All other elements.

The periodic table is a fundamental tool for organizing and understanding the elements.

The Chemical Equation

🧭 Overview

🧠 One-sentence thesis

Chemical equations are balanced not only in terms of individual molecules but also in terms of moles, allowing stoichiometric calculations to relate quantities of reactants and products through mole ratios.

📌 Key points (3–5)

Balanced equations work in moles: Any balanced chemical equation can be interpreted in terms of moles, not just molecules.
Mole ratios enable conversions: The coefficients in a balanced equation provide equivalences that allow conversion between moles of different substances.
Mole-mole calculations: Starting with moles of one substance, you can calculate moles of another substance using the balanced equation.
Common confusion: The coefficients in a balanced equation represent moles (or molecules), not grams or other mass units—stoichiometry problems must work through moles.
Yields distinguish theory from reality: Theoretical yield is calculated assuming complete reaction; actual yield is what is obtained; percent yield compares the two.

🔢 Balanced equations as mole relationships

🔢 Interpreting coefficients as moles

A balanced chemical equation can be read in terms of moles: the coefficients represent the number of moles of each substance that react or are produced.

The equation 2H₂ + O₂ → 2H₂O means "two moles of hydrogen react with one mole of oxygen to make two moles of water."
This interpretation is valid as long as the coefficients are in the correct ratio (e.g., 2:1:2).
Even large numbers (like Avogadro's number) maintain the same ratio, confirming that equations are balanced in moles.

Example: The equation P₄ + 5O₂ → P₄O₁₀ means one mole of molecular phosphorus reacts with five moles of elemental oxygen to make one mole of tetraphosphorus decoxide.

⚖️ Equivalences from balanced equations

A balanced chemical equation provides equivalences between reactants and products expressed in moles.
For 2H₂ + O₂ → 2H₂O, the equivalences are: 2 mol H₂ ⇔ 1 mol O₂ ⇔ 2 mol H₂O.
Any two of these quantities can be used to construct a conversion factor.

Don't confuse: These equivalences are in moles, not grams—mass conversions require additional steps using molar mass.

🔄 Mole-mole calculations

🔄 Converting between moles of substances

A mole-mole calculation starts with moles of one substance and converts to moles of another substance using the balanced chemical equation.

Use the coefficients from the balanced equation to create a conversion factor.
The conversion factor relates the moles of the known substance to the moles of the unknown substance.

Example: For 2C₄H₁₀ + 13O₂ → 8CO₂ + 10H₂O, if 154 mol of O₂ react, how many moles of CO₂ are produced?

The equivalence is 13 mol O₂ ⇔ 8 mol CO₂.
Calculation: 154 mol O₂ × (8 mol CO₂ / 13 mol O₂) = 94.8 mol CO₂.

📐 Setting up the conversion

Identify the given quantity (in moles) and the substance you need to find.
Write the equivalence from the balanced equation.
Construct a conversion factor so that the starting unit cancels and the desired unit remains.

Why this works: The balanced equation guarantees that the mole ratios are exact, so the conversion is mathematically valid.

📊 Theoretical yield, actual yield, and percent yield

📊 Theoretical yield

Theoretical yield is the amount of product calculated assuming all reactant reacts completely, based on stoichiometry from the balanced chemical equation.

It represents the maximum possible amount of product.
Calculated using mole ratios and molar masses.
Always expressed in units of moles or grams.

Example: If 30.5 g of Zn react with excess HNO₃, the theoretical yield of Zn(NO₃)₂ is calculated by converting grams of Zn to moles, using the mole ratio from the balanced equation, then converting moles of product to grams.

🎯 Actual yield

Actual yield is the amount of product actually produced in a reaction, which is measured experimentally.

By definition, actual yield is less than or equal to theoretical yield.
If actual yield exceeds theoretical yield, an error has been made.

📈 Percent yield

Percent yield is the ratio of actual yield to theoretical yield, multiplied by 100.

Formula (in words): percent yield = (actual yield / theoretical yield) × 100

Both yields must be in the same units (moles or grams).
Proper percent yields range from 0% to 100%.
A percent yield greater than 100% indicates an error.

Example: If theoretical yield is 88.3 g and actual yield is 65.2 g, then percent yield = (65.2 / 88.3) × 100 = 73.8%.

Why it matters: Percent yield indicates the efficiency of a reaction; low yields may be due to side reactions, incomplete reactions, or loss of product during purification.

🏭 Real-world application: drug synthesis

Multi-step syntheses have an overall percent yield equal to the product of the individual step yields.
A 10-step synthesis with 90% yield per step has an overall yield of only 35%.
Purification steps also have percent yields, which can be very low (e.g., 7.5% for albuterol purification).
Low overall yields contribute to the high cost of pharmaceuticals.

Don't confuse: Theoretical yield (calculated) versus actual yield (measured)—they are rarely the same in practice.

🔑 Key principles

🔑 All stoichiometry goes through moles

Balanced chemical equations are balanced in terms of moles, not grams, kilograms, or liters.
Any stoichiometry problem will need to work through the mole unit at some point.

Why: Moles are the counting unit that connects the microscopic world (atoms and molecules) to the macroscopic world (grams and liters).

🔑 Coefficients are exact numbers

The coefficients in a balanced equation (e.g., 2, 13, 8) are exact and do not limit significant figures in calculations.
Only measured quantities (masses, volumes, concentrations) determine significant figures in the final answer.

Introductory Chemistry 605

Types of Chemical Reactions: Single- and Double-Displacement Reactions

🧭 Overview

🧠 One-sentence thesis

Single-displacement and double-displacement reactions represent two fundamental patterns of chemical change in which elements or ions exchange positions to form new compounds.

📌 Key points (3–5)

Single-displacement reactions: One element replaces another element in a compound, following the pattern A + BC → AC + B.
Double-displacement reactions: Two compounds exchange components, following the pattern AB + CD → AD + CB.
Activity series: A ranked list predicts which elements will displace others in single-displacement reactions; more active elements displace less active ones.
Common confusion: Don't confuse single-displacement (one element swaps in) with double-displacement (two compounds swap partners); single involves an element and a compound, double involves two compounds.
Practical importance: These reaction types help predict whether reactions will occur and what products will form, essential for understanding precipitation, acid-base, and redox chemistry.

🔄 Single-Displacement Reactions

🔄 What happens in single-displacement

Single-displacement reaction: A reaction where one element replaces another element in a compound.

The general pattern is: A + BC → AC + B
An element (A) reacts with a compound (BC)
The free element displaces one of the elements in the compound
The displaced element becomes free

Example: If zinc metal is placed in a copper sulfate solution, zinc displaces copper: Zn + CuSO₄ → ZnSO₄ + Cu

⚡ The activity series determines what displaces what

Activity series: A list of elements that will replace elements below them in single-replacement reactions.

Elements higher on the activity series are more reactive
A more active element will displace a less active element from a compound
A less active element cannot displace a more active element
The activity series must be consulted to predict if a reaction will occur

Example: Sodium is more active than hydrogen, so sodium will displace hydrogen from water. However, copper is less active than hydrogen, so copper will not displace hydrogen from acids.

Don't confuse: The activity series ranking with simple alphabetical order or atomic number; activity is based on reactivity, not position in the periodic table.

🔀 Double-Displacement Reactions

🔀 What happens in double-displacement

Double-displacement reaction: A reaction where two compounds exchange components.

The general pattern is: AB + CD → AD + CB
Two compounds react together
The positive ions (cations) switch places
The negative ions (anions) switch places
Both compounds exchange partners

Example: When silver nitrate solution mixes with sodium chloride solution: AgNO₃ + NaCl → AgCl + NaNO₃

💧 Common types of double-displacement

Precipitation reactions:

One product is insoluble and forms a solid precipitate
Example: Mixing solutions of lead nitrate and potassium iodide produces solid lead iodide

Neutralization reactions:

An acid reacts with a base to produce water and a salt
Example: Hydrochloric acid reacts with sodium hydroxide to form water and sodium chloride

Gas-forming reactions:

One product is a gas that escapes from solution
Example: Carbonate compounds react with acids to produce carbon dioxide gas

🔬 Predicting Reaction Outcomes

🔬 Will a single-displacement reaction occur?

To determine if a single-displacement reaction will proceed:

Identify the free element and the element in the compound
Consult the activity series
If the free element is higher (more active), the reaction occurs
If the free element is lower (less active), no reaction occurs

Example: Will iron displace copper from copper sulfate?

Iron is above copper in the activity series
Yes, the reaction will occur: Fe + CuSO₄ → FeSO₄ + Cu

🔬 Will a double-displacement reaction occur?

A double-displacement reaction typically occurs if one of these happens:

Driving Force	What Happens	Example Product
Precipitation	Insoluble solid forms	AgCl(s)
Neutralization	Water forms from H⁺ and OH⁻	H₂O(l)
Gas formation	Gas escapes from solution	CO₂(g)

Don't confuse: A reaction occurring with a reaction being useful; even if ions switch partners, if all products remain dissolved and separated, no observable change occurs.

⚖️ Balancing These Reactions

⚖️ Key principles for balancing

Both single- and double-displacement reactions must be balanced:

The number of atoms of each element must be equal on both sides
Charges must balance in ionic equations
Coefficients are adjusted, never subscripts

For single-displacement:

Balance the element being displaced first
Then balance the element doing the displacing
Check that all atoms balance

For double-displacement:

Write correct formulas for all products first
Balance polyatomic ions as units when possible
Adjust coefficients to balance all atoms

Example of balancing: Unbalanced: Al + CuSO₄ → Al₂(SO₄)₃ + Cu Balanced: 2Al + 3CuSO₄ → Al₂(SO₄)₃ + 3Cu

⚖️ Common balancing mistakes

Don't change subscripts in formulas to balance equations; this changes the identity of compounds
Don't forget to balance charges in ionic equations
Don't assume coefficients of 1 are unnecessary to write when showing your work

🎯 Why These Reactions Matter

🎯 Practical applications

Single-displacement reactions:

Metal refining and purification
Electroplating processes
Corrosion of metals
Displacement of hydrogen from acids by active metals

Double-displacement reactions:

Water treatment (removing dissolved ions as precipitates)
Qualitative analysis (identifying ions by precipitation)
Acid-base neutralization in everyday life
Formation of useful insoluble products

🎯 Connection to other chemistry concepts

These reaction patterns connect to:

Redox chemistry: Single-displacement reactions involve electron transfer
Solubility rules: Predict which double-displacement reactions form precipitates
Acid-base chemistry: Neutralization is a special case of double-displacement
Electrochemistry: Activity series relates to electrode potentials

Don't confuse: The classification of a reaction type with its mechanism; these patterns describe what happens overall, not necessarily how it happens at the molecular level.

Ionic Equations: A Closer Look

🧭 Overview

🧠 One-sentence thesis

Complete ionic equations show dissolved ionic compounds as separated ions rather than as intact formulas, revealing the actual species present in solution.

📌 Key points (3–5)

What a complete ionic equation is: a chemical equation in which dissolved ionic compounds are written as separated ions.
Why it matters: it shows the true form of substances in solution—ions exist independently, not as intact compounds.
How it differs from molecular equations: molecular equations show compounds as whole units; complete ionic equations break dissolved ionic compounds into their component ions.
Common confusion: not all compounds are written as ions—only dissolved ionic compounds are separated; insoluble compounds, molecular compounds, and gases remain as whole formulas.

🧪 What complete ionic equations show

🧪 Definition and purpose

Complete ionic equation: A chemical equation in which the dissolved ionic compounds are written as separated ions.

In water, many ionic compounds dissociate (break apart) into individual cations and anions.
A complete ionic equation reflects this reality by showing each ion separately.
Example: If an ionic compound dissolves, instead of writing "NaCl," you write "Na⁺ + Cl⁻" (using generic placeholders; the excerpt does not provide specific examples).

🔍 What gets separated and what doesn't

Dissolved ionic compounds: written as separated ions.
Insoluble ionic compounds, molecular compounds, gases, and pure liquids: remain as whole formulas.
Don't confuse: "ionic" does not automatically mean "separated"—only dissolved ionic compounds are written as ions.

🔄 Relationship to other equation types

🔄 Molecular vs complete ionic equations

Equation type	How ionic compounds appear	What it shows
Molecular equation	As intact formulas (e.g., "AB")	Overall reactants and products
Complete ionic equation	As separated ions (e.g., "A⁺ + B⁻")	Actual species in solution

The molecular equation is simpler but hides the ionic nature of dissolved substances.
The complete ionic equation is more detailed and chemically accurate for reactions in solution.

🧩 Why this distinction exists

In solution, dissolved ionic compounds do not exist as neutral pairs; the ions move independently.
Writing them as separated ions helps identify spectator ions and the net ionic equation (though the excerpt does not elaborate on these concepts).
This approach clarifies what is actually reacting versus what is simply present in solution.

Composition, Decomposition, and Combustion Reactions

🧭 Overview

🧠 One-sentence thesis

Composition, decomposition, and combustion reactions represent three fundamental reaction types where substances either combine into one product, break apart into multiple products, or react with oxygen to form oxides.

📌 Key points (3–5)

Composition reactions: multiple reactants combine to form a single product.
Decomposition reactions: a single reactant breaks down into two or more products.
Combustion reactions: a reactant combines with oxygen to produce oxides of all elements present.
Common confusion: composition vs combustion—both involve combining, but combustion specifically requires oxygen and produces oxides, while composition can involve any reactants forming one product.
Direction of change: composition builds complexity (many → one), decomposition reduces it (one → many), combustion transforms via oxidation (reactant + O₂ → oxides).

🔨 Composition reactions

🔨 What happens in composition

Composition reaction: A chemical reaction in which a single substance is produced from multiple reactants.

The defining feature is multiple starting materials → one product.
"Composition" means "putting together" or "building up."
The reaction increases chemical complexity by combining separate substances.

🧪 How composition works

Two or more reactants (elements or compounds) join together.
The product is a single, more complex substance.
Example: Element A + Element B → Compound AB (one product formed from two reactants).

⚠️ Don't confuse with combustion

Composition is a general term for any "many → one" reaction.
Combustion is a specific type where oxygen is always one of the reactants and oxides are always the products.
Not all composition reactions involve oxygen.

💥 Decomposition reactions

💥 What happens in decomposition

Decomposition reaction: A chemical reaction in which a single substance becomes more than one substance.

The defining feature is one starting material → multiple products.
"Decomposition" means "breaking apart" or "breaking down."
The reaction decreases chemical complexity by splitting a compound.

🧪 How decomposition works

A single reactant (usually a compound) breaks into two or more simpler products.
The products can be elements or simpler compounds.
Example: Compound AB → Element A + Element B (one reactant splits into two products).

🔄 Relationship to composition

Decomposition is the reverse process of composition.
Composition builds; decomposition breaks down.

Reaction type	Direction	Reactants	Products
Composition	Many → one	Multiple	Single
Decomposition	One → many	Single	Multiple

🔥 Combustion reactions

🔥 What happens in combustion

Combustion reaction: A chemical reaction in which a reactant combines with oxygen to produce oxides of all other elements as products.

The defining feature is reactant + oxygen → oxides of all elements.
Oxygen (O₂) is always one of the reactants.
All elements in the original reactant form oxides in the products.

🧪 How combustion works

A substance reacts with oxygen gas.
Each element in the reactant bonds with oxygen.
The products are oxides—compounds containing oxygen and the other elements.
Example: A hydrocarbon (containing C and H) combusts → produces carbon oxide (CO₂) and hydrogen oxide (H₂O).

🔍 Why combustion is distinct

Combustion is a specific type of reaction, not a general category like composition or decomposition.
It always involves oxidation (gaining oxygen).
It is not simply "combining"—it specifically means combining with oxygen to form oxides.
Don't confuse: composition can combine any substances; combustion must involve O₂ and produce oxides.

Oxidation-Reduction Reactions

🧭 Overview

🧠 One-sentence thesis

Oxidation-reduction (redox) reactions involve the transfer of electrons between atoms, tracked by changes in oxidation numbers, where one atom loses electrons (oxidation) and another gains electrons (reduction).

📌 Key points (3–5)

What redox reactions are: chemical reactions that involve the transfer of electrons between substances.
Oxidation defined: the loss of one or more electrons by an atom, which increases its oxidation number.
Reduction defined: the gain of one or more electrons by an atom, which decreases its oxidation number.
Tracking tool: oxidation numbers are assigned to atoms to help keep track of how many electrons each atom has during the reaction.
Common confusion: oxidation and reduction always occur together—when one atom loses electrons, another must gain them; they are paired processes in the same reaction.

⚡ What happens in redox reactions

⚡ Electron transfer

Oxidation-reduction (redox) reactions: a chemical reaction that involves the transfer of electrons.

The defining feature is that electrons move from one atom to another.
This is not about sharing electrons (as in covalent bonds), but about one atom giving up electrons and another accepting them.
Example: In a redox reaction, Atom A transfers electrons to Atom B; A loses electrons, B gains them.

🔄 Oxidation and reduction are paired

Oxidation and reduction cannot happen independently; they occur simultaneously in the same reaction.
When one substance is oxidized (loses electrons), another must be reduced (gains electrons).
Don't confuse: "oxidation" does not mean "reacting with oxygen" in this context—it specifically means electron loss, regardless of which element is involved.

🔢 Tracking electrons with oxidation numbers

🔢 What oxidation numbers do

Oxidation number: a number assigned to an atom that helps keep track of the number of electrons on the atom.

Oxidation numbers are a bookkeeping tool, not a physical property.
They allow chemists to see which atoms have gained or lost electrons during a reaction.
Example: If an atom's oxidation number increases from +1 to +3, it has lost electrons (oxidation); if it decreases from +2 to 0, it has gained electrons (reduction).

📈 Changes in oxidation number signal redox

Process	Electron change	Oxidation number change
Oxidation	Loss of electrons	Increase
Reduction	Gain of electrons	Decrease

An increase in oxidation number means oxidation has occurred.
A decrease in oxidation number means reduction has occurred.
By comparing oxidation numbers before and after the reaction, you can identify which atoms were oxidized and which were reduced.

🧪 Oxidation and reduction processes

🧪 Oxidation: losing electrons

Oxidation: the loss of one or more electrons by an atom; an increase in oxidation number.

The atom that is oxidized becomes more positive (or less negative) because it has fewer electrons.
Example: An atom with oxidation number +1 loses an electron and becomes +2.

🧪 Reduction: gaining electrons

Reduction: the gain of one or more electrons by an atom; a decrease in oxidation number.

The atom that is reduced becomes more negative (or less positive) because it has more electrons.
Example: An atom with oxidation number +3 gains two electrons and becomes +1.

🔗 Why both must occur

Electrons cannot simply disappear; if one atom loses them, another must accept them.
This pairing is the reason the term "oxidation-reduction" (or "redox") describes a single type of reaction, not two separate types.

Neutralization Reactions

🧭 Overview

🧠 One-sentence thesis

Neutralization reactions produce salts—ionic compounds formed when an acid reacts with a base.

📌 Key points (3–5)

What a salt is: any ionic compound formed from the reaction between an acid and a base.
Where the definition appears: the excerpt lists "salt" under both "Neutralization Reactions" and "Arrhenius Acids and Bases," showing the concept applies to acid-base chemistry.
Common confusion: "salt" in chemistry is not just table salt; it refers to any ionic compound produced by an acid-base reaction.

🧂 What is a salt?

🧂 Definition and formation

Salt: Any ionic compound that is formed from a reaction between an acid and a base.

A salt is the product of a neutralization reaction.
It is not limited to sodium chloride (table salt); the term covers all ionic compounds produced this way.
The excerpt emphasizes that the formation requires both an acid and a base as reactants.

🔗 Connection to acid-base frameworks

The excerpt lists the same definition under "Neutralization Reactions" and "Arrhenius Acids and Bases."
This indicates that the concept of salts applies within the Arrhenius acid-base framework (acids produce H⁺, bases produce OH⁻).
Example: When an acid donates a proton and a base accepts it, the remaining ions combine to form the ionic compound (salt).

⚠️ Common misunderstanding

⚠️ "Salt" is broader than everyday usage

In everyday language, "salt" usually means table salt (sodium chloride).
In chemistry, "salt" means any ionic compound from an acid-base reaction.
Don't confuse: not all salts taste salty or are safe to eat; the term is a classification based on how the compound forms, not its properties or uses.

Stoichiometry

🧭 Overview

🧠 One-sentence thesis

Stoichiometry allows chemists to use balanced chemical equations and enthalpy changes as quantitative relationships to calculate amounts of reactants, products, and energy involved in chemical reactions.

📌 Key points (3–5)

Balanced equations provide equivalences: coefficients in balanced equations create mole-to-mole conversion factors between substances
Energy as a stoichiometric quantity: enthalpy change (ΔH) can be treated like any other stoichiometric quantity, related to moles of reactants or products
Energy units matter: ΔH is expressed in kJ (not kJ/mol) because it refers to the specific molar amounts shown by coefficients in the balanced equation
Bidirectional calculations: you can start with moles and find energy, or start with energy and find moles/mass
Common confusion: the energy value relates to the exact coefficients in the equation as written, not per mole unless the coefficient is 1

🔗 Stoichiometric equivalences from balanced equations

🔗 Mole-to-mole relationships

The excerpt reviews that balanced chemical equations establish equivalences between substances based on their coefficients.

Each coefficient represents moles of that substance
These equivalences become conversion factors for stoichiometry calculations
Example: In 2H₂ + O₂ → 2H₂O, we have 2 mol H₂ ⇔ 1 mol O₂ ⇔ 2 mol H₂O

⚡ Adding energy to the equivalences

When a thermochemical equation includes an enthalpy change, that energy value becomes another equivalence:

Thermochemical equation: a chemical equation that includes an enthalpy change on the same line

The ΔH value relates to the number of moles indicated by the coefficients
Example: 2H₂(g) + O₂(g) → 2H₂O(ℓ) ΔH = −570 kJ means 2 mol H₂ ⇔ −570 kJ and 1 mol O₂ ⇔ −570 kJ
This answers the key question: "What amount of substance does this energy refer to?" — it refers to the molar amounts shown by the coefficients

📏 Why kJ, not kJ/mol?

The unit is kJ (not kJ/mol) because the energy change corresponds to the specific stoichiometric amounts in the balanced equation, not necessarily one mole.

🧮 Calculating energy from amounts of substance

🧮 From moles to energy

You can calculate energy released or absorbed by using the thermochemical equation as a conversion factor.

Set up a conversion factor between moles of substance and kJ
The sign of ΔH tells you whether energy is released (negative) or absorbed (positive)
Example: For 2H₂(g) + O₂(g) → 2H₂O(g) ΔH = −484 kJ, if 8.22 mol H₂ react:
- 8.22 mol H₂ × (−484 kJ / 2 mol H₂) = −1,990 kJ
- The negative sign means energy is given off

⚖️ From grams to energy

When given mass instead of moles, convert mass → moles → energy.

First convert grams to moles using molar mass
Then use the thermochemical equation to find energy
Example: For N₂ + O₂ → 2NO ΔH = 181 kJ, if 222.4 g N₂ reacts:
- 222.4 g N₂ × (1 mol N₂ / 28.0 g N₂) × (181 kJ / 1 mol N₂) = 1,436 kJ given off

Don't confuse: The molar mass step is separate from the stoichiometry step; always convert to moles first.

🔄 Calculating amounts from energy

🔄 Energy as the starting point

Stoichiometry works in reverse: you can start with an amount of energy and determine how much substance reacted or was produced.

Use the thermochemical equation as a conversion factor, but solve for moles or grams
The process is: kJ → moles → grams (if needed)
Example: If 558 kJ of energy are supplied to N₂ + O₂ → 2NO ΔH = 181 kJ:
- 558 kJ × (2 mol NO / 181 kJ) = 6.16 mol NO produced
- Then convert to grams if needed: 6.16 mol NO × (30.0 g/mol) = 185 g NO

🎯 Practical applications

This reverse calculation is useful when you know how much energy is available and need to know how much product you can make.

Energy input determines reaction extent
Useful for planning reactions or understanding energy requirements
Example scenario: A reaction requires 100.0 kJ; how many grams of reactant are needed?

🔥 Real-world example: thermite reactions

🔥 High-energy reactions

The excerpt describes thermite reactions as very energetic:

Classic reactants: aluminum metal + iron(III) oxide
Products: iron metal + aluminum oxide
The reaction releases so much energy that iron is produced as a liquid (melting point normally 1,536°C)

🛠️ Practical uses

Thermite reactions have both civilian and military applications:

Civilian: re-welding broken locomotive axles, welding railroad tracks together
Military: incendiary devices, disabling enemy weapons by melting holes in them
The high energy output makes them useful where extreme heat is needed in a localized area

Why it matters: This demonstrates that stoichiometric calculations with energy have real practical importance in engineering and industry.

🧪 Measuring enthalpy changes experimentally

🧪 Calorimetry basics

The excerpt explains how ΔH values are actually measured:

Calorimeter: a container (typically insulated) in which energy changes are measured

Calorimetry: the process of measuring changes in enthalpy

We don't measure ΔH directly; we measure heat (q) under constant pressure conditions
At constant pressure, ΔH = q

📐 The measurement equation

The heat absorbed or released is calculated using:

q = m × c × ΔT

Where:

m = mass of the system
c = specific heat capacity
ΔT = change in temperature (final − initial)

🔬 Experimental procedure

A typical calorimetry experiment:

Premeasure the mass of chemicals
Let the reaction occur in an insulated container
Measure the temperature change
Calculate q using the equation above
Scale up to molar quantities

Example: Mixing 0.10 mol NaOH with 0.10 mol HCl in 200.0 g water, temperature increases from 22.4°C to 29.1°C:

ΔT = 29.1 − 22.4 = 6.7°C
q = 200.0 g × 4.184 J/(g·°C) × 6.7°C = 5,600 J
Since this is for 0.10 mol, scale up: ΔH = −56 kJ/mol (negative because energy is released)

Don't confuse: The insulation keeps energy from escaping, so all energy change goes into temperature change, not into the surroundings.

⚠️ Important conventions and units

⚠️ Sign conventions

Negative ΔH: exothermic (energy released, system loses energy)
Positive ΔH: endothermic (energy absorbed, system gains energy)

📊 Scaling equations

When you multiply coefficients in a thermochemical equation, you must multiply ΔH by the same factor:

If 0.1 mol reacts with ΔH = −5.6 kJ, then 1 mol reacts with ΔH = −56 kJ
The energy scales proportionally with the amount of substance

🔢 Unit consistency

Energy: typically kJ (kilojoules)
Temperature: °C or K (the change is the same in both)
Mass: grams
Moles: mol

Molecular Orbitals

The Mole

🧭 Overview

🧠 One-sentence thesis

Molecular orbital (MO) theory explains bonding by mathematically combining atomic orbitals to create new molecular orbitals that are filled with electrons according to energy levels, allowing us to predict bond strength and molecular properties.

📌 Key points (3–5)

What MO theory does: generates new molecular orbitals by mathematically combining atomic orbitals (LCAO method), providing a more sophisticated model than valence bond theory
How electrons fill MOs: follow the same principles as atomic orbitals (aufbau, Pauli exclusion) but the orbitals are delocalized over the entire molecule
Bonding vs. antibonding orbitals: bonding orbitals are lower energy and stabilize molecules; antibonding orbitals are higher energy with nodes and destabilize molecules
Bond order calculation: evaluates bond strength by comparing electrons in bonding vs. antibonding orbitals
Common confusion: molecular orbitals are NOT the same as atomic orbitals—MOs belong to the whole molecule, not individual atoms

🔬 Core MO theory concepts

🔬 What molecular orbital theory adds

Valence bond theory explains many aspects of bonding but not all. MO theory complements it by:

Taking atomic orbital overlap to a new level
Generating entirely new orbitals (molecular orbitals) through mathematical combination
Treating electrons as belonging to the entire molecule, not just one atom

Molecular orbital (MO) theory: A model that generates new molecular orbitals by mathematically combining atomic orbitals, where electrons are delocalized over the entire molecule.

🧮 LCAO method

Linear combination of atomic orbitals (LCAO): The mathematical process used to generate molecular orbitals from atomic orbitals.

The excerpt doesn't detail the mathematics, but emphasizes that this is how MOs are created.

🔄 How MOs differ from atomic orbitals

Similarities:

Filled from lowest to highest energy (aufbau principle)
Hold maximum two electrons of opposite spin per orbital (Pauli exclusion)

Key difference:

Atomic orbitals: electron density associated with a particular atom
Molecular orbitals: electron density delocalized (spread out) over more than one atom in the molecule

Example: In H₂, the electrons occupy a molecular orbital that encompasses both hydrogen nuclei, not just one.

🔗 Bonding and antibonding orbitals

🔗 Bonding molecular orbitals

When two atomic orbitals combine constructively (wave functions reinforce/add):

Lower energy than the original atomic orbitals
Electron density concentrated between the two nuclei
Electrons stabilized by attractions to both nuclei
Hold atoms together with a covalent bond

Example: In H₂, the σ₁s orbital is the bonding molecular orbital formed from two 1s atomic orbitals.

⚡ Antibonding molecular orbitals

When two atomic orbitals combine destructively (wave functions cancel):

Higher energy than the original atomic orbitals
Area of zero electron density between nuclei (nodal plane or node)
Destabilizing toward the bond
Denoted with an asterisk (e.g., σ*₁s)

Don't confuse: The node is not just "less" electron density—it is zero electron density, which actively destabilizes bonding.

📊 Energy diagrams

Molecular orbital electron configuration energy diagrams show:

Atomic orbitals of each atom on either side
Newly formed molecular orbitals in the center
Bonding MO is lower in energy than contributing atomic orbitals
Antibonding MO is higher in energy

Example: For H₂, the bonding σ₁s orbital is filled with two electrons and is lower in energy than the 1s atomic orbitals, explaining why H₂ molecules are more stable than separate H atoms.

🧮 Bond order and molecular stability

🧮 What bond order measures

Bond order: A method of evaluating the strength of a covalent bond based on the number of electrons in bonding vs. antibonding orbitals.

Formula: Bond order = (number of bonding electrons − number of antibonding electrons) / 2

🔢 Interpreting bond order values

Whole numbers correspond to valence bond model:
- Bond order = 1 → single bond
- Bond order = 2 → double bond
Fractions are possible (indicates partial bonding)
Zero means no bond; atoms exist separately

Example: For H₂, there are 2 bonding electrons and 0 antibonding electrons, so bond order = (2 − 0)/2 = 1, indicating a single bond.

📉 Bond order and stability

Higher bond order → stronger, more stable bond

🏗️ Building MO diagrams for larger molecules

🏗️ Guidelines for combining atomic orbitals

When generating MOs for molecules more complex than H₂:

Number of MOs = number of atomic orbitals combined
Similar energy levels: only atomic orbitals of similar energy combine effectively
Overlap matters: greater overlap → bonding MO energy lowered more, antibonding MO energy raised more

🔗 Example: Li₂ (dilithium)

Combine 1s atomic orbitals → bonding and antibonding MOs (completely filled)
Combine 2s atomic orbitals → bonding and antibonding MOs (filled with remaining valence electrons)
Key rule: 1s orbitals do NOT combine with 2s orbitals (different energy levels)
Bond order calculation shows Li₂ has a single bond

Don't confuse: You cannot mix orbitals from vastly different energy levels (e.g., 1s with 2s).

🌐 p orbital combinations

🌐 Two ways p orbitals overlap

Head-to-head overlap → σ orbitals (electron density along internuclear axis)
Sideways overlap → π orbitals (electron density on opposite sides of internuclear axis)

⚖️ Energy ordering

Head-to-head (σ) overlap: greater overlap → bonding MO most stable (lowest energy), antibonding σ* least stable (highest energy)
Sideways (π) overlap: four π MOs created (two lower-energy degenerate bonding, two higher-energy antibonding)

🔄 Variation by atomic number

The energy diagram described fits O₂, F₂, and Ne₂ experimentally.

For B₂, C₂, and N₂: interactions between 2s and 2p atomic orbitals swap the ordering of σ₂p and π₂p molecular orbitals.

Don't confuse: The MO energy ordering is not universal—it depends on the specific atoms involved.

🔀 Heteronuclear diatomic molecules

When two different atoms bond:

Energy levels of individual atomic orbitals may differ
Can still use similar MO diagrams to estimate electron configuration and bond order

🎯 Frontier molecular orbitals

🎯 HOMO and LUMO definitions

HOMO (highest occupied molecular orbital): The molecular orbital with the highest energy that contains electrons.

LUMO (lowest unoccupied molecular orbital): The lowest energy molecular orbital that does not contain electrons.

Collectively called frontier molecular orbitals.

🔬 Why frontier orbitals matter

In spectroscopy: When molecules absorb energy, a HOMO electron typically transitions to the LUMO (ground state → excited state). This can be observed in UV-Vis spectroscopy experiments.

In chemical reactions: One reactant molecule may donate HOMO electrons to the LUMO of another reactant, forming a new bonding molecular orbital.

Understanding frontier MO energy levels provides insight into:

Molecular spectroscopy
Chemical reactivity

Example: The excerpt shows a diagram of HOMO electrons from one reactant combining with the LUMO of another to form a new bond.

📝 Key takeaways from the excerpt

The excerpt explicitly lists these main points:

Atomic orbitals can combine to make bonding and antibonding molecular orbitals
Bonding orbitals are lower in energy than antibonding orbitals
Molecular orbitals are filled using similar principles to atomic orbitals
Bond order can be used to evaluate bond strength
Frontier molecular orbitals are particularly important in molecular spectroscopy and reactivity

Mole-Mass and Mass-Mass Calculations

🧭 Overview

🧠 One-sentence thesis

Mass-mass calculations allow you to start with the mass of one substance and determine the mass of another substance in the same chemical equation.

📌 Key points (3–5)

What mass-mass calculation is: a calculation method that converts from the given mass of one substance to the mass of another substance involved in a chemical equation.
Starting point: you begin with a known mass of a substance.
Ending point: you calculate the mass of a different substance in the reaction.
Key connection: the calculation relies on the chemical equation linking the two substances.

🧮 What mass-mass calculations do

🧮 The core definition

Mass-mass calculation: A calculation in which you start with a given mass of a substance and calculate the mass of another substance involved in the chemical equation.

This is a stoichiometry tool that bridges two substances in a reaction.
You are not calculating amounts of the same substance; you are moving from one chemical species to another.
The chemical equation provides the relationship between the substances.

🔗 The two substances involved

Given substance: the starting material whose mass you know.
Target substance: the material whose mass you want to find.
Both substances must appear in the same balanced chemical equation.

🔄 How the calculation works

🔄 The conversion pathway

The calculation connects mass of substance A to mass of substance B through the chemical equation:

Start: mass of substance A (given).
Middle step: use the chemical equation to relate A and B (typically through mole ratios).
End: mass of substance B (calculated).

⚖️ Why the chemical equation matters

The balanced equation tells you the proportions in which substances react or form.
Without the equation, you cannot relate the mass of one substance to another.
Example: If the equation shows 2 moles of A produce 3 moles of B, that ratio is essential for the mass-mass calculation.

🎯 When to use mass-mass calculations

🎯 Practical scenarios

When you know how much of one reactant or product you have (in grams, kilograms, etc.).
When you need to predict how much of another substance will be consumed or produced.
Example: Given 10 grams of reactant A, calculate how many grams of product B will form.

🔍 Don't confuse with

Mole-mass calculations: those start or end with moles, not mass-to-mass directly.
Mass-mass calculations may involve moles as an intermediate step, but the defining feature is that both the starting point and the answer are expressed in mass units.

Limiting Reagents

🧭 Overview

🧠 One-sentence thesis

The limiting reagent is the reactant that runs out first in a chemical reaction, determining how much product can be formed.

📌 Key points (3–5)

What it is: the reactant that is completely consumed first during a reaction.
Why it matters: it controls the maximum amount of product that can be made.
Common confusion: don't confuse "limiting" with "smallest amount present"—it depends on the stoichiometric ratios, not just the starting quantities.
Practical implication: once the limiting reagent is used up, the reaction stops, even if other reactants remain.

🧪 Core concept

🔬 What a limiting reagent is

Limiting reagent: The reactant that runs out first for a given chemical reaction.

In any chemical reaction with multiple reactants, one reactant will be completely consumed before the others.
This reactant "limits" how much product can form because the reaction cannot continue once it is gone.
The other reactants are present in excess—they are left over after the reaction stops.

⚗️ How it controls the reaction

The limiting reagent determines the theoretical yield (maximum product amount).
Once this reactant is exhausted, no more product can be generated, regardless of how much of the other reactants remain.
Example: If a recipe requires 2 eggs and 1 cup of flour, but you have 10 eggs and only 3 cups of flour, the flour limits how many batches you can make—you can only make 3 batches, and 4 eggs will be left over.

🔍 Common confusion

⚠️ Amount vs. stoichiometry

Don't assume: the reactant with the smallest mass or moles is automatically the limiting reagent.
What matters is the stoichiometric ratio from the balanced equation compared to the actual amounts present.
A reactant present in a larger quantity can still be the limiting reagent if the reaction requires it in an even larger proportion.
Example: A reaction might need 3 moles of reactant A for every 1 mole of reactant B. If you start with 6 moles of A and 3 moles of B, reactant A runs out first (6 moles can only react with 2 moles of B), making A the limiting reagent despite B having fewer moles initially.

The Mole in Chemical Reactions

🧭 Overview

🧠 One-sentence thesis

Mole-mole calculations use the balanced chemical equation to convert between moles of one substance and moles of another substance in a stoichiometry problem.

📌 Key points (3–5)

What a mole is: the number of things equal to the number of atoms in exactly 12 g of carbon-12; equals 6.022×10²³ things.
What molar mass means: the mass of 1 mol of a substance in grams.
Mole-mole calculation: a stoichiometry calculation that starts with moles of one substance and converts to moles of another using the balanced equation.
Mole-mass calculation: a calculation that starts with moles of a substance and finds the mass of another substance (or vice versa) using the chemical equation.
Common confusion: mole-mole vs mole-mass—the first converts between moles only; the second involves converting between moles and mass.

🔢 The mole as a counting unit

🔢 Definition of the mole

Mole: The number of things equal to the number of atoms in exactly 12 g of carbon-12; equals 6.022×10²³ things.

The mole is a counting unit, like "dozen" but for chemistry.
It is defined by reference to carbon-12: the number of atoms in exactly 12 g of that isotope.
The numerical value is 6.022×10²³ (Avogadro's number).
Example: 1 mole of any substance contains 6.022×10²³ particles (atoms, molecules, ions, etc.).

⚖️ Molar mass

Molar mass: The mass of 1 mol of a substance in grams.

This connects the counting unit (mole) to measurable mass.
Each substance has its own molar mass based on its atomic or molecular composition.
Example: if a substance has a molar mass of 18 g/mol, then 1 mole of it weighs 18 grams.

🧮 Stoichiometry calculations with moles

🧮 Mole-mole calculation

Mole-mole calculation: A stoichiometry calculation when one starts with moles of one substance and converts to moles of another substance using the balanced chemical equation.

This is the most direct stoichiometry calculation.
The balanced equation provides the mole ratio between reactants and products.
You start with a known number of moles of substance A and use the equation's coefficients to find moles of substance B.
Example: if the equation shows 2 moles of A react with 3 moles of B, and you have 4 moles of A, you can calculate the moles of B needed (6 moles).

⚖️ Mole-mass calculation

Mole-mass calculation: A calculation in which you start with a given number of moles of a substance and calculate the mass of another substance involved in the chemical equation, or vice versa.

This extends mole-mole calculations by adding a mass conversion step.
You can start with moles and end with mass, or start with mass and end with moles.
The molar mass is the conversion factor between moles and grams.
Example: start with 2 moles of substance A, use the balanced equation to find moles of substance B, then multiply by B's molar mass to get grams of B.

🔄 How these calculations relate

🔄 The role of the balanced equation

Both mole-mole and mole-mass calculations depend on the balanced chemical equation.
The equation's coefficients give the mole ratios—the foundation of all stoichiometry.
Without a balanced equation, you cannot convert between substances accurately.

🔄 Don't confuse: mole-mole vs mole-mass

Calculation type	What you convert	Key tool
Mole-mole	Moles of one substance → moles of another	Balanced equation coefficients
Mole-mass	Moles ↔ mass (involves both substances)	Balanced equation + molar mass

Mole-mole stays in the "mole" unit throughout.
Mole-mass requires an additional step using molar mass to switch between moles and grams.

Yields

🧭 Overview

🧠 One-sentence thesis

Percent yield compares the actual amount of product obtained from a chemical reaction to the theoretical maximum, expressed as a percentage between 0% and 100%.

📌 Key points (3–5)

What percent yield measures: the ratio of actual yield to theoretical yield, converted to a percentage.
The calculation: actual yield divided by theoretical yield, then multiplied by 100%.
The range: percent yield always falls between 0% and 100%.
Common confusion: percent yield is not the same as theoretical yield—it measures how much of the theoretical maximum was actually obtained.

🧮 Understanding percent yield

📐 Definition and formula

Percent yield: Actual yield divided by theoretical yield times 100% to give a percentage between 0% and 100%.

This metric tells you how efficient a chemical reaction was in practice.
The formula structure: (actual yield ÷ theoretical yield) × 100%
The result is always expressed as a percentage.

🎯 The two components

Actual yield:

The amount of product you actually obtained from the reaction.
This is measured experimentally.

Theoretical yield:

The maximum amount of product predicted by stoichiometry.
This is calculated from the balanced chemical equation and starting amounts.

📊 The bounded range

Minimum	Maximum	Meaning
0%	100%	Percent yield cannot exceed this range

0% would mean no product was obtained.
100% would mean the reaction produced exactly the theoretical maximum.
In practice, percent yields are typically less than 100% due to losses, side reactions, or incomplete reactions.

🔍 Why it matters

🔍 Measuring reaction efficiency

Percent yield provides a standardized way to compare how well different reactions perform.
It accounts for the difference between what chemistry predicts (theoretical) and what actually happens (actual).
Example: If theoretical yield is 10 grams but actual yield is 8 grams, percent yield = (8 ÷ 10) × 100% = 80%.

Pressure

🧭 Overview

🧠 One-sentence thesis

Pressure is the force exerted by gas particles colliding with container walls distributed over the wall area, and it can be measured in several interconvertible units including pascals, atmospheres, millimeters of mercury, and torr.

📌 Key points (3–5)

What causes pressure: gas particles constantly collide with container walls, and the accumulation of all collision forces over the wall area creates pressure.
Definition: pressure equals force divided by area.
Multiple units exist: pascal (Pa), atmosphere (atm), millimeter of mercury (mmHg), and torr are all pressure units with exact conversion relationships.
Common confusion: the original atmosphere definition (average atmospheric pressure at sea level) was imprecise because atmospheric pressure varies; the modern definition uses exact equivalences (1 atm = 760 mmHg = 760 torr).
SI vs practical units: the formal SI unit (pascal) is often too small for practical use, so atmospheres, mmHg, and torr are commonly used instead.

💥 What pressure is and why it exists

💥 The collision mechanism

Pressure (P) is defined as the force of all the gas particle/wall collisions divided by the area of the wall.

Gas particles are always in motion (kinetic theory of gases).
They constantly collide with container walls.
Each collision is elastic (no net energy loss), but each particle exerts a force during impact.
The accumulation of all these tiny forces spread over the wall area is what we measure as pressure.

🌍 Atmospheric pressure

Even Earth's atmosphere exerts pressure.
In this case, gravity "holds in" the gas instead of a physical container.
Atmospheric pressure at sea level is 101,325 Pa.
Example: All gases exert pressure—it is a fundamental measurable quantity of the gas phase.

📏 Units of pressure

📏 The SI unit: pascal

The pascal (Pa) is the formal, SI-approved unit of pressure, defined as 1 N/m² (one newton of force over an area of one square meter).

This unit is usually too small in magnitude to be useful for everyday measurements.
1 atm = 101,325 Pa (the formal relationship).

🌡️ Practical units: atmosphere, mmHg, and torr

Unit	Definition	Notes
Atmosphere (atm)	Originally: average atmospheric pressure at sea level; Modern: exactly 760 mmHg	The original definition was unreliable due to atmospheric variations
Millimeter of mercury (mmHg)	Pressure exerted by a column of mercury exactly 1 mm high	More reliable than the original atmosphere definition
Torr	Equals 1 mmHg	Named after Evangelista Torricelli, inventor of the mercury barometer

🔗 Exact equivalences

The excerpt provides these exact conversion relationships:

1 atm = 760 mmHg = 760 torr
1 atm = 101,325 Pa

Don't confuse: Because these are defined equivalences (not measured approximations), they don't limit significant figures in conversions—the initial measurement determines significant figures.

🔄 Converting between pressure units

🔄 How to convert

Use the exact equivalences as conversion factors.
The numbers in conversion factors are exact, so significant figures come from the measured value, not the conversion factor.

🔄 Example scenarios

Example: Converting 595 torr to atmospheres using 1 atm = 760 torr gives 0.783 atm (significant figures determined by 595, not by the conversion factor).

Example: Mars has an atmospheric pressure of 6.01 mmHg; converting to atmospheres requires using the equivalence 1 atm = 760 mmHg, yielding a very small value that should be expressed in scientific notation.

Example: A hurricane eye pressure of 0.859 atm converts to 652 torr using the standard equivalence.

Gas Laws

🧭 Overview

🧠 One-sentence thesis

Gas laws are simple mathematical formulas that predict how pressure, volume, and temperature of a gas relate to each other when certain conditions are held constant.

📌 Key points (3–5)

Boyle's law: pressure and volume are inversely related when temperature and amount are constant (as one increases, the other decreases).
Charles's law: volume and temperature are directly related when pressure and amount are constant (both increase or decrease together).
Common confusion: Charles's law requires absolute temperature (Kelvin), not Celsius—always convert to Kelvin before calculating.
Mathematical approach: isolate the unknown variable in the numerator, ensure matching units for similar variables, and check that the answer makes physical sense.
Why it matters: gas laws allow scientists to model and predict gas behavior under changing conditions.

🔬 What gas laws are

🔬 Definition and purpose

Gas law: a simple mathematical formula that allows you to model, or predict, the behaviour of a gas.

Scientists in the seventeenth century noticed simple relationships between measurable properties of gases (pressure, volume, temperature, amount).
These relationships can be expressed as equations that let you calculate one property when others change.
The laws apply to a given amount of gas (usually expressed in moles, n).

📏 Unit requirements

Consistency is key: similar variables must have the same units on both sides of the equation.
Example: both pressure values must use the same unit (atm, torr, or mmHg); both volume values must use the same unit (L or mL).
It usually doesn't matter which unit you choose, as long as both sides match.
Temperature exception: gas laws require absolute temperature in Kelvin, not Celsius.

🔽 Boyle's Law (pressure and volume)

🔽 The inverse relationship

What it describes: for a given amount of gas at constant temperature, pressure and volume are inversely related.
As pressure increases, volume decreases; as pressure decreases, volume increases.
The product of pressure and volume equals a constant: P × V = constant (at constant n and T).

🧮 The formula

The mathematical expression is:

P₁V₁ = P₂V₂ at constant n and T

P₁ and V₁ are initial pressure and volume.
P₂ and V₂ are final pressure and volume.
Named after Robert Boyle, an English scientist who announced it in 1662.

🔍 How to use Boyle's law

Identify known quantities: assign initial and final values to P₁, V₁, P₂, V₂.
Isolate the unknown: use algebra to get the unknown variable by itself in the numerator.
Check units: convert if necessary so both pressures match and both volumes match.
Verify the answer: does it make physical sense? If pressure decreases, volume should increase.

Example: A gas at 2.44 atm and 4.01 L changes to 1.93 atm. The new volume is 5.07 L—pressure decreased, so volume increased, which matches the inverse relationship.

⚠️ Don't confuse

The relationship is inverse, not direct: when one goes up, the other goes down.
Temperature and amount must stay constant for Boyle's law to apply.

🔼 Charles's Law (volume and temperature)

🔼 The direct relationship

What it describes: for a given amount of gas at constant pressure, volume and temperature are directly related.
As temperature increases, volume increases; as temperature decreases, volume decreases.
The ratio of volume to temperature is constant: V / T = constant (at constant n and P).

🧮 The formula

The mathematical expression is:

V₁ / T₁ = V₂ / T₂ at constant n and P

V₁ and T₁ are initial volume and temperature.
V₂ and T₂ are final volume and temperature.
Named after Jacques Charles, a French scientist who performed gas experiments in the 1780s.

🌡️ Temperature must be in Kelvin

Experiments show volume relates to absolute temperature (Kelvin), not Celsius.
Conversion formula: K = °C + 273
Always convert Celsius to Kelvin before substituting into Charles's law.
Don't confuse: using Celsius will give incorrect results.

🔍 How to use Charles's law

Convert temperature to Kelvin if given in Celsius.
Identify known quantities: assign values to V₁, T₁, V₂, T₂.
Isolate the unknown: multiply or divide to get the unknown variable alone in the numerator.
Reciprocal form for finding temperature: if solving for T₂, use T₁ / V₁ = T₂ / V₂ to keep temperature in the numerator and simplify algebra.
Verify the answer: if temperature increases, volume should increase.

Example: A gas at 34.8 mL and 315 K is heated to 559 K. The new volume is 61.8 mL—temperature increased, so volume increased, which matches the direct relationship.

📊 Comparison of the two laws

Law	Variables related	Relationship type	What stays constant	Key formula
Boyle's law	Pressure and volume	Inverse (one up, other down)	Temperature and amount	P₁V₁ = P₂V₂
Charles's law	Volume and temperature	Direct (both up or both down)	Pressure and amount	V₁/T₁ = V₂/T₂

⚠️ Common confusion

Boyle's law: pressure and volume move in opposite directions.
Charles's law: volume and temperature move in the same direction.
Both laws require certain properties to remain constant—check which law applies to your situation.

Other Gas Laws

🧭 Overview

🧠 One-sentence thesis

Beyond Boyle's and Charles's laws, other gas laws relate different pairs of the four independent gas properties (pressure, volume, temperature, and amount), and the combined gas law allows tracking changes in pressure, volume, and temperature simultaneously.

📌 Key points (3–5)

Four independent properties: only pressure (P), volume (V), temperature (T), and amount (n) are independent; all other gas properties relate to these four.
Gay-Lussac's law: relates pressure and absolute temperature when volume and amount are constant.
Avogadro's law: equal volumes of different gases at the same temperature and pressure contain the same number of particles (or moles).
Combined gas law: merges pressure, volume, and temperature into one equation, allowing prediction when multiple properties change at once.
Common confusion: temperature must always be in Kelvin for gas law calculations; units for similar variables must match.

🔬 Individual gas laws

🌡️ Gay-Lussac's law

Gay-Lussac's law: relates pressure with absolute temperature.

Structure is similar to Charles's law but uses pressure instead of volume.
Mathematical form (in terms of two sets of data): pressure₁ / temperature₁ = pressure₂ / temperature₂
The other two properties (volume and amount) must be held constant.
Example: if initial pressure is 602 torr at 356 K, and temperature drops to 277 K, you can calculate the new pressure using this relationship.

🧪 Avogadro's law

Avogadro's law: equal volumes of different gases at the same temperature and pressure contain the same number of particles of gas.

First announced in 1811; this proposal eventually led to naming Avogadro's number.
Mathematically: volume₁ / amount₁ = volume₂ / amount₂
Amount can be expressed as number of particles or number of moles (1 mol = 6.022 × 10²³ particles).
This is the first gas law where amount (n) appears as a variable.
Example: if 2.45 L contains 4.5 × 10²¹ particles, you can find how many particles are in 3.87 L at constant temperature and pressure by setting up the ratio and solving algebraically.

Don't confuse: Avogadro's law applies only when temperature and pressure are constant; it does not work if these conditions change.

🔗 Combined gas law

🧮 What it combines

Combined gas law: a gas law that combines pressure, volume, and temperature into one equation.

Mathematical form: (pressure₁ × volume₁) / temperature₁ = (pressure₂ × volume₂) / temperature₂
Notice the pattern: volume and pressure are always in the numerator; temperature is always in the denominator.
Allows tracking changes when all three major properties change simultaneously.

📐 How to use it

Unit consistency: units must be the same for the two similar variables of each type (e.g., both pressures in atm or both in torr).
Temperature requirement: temperature must always be in Kelvin.
Algebraic isolation: solve for the unknown by isolating it on one side of the equation in the numerator.
Example: if a gas starts at 8.33 L, 1.82 atm, and 286 K, then changes to 355 K and 5.72 L, you can find the final pressure by substituting into the combined gas law and rearranging to isolate P₂.

🎯 When to use it

Use when two or more of the three properties (pressure, volume, temperature) are changing.
Makes predictions easier when multiple variables change, which would be difficult to predict intuitively.
If you need to determine a variable in the denominator, you can either cross-multiply all terms or take the reciprocal of the combined gas law.

Don't confuse: The combined gas law assumes amount (n) remains constant; if the amount of gas changes, you need a different approach.

📊 Comparison of gas laws

Gas Law	Variables Related	What's Held Constant	Key Pattern
Boyle's law	Pressure, Volume	Temperature, Amount	Inverse relationship
Charles's law	Volume, Temperature	Pressure, Amount	Direct relationship
Gay-Lussac's law	Pressure, Temperature	Volume, Amount	Direct relationship
Avogadro's law	Volume, Amount	Pressure, Temperature	Direct relationship
Combined gas law	Pressure, Volume, Temperature	Amount only	Combines all three

The Ideal Gas Law and Some Applications

🧭 Overview

🧠 One-sentence thesis

The ideal gas law (PV = nRT) relates all four independent physical properties of a gas at any time, enabling calculations of gas behavior under any conditions and applications to stoichiometry, molar volume, and density problems.

📌 Key points (3–5)

What the ideal gas law does: relates pressure, volume, temperature, and amount of gas at any single moment—no change in conditions required.
The constant R: the ideal gas law constant has different numerical values depending on the units used for pressure and volume.
Standard conditions (STP): defined as 1 atm pressure and 273 K (0°C), allowing direct comparison of gas properties; at STP, any gas has a molar volume of 22.4 L/mol.
Common confusion: the ideal gas law does not require a change in conditions, unlike the combined gas law; it can find any one property if the other three are known.
Applications: the law can be used for stoichiometry problems involving gases, calculating gas densities, and converting between moles and volume at STP.

🔬 The ideal gas law equation

🔬 Deriving the law

The combined gas law can be extended to include n (amount in moles), positioned in the denominator opposite volume, by analogy to Avogadro's law.
The resulting constant is the same for all gases because pressure, volume, temperature, and amount are the only four independent physical properties of a gas.
This universal constant is called R, the ideal gas law constant.

📐 The equation itself

Ideal gas law: PV = nRT

P = pressure
V = volume
n = amount (moles)
T = temperature (must be in kelvins)
R = ideal gas law constant

📊 Values of R

Numerical Value	Units
0.08205	L·atm/(mol·K)
62.36	L·mmHg/(mol·K)
8.314	J/(mol·K)

The value depends on the units used for pressure and volume.
Choose the R value that matches your pressure units to simplify cancellation.

🎯 Using the ideal gas law

🎯 Key difference from other gas laws

The ideal gas law does not require a change in the conditions of a gas sample.
Other gas laws (Boyle's, Charles's, etc.) predict how one property changes when another changes.
The ideal gas law relates properties at any single moment in time.

🧮 Solving for any property

If you know any three of the four physical properties (P, V, n, T), you can calculate the fourth.
Always convert temperature to kelvins before substituting.
Pay attention to units and choose the appropriate R value.

Example: A 4.22 mol sample of Ar has pressure 1.21 atm and temperature 34°C (307 K). Find volume.

Substitute into PV = nRT: (1.21 atm)(V) = (4.22 mol)(0.08205 L·atm/mol·K)(307 K)
Solve: V = 87.9 L

⚗️ Stoichiometry applications

The ideal gas law can be used in stoichiometry problems where chemical reactions involve gases.
First, use stoichiometry to find moles of gas produced or consumed.
Then use the ideal gas law with given temperature and pressure to find volume (or vice versa).

Example: What volume of H₂ is produced at 299 K and 1.07 atm when 55.8 g of Zn reacts with excess HCl?

First find moles of H₂ from stoichiometry: 0.853 mol
Then use PV = nRT to find volume: V = 19.6 L

🌡️ Standard temperature and pressure (STP)

🌡️ Definition of STP

Standard temperature and pressure (STP): exactly 100 kPa (0.986 atm, simplified to 1 atm) of pressure and 273 K (0°C).

STP provides a set of benchmark conditions so properties of different gases can be properly compared.
Allows direct comparison without needing to account for different conditions.

📦 Molar volume at STP

Molar volume: the volume of 1 mol of a gas.

At STP, the molar volume can be calculated using the ideal gas law:
- PV = nRT with P = 1 atm, n = 1 mol, T = 273 K
- V = (1 mol)(0.08205 L·atm/mol·K)(273 K) / (1 atm) = 22.4 L
Any gas at STP has a volume of 22.4 L per mole of gas.
This is independent of the gas identity.

🔄 Using molar volume as a conversion factor

The molar volume of 22.4 L/mol makes a useful conversion factor in stoichiometry problems only if conditions are at STP.
If conditions are not at STP, you must use the full ideal gas law or first convert to STP conditions using the combined gas law.

Example: How many moles of Ar are in 38.7 L at STP?

Use 22.4 L/mol as conversion factor: (38.7 L) × (1 mol / 22.4 L) = 1.73 mol

Don't confuse: The 22.4 L/mol value is valid only at STP; at other conditions, you must use the ideal gas law directly.

⚖️ Calculating gas density

⚖️ Density formula

Density = mass / volume

For exactly 1 mol of a gas, the mass equals the molar mass.
Use the ideal gas law to find the volume of 1 mol under given conditions.
Then calculate density = (molar mass) / (molar volume at those conditions).

🧪 Procedure

Convert temperature to kelvins if needed.
Assume exactly 1 mol of the gas (so mass = molar mass).
Use PV = nRT with n = 1 to find volume.
Calculate density = (molar mass) / V.

Example: What is the density of N₂ at 25°C (298 K) and 0.955 atm?

Molar mass of N₂ = 28.0 g/mol
Volume of 1 mol: V = (1)(0.08205)(298) / (0.955) = 25.6 L
Density = 28.0 g / 25.6 L = 1.09 g/L

🫁 Real-world application: Breathing

🫁 How breathing uses pressure differences

Breathing (respiration) draws air into lungs by reducing pressure inside the lungs.
The diaphragm moves down to reduce lung pressure, causing external air to rush in.
Expelling air: diaphragm pushes against lungs, increasing pressure and forcing air out.

📏 Pressure changes involved

Under normal conditions, a pressure difference of only 1 or 2 torr makes us breathe in and out.
This is a very small fraction of atmospheric pressure (about 0.001–0.003 atm).

🔢 Amount of air per breath

A normal breath is about 0.50 L at room temperature (22°C = 295 K) and 1.0 atm.
Using PV = nRT: n = (1.0 atm)(0.50 L) / [(0.08205)(295 K)] = 0.021 mol air
This equals about 0.6 g of air per breath—not much, but enough to sustain life.

Gas Mixtures

🧭 Overview

🧠 One-sentence thesis

Dalton's law of partial pressures shows that each gas in a mixture behaves independently, allowing us to calculate total pressure by summing individual gas pressures and to account for complications like water vapour when collecting gases.

📌 Key points (3–5)

Partial pressure definition: each gas in a mixture has its own pressure, called partial pressure, even though all gases share the same temperature and volume.
Dalton's law: total pressure equals the sum of all partial pressures in the mixture.
Water vapour complication: when collecting gas over water, the total pressure includes water's vapour pressure, which must be subtracted to find the actual gas pressure.
Common confusion: don't confuse "pressure" (pure gas) with "partial pressure" (gas in a mixture) or "vapour pressure" (liquid evaporating into gas phase).
Mole fraction: another way to express composition—the ratio of one component's moles (or partial pressure) to the total.

🧪 How gases behave in mixtures

🧪 Independent behavior of mixed gases

Gas mixtures form a solution—a homogeneous mixture where gases mix completely.

Each component in a gas mixture can be treated separately.
All gases in the mixture share the same temperature and volume (gases expand to fill their container).
However, each gas has its own pressure.

🔢 Partial pressure concept

Partial pressure of a gas, P_i, is the pressure that an individual gas in a mixture has.

Partial pressures are expressed in torr, millimeters of mercury, or atmospheres, just like regular gas pressure.
Terminology matters:
- Use "pressure" when talking about pure gases.
- Use "partial pressure" when talking about individual gas components in a mixture.
Don't confuse: partial pressure is not the total pressure; it's just one component's contribution.

⚖️ Dalton's law of partial pressures

⚖️ The law statement

Dalton's law of partial pressures states that the total pressure of a gas mixture, P_tot, is equal to the sum of the partial pressures of the components, P_i.

Formula in words: total pressure = sum of all partial pressures
Example: A mixture of H₂ at 2.33 atm and N₂ at 0.77 atm has total pressure = 2.33 + 0.77 = 3.10 atm

🔍 Why this law matters

It reinforces that gases behave independently of each other.
You can calculate the total pressure by simply adding up individual pressures.
Example: Air can be thought of as a mixture of N₂ and O₂. In 760 torr of air, if N₂ is 608 torr, then O₂ must be 760 − 608 = 152 torr.

🔗 Connected containers scenario

When containers with different gases are connected and opened:

The gases mix and spread throughout the total combined volume.
Use Boyle's law for each gas separately to find its new partial pressure in the larger volume.
Then add the resulting partial pressures to get the total pressure.

Example: A 2.00 L container with 2.50 atm of H₂ connects to a 5.00 L container with 1.90 atm of O₂. Total volume becomes 7.00 L. Calculate each gas's new pressure using Boyle's law, then sum them for the final total pressure.

💧 Collecting gases over water

💧 The water vapour problem

Vapour pressure is the partial pressure of a vapour when the liquid is the normal phase under a given set of conditions.

Liquids constantly evaporate into vapour until the vapour reaches a characteristic partial pressure (the vapour pressure).
Water has a specific vapour pressure at each temperature (given in tables).
When a gas is collected by bubbling through water, the collected gas is mixed with water vapour.

🧮 Accounting for water vapour

Key principle: Total pressure = partial pressure of the collected gas + vapour pressure of water

To find the actual amount of gas collected, subtract water's vapour pressure from the total pressure.
Example: H₂ gas collected over water at 22°C shows total pressure of 733 torr. Water's vapour pressure at 22°C is 19.84 torr. Therefore, H₂ partial pressure = 733 − 19.84 = 713 torr.
Don't confuse: the total pressure reading includes both the gas you want and the water vapour; you must separate them.

📊 Vapour pressure and temperature

Temperature increases	Vapour pressure behavior
Higher temperature	Higher vapour pressure
Example: 22°C	19.84 torr
Example: 50°C	92.59 torr
Example: 100°C	760.0 torr (boiling point)

🧮 Mole fraction

🧮 Definition and calculation

Mole fraction, χ_i, is the ratio of the number of moles of component i in a mixture divided by the total number of moles in the sample.

Formula in words: mole fraction = moles of component ÷ total moles
Mole fraction is not a percentage; its values range from 0 to 1.
The sum of all mole fractions in a mixture equals exactly 1.

Example: A mixture of 4.00 g He (1.00 mol) and 5.0 g Ne (0.25 mol) has total moles = 1.25 mol. Mole fraction of He = 1.00 ÷ 1.25 = 0.80; mole fraction of Ne = 0.25 ÷ 1.25 = 0.20.

🎯 Shortcut for gases

For gas mixtures at the same temperature and volume:

Mole fraction = partial pressure of component ÷ total pressure
This allows you to determine mole fractions without calculating moles directly.

Example: He at 0.80 atm and Ne at 0.60 atm give total pressure = 1.40 atm. Mole fraction of He = 0.80 ÷ 1.40 ≈ 0.57; mole fraction of Ne = 0.60 ÷ 1.40 ≈ 0.43.

🥤 Real-world application: carbonated beverages

🥤 How carbonation works

Carbonated beverages (sodas, beer, sparkling wines) have CO₂ gas dissolved in them.

Two methods to carbonate:

High-pressure method: Flat beverage is subjected to high pressure of CO₂ gas, forcing it into solution. When the container opens, pressure releases (the "hiss"), and CO₂ bubbles come out of solution.
Fermentation method: Yeast ingests sugar and generates CO₂ as a digestion product. The overall reaction converts sugar (C₆H₁₂O₆) into ethanol (C₂H₅OH) and CO₂. When this occurs in a closed container, the CO₂ dissolves, then releases when opened.

Fine sparkling wines and champagnes typically use fermentation.
Less-expensive sparkling wines, sodas, and beer use the high-pressure method.
Don't confuse: both methods result in dissolved CO₂, but the source differs (external pressure vs. biological production).

Kinetic Molecular Theory of Gases

🧭 Overview

🧠 One-sentence thesis

The kinetic molecular theory explains gas behavior by modeling gases as tiny particles in constant random motion, where temperature determines their average kinetic energy and molecular speed.

📌 Key points (3–5)

What the theory models: gases as particles in constant random motion with negligible volume and no interactive forces between them.
How pressure arises: from the number and force of collisions gas particles make with container walls.
Temperature-energy relationship: average kinetic energy is proportional to absolute temperature; all gases at the same temperature have the same average kinetic energy.
Speed distribution: individual molecules have different speeds, but share an average kinetic energy; lighter molecules move faster than heavier ones at the same temperature.
Common confusion: don't confuse the three speed measures—most probable speed (peak of distribution), average speed (mean), and root-mean-square speed (corresponds to average kinetic energy).

🧱 Five core concepts of the theory

🔄 Constant random motion

Gases consist of particles (molecules or atoms) that are in constant random motion.

This motion never stops as long as the gas exists.
The randomness means particles move in all directions.
Because particles are always moving, two or more gases will always mix when combined.

💥 Elastic collisions

Gas particles are constantly colliding with each other and the walls of their container. These collisions are elastic; that is, there is no net loss of energy from the collisions.

"Elastic" means no net energy is lost overall.
Individual molecule speeds may change after a collision (one faster, one slower), but the average kinetic energy stays constant.
Example: two molecules collide—one deflects at slightly higher speed, the other at slightly lower speed, but total energy is conserved.

📏 Negligible particle volume

Gas particles are small and the total volume occupied by gas molecules is negligible relative to the total volume of their container.

Most of the volume occupied by a gas is empty space.
This explains why gases have low density.
This also explains why gases can expand or contract easily under appropriate influence.

🚫 No interactive forces

There are no interactive forces (i.e., attraction or repulsion) between the particles of a gas.

Particles do not attract or repel each other.
They only interact through collisions.
This is an idealization that works well for many real gases under normal conditions.

🌡️ Temperature and kinetic energy

The average kinetic energy of gas particles is proportional to the absolute temperature of the gas, and all gases at the same temperature have the same average kinetic energy.

Higher temperature = higher average kinetic energy.
This relationship is universal: different gases at the same temperature share the same average kinetic energy.
Don't confuse: same average kinetic energy does not mean same speed—lighter molecules move faster.

⚡ Kinetic energy and molecular speed

⚡ What kinetic energy means

Kinetic energy (Ek): the energy an object has due to its motion.

For an individual atom, kinetic energy depends on mass (m) and speed (u).
Gas molecules share an average kinetic energy.
Individual molecules exhibit a distribution of kinetic energies because they have a distribution of speeds.

📊 Distribution of speeds

Molecules in a gas sample do not all move at the same speed.
The distribution arises from collisions between molecules.
Three important speed measures:
- Most probable speed (u_mp): the speed of the largest number of molecules; corresponds to the peak of the distribution curve.
- Average speed (u_av): the mean speed of all gas molecules in the sample.
- Root-mean-square (rms) speed (u_rms): the speed of molecules having exactly the same kinetic energy as the average kinetic energy of the sample.

🔗 Relationship between temperature and speed

Average kinetic energy is proportional to absolute temperature (involves the Boltzmann constant k, which is the gas constant R divided by Avogadro's constant).
The rms speed is related to both temperature and molar mass.
Key insight: rms speed increases with temperature and decreases with molar mass.
Example: at 25°C, nitrogen molecules have an rms speed that can be calculated using the relationship between temperature, molar mass, and the gas constant.

⚖️ Comparing gases at the same temperature

Two gases at the same temperature have the same average kinetic energy.
But the gas with smaller molar mass will have a higher rms speed.
Example: lighter noble gases (like helium) move faster than heavier ones (like xenon) at the same temperature.

🔍 Applying the theory to gas laws

📉 Volume decrease at constant temperature

What happens to pressure when volume decreases?

Two ways to understand this:

Using the ideal gas law: Pressure equals (number of moles × gas constant × temperature) divided by volume. Volume is in the denominator, so decreasing volume increases pressure.
Using kinetic molecular theory: Temperature stays constant, so average kinetic energy and rms speed remain the same. The container is smaller, so molecules travel a shorter distance between collisions with walls. More collisions per second means higher pressure.

🌡️ Temperature increase at constant volume

What happens to pressure when temperature increases?

Two ways to understand this:

Using the ideal gas law: Temperature is in the numerator, so there is a direct relationship—increasing temperature increases pressure.
Using kinetic molecular theory: Higher temperature means higher average kinetic energy and higher rms speed. Molecules hit the container walls more frequently and with greater force. This increases pressure.

➕ Mole increase at constant volume and temperature

What happens to pressure when the number of moles increases?

Temperature stays the same, so average kinetic energy and rms speed remain the same.
More moles means more molecules available to collide with walls at any given time.
Therefore pressure increases.
Don't confuse: it's not that molecules hit harder (energy is constant), but that there are more collisions happening.

🎯 Why pressure exists

🎯 The collision mechanism

Pressure is determined by two factors:
1. Number of collisions gas particles make with container walls.
2. Force with which they collide.
Both factors depend on molecular speed and the number of molecules.
This explains why pressure changes with temperature, volume, and amount of gas.

Molecular Effusion and Diffusion

🧭 Overview

🧠 One-sentence thesis

Lighter gases move faster through tiny openings (effusion) and through other gases (diffusion) because their lower molar mass gives them higher molecular speeds.

📌 Key points

Effusion definition: gas molecules moving from one container to another through a tiny hole, typically toward lower pressure.
Graham's law: effusion rate is inversely proportional to the square root of molar mass—lighter gases effuse faster.
Why lighter is faster: gases with lower molar mass have higher rms (root-mean-square) speed, so they hit and pass through holes more often.
Common confusion: effusion vs diffusion—effusion is movement through a tiny hole between containers; diffusion is movement through one or more other gases.
Practical use: comparing effusion rates lets you identify unknown gases by calculating their molar mass.

🔬 What is effusion

🔬 Definition and setup

Effusion: the movement of gas molecules from one container to another via a tiny hole.

The container receiving the gas is typically kept at lower pressure.
The process depends on individual molecules hitting and passing through the hole.
Not bulk flow—each molecule must randomly strike the opening.

🎯 Why molecular speed matters

For a molecule to effuse, it must hit the tiny hole and pass through.
Gases with higher rms speed are more likely to hit and pass through the hole in a given time.
Therefore, effusion rate depends directly on rms speed.

⚖️ Graham's law of effusion

⚖️ The relationship

Graham's law of effusion (1846, Thomas Graham): the rate of effusion of a gas is inversely proportional to the square root of its molar mass.

In words: rate of effusion is proportional to one divided by the square root of molar mass.
Lighter molecular weight → higher effusion rate.
Heavier molecular weight → lower effusion rate.

🧮 How to use it

The law compares two gases: the ratio of their effusion rates equals the inverse ratio of the square roots of their molar masses.
Example from the excerpt: an unknown halogen gas effuses at approximately 1.89 times the rate of I₂ at the same temperature.
- Set up the ratio: rate of unknown / rate of I₂ = 1.89.
- By Graham's law, this ratio also equals the square root of (molar mass of I₂ / molar mass of unknown).
- Solve for the unknown molar mass, then identify the gas (the excerpt concludes it is Cl₂).

🔗 Connection to kinetic theory

Effusion depends on rms speed (from kinetic molecular theory).
Rms speed is inversely related to the square root of molar mass.
Therefore, effusion rate follows the same inverse square-root relationship.

🌫️ Diffusion

🌫️ Definition

Diffusion: the movement of gas molecules through one or more additional types of gas via random molecular motion.

Unlike effusion (through a hole), diffusion is movement through a mixture of gases.
The excerpt introduces the term but does not elaborate further on mechanisms or laws.

🔄 Don't confuse effusion and diffusion

Type	What it is	Key feature
Effusion	Movement through a tiny hole between containers	Depends on hitting the hole; typically toward lower pressure
Diffusion	Movement through other gases	Random molecular motion through a gas mixture

Both involve gas movement, but the physical setup and pathway differ.
Effusion: container-to-container via a small opening.
Diffusion: molecule-to-molecule mixing within or across gas volumes.

Real Gases

🧭 Overview

🧠 One-sentence thesis

Real gases deviate from ideal behavior at high pressures and low temperatures, and the van der Waals equation corrects for these deviations by accounting for molecular volume and intermolecular forces.

📌 Key points (3–5)

Ideal vs. real gases: Ideal gases follow kinetic molecular theory perfectly (negligible particle volume, no intermolecular forces), but real gases deviate under certain conditions.
When deviation occurs: Real gases behave less ideally at high pressures (molecules crowded together) and low temperatures (molecules move slower and attract more).
Compressibility factor: Measures deviation from ideal behavior; under ideal conditions it equals exactly 1, but real gases show values above or below 1.
Common confusion: Two competing effects at high pressure—intermolecular attraction lowers pressure below ideal, but molecular volume increases pressure above ideal.
Van der Waals correction: Uses two constants (a for intermolecular forces, b for molecular volume) to adjust the ideal gas law for real conditions.

🔬 Ideal vs. Real Gas Behavior

🔬 What makes a gas "ideal"

An ideal gas is one that conforms exactly to the tenets of the kinetic molecular theory, where the volume occupied by the gas particles is negligible relative to the total volume of the container, and there are no appreciable intermolecular attractions or repulsions.

Two key assumptions: (1) gas particles take up essentially zero space, (2) particles don't attract or repel each other.
These assumptions work well under normal conditions but break down under extreme conditions.

🌡️ What makes gases "real"

Real gases can deviate from ideal behavior, especially at high pressures and low temperatures.

Real gas molecules do occupy finite volume.
Real gas molecules do experience intermolecular forces.
The extent of deviation depends on the specific conditions and the gas itself.

📏 Measuring deviation: compressibility factor

The compressibility factor is calculated by dividing the product of pressure and volume by the product of the gas constant and temperature for one mole.
Under ideal conditions, this ratio equals exactly 1.
Real gases show compressibility factors above or below 1, indicating deviation.

🔴 High Pressure Effects

🔴 Two competing effects at high pressure

At higher pressures, gas molecules are closer together, causing two simultaneous changes:

Effect 1: Intermolecular forces (lowers pressure)

Molecules experience greater attractive intermolecular forces when crowded.
Attractions hold molecules together more, reducing collision force and frequency with container walls.
Result: pressure drops below ideal values.

Effect 2: Molecular volume (raises pressure)

Molecules occupy a larger proportion of the container volume.
The unoccupied volume available to any one molecule is smaller than under ideal conditions.
Result: pressure increases beyond ideal values.

⚖️ Don't confuse

These two effects work in opposite directions. The net deviation depends on which effect dominates for a particular gas under specific conditions.

🥶 Low Temperature Effects

🥶 Why cold gases deviate

As temperature decreases, average kinetic energy of gas particles decreases.
A larger proportion of molecules have insufficient kinetic energy to overcome attractive intermolecular forces from neighbors.
Gas molecules become "stickier" to each other.

📉 Impact on pressure

Molecules collide with container walls with less frequency and force.
Pressure decreases below ideal values.
Example: The excerpt shows nitrogen's compressibility factor changing at different temperatures, demonstrating this temperature dependence.

🧮 The Van der Waals Equation

🧮 Purpose and structure

In 1873, Johannes van der Waals developed an equation that compensates for deviations from ideal gas behavior.

The van der Waals equation uses two additional experimentally determined constants: a, which is a term to correct for intermolecular forces, and b, which corrects for the volume of the gas molecules.

The equation structure:

Takes the ideal gas law (PV = nRT) as a starting point.
Adds correction terms using constants a and b.
If a and b equal zero (ideal conditions), the equation simplifies back to the ideal gas law.

🔧 The two correction constants

Constant	What it corrects	Physical meaning
a	Intermolecular forces	Accounts for attractive forces between molecules
b	Molecular volume	Accounts for the finite space molecules occupy

Both constants are experimentally determined for each gas.
Different gases have different values (e.g., helium has smaller values than ammonia).
Larger molecules and those with stronger intermolecular forces have larger constants.

📊 Using van der Waals constants

The excerpt provides a table of constants for various gases:

Noble gases (helium, neon, argon) generally have smaller values.
Polar molecules (ammonia, hydrogen chloride) have larger a values due to stronger intermolecular forces.
Larger molecules (xenon, carbon dioxide) have larger b values due to greater molecular volume.

💡 Practical application

Example from the excerpt: To find the pressure of 2.00 moles of oxygen gas in a 30.00 L flask at 25.0°C, you would:

Look up oxygen's a and b constants from the table.
Substitute values into the van der Waals equation.
Solve for pressure, getting a more accurate result than the ideal gas law would provide.

Formation Reactions

🧭 Overview

🧠 One-sentence thesis

Formation reactions serve as benchmark reactions whose measured enthalpy changes allow us to predict the enthalpy of any possible reaction through algebraic construction, eliminating the need to measure every reaction individually.

📌 Key points (3–5)

Why formation reactions matter: they provide agreed-on benchmark data so we don't have to measure the enthalpy change of every possible reaction.
How they work with Hess's law: Hess's law lets us construct new reactions algebraically and combine benchmark enthalpies to predict unknown reaction enthalpies.
What formation reactions are: a specific set of chemical reactions (definition cut off in excerpt).
Key distinction: formation reactions are not arbitrary—they are agreed-on standard reactions that serve as central thermochemical data.

🔧 The problem formation reactions solve

🔧 Why we need benchmark reactions

Measuring the enthalpy change of every possible chemical reaction would be impractical.
Instead, chemistry uses a set of agreed-on benchmark reactions whose enthalpy changes are measured once.
All other reactions can then be constructed algebraically from these benchmarks.

🧮 How Hess's law enables this approach

Hess's law allows us to construct new chemical reactions and predict what their enthalpies of reaction will be.

Hess's law is the tool that makes benchmarking possible.
You combine the enthalpies of benchmark reactions according to how you algebraically construct the target reaction.
Example: if a target reaction can be written as (benchmark A) + 2×(benchmark B), then its enthalpy is (enthalpy of A) + 2×(enthalpy of B).

📐 What formation reactions are

📐 Definition and role

The excerpt states:

Formation reactions are chemical...

(The excerpt cuts off here, so the full definition is not provided.)

The excerpt identifies formation reactions as the agreed-on set of benchmark reactions.
They provide "the central data for any thermochemical equation."
Don't confuse: formation reactions are not just any reaction—they are specifically chosen standards used across chemistry.

📊 How formation reactions are used

Concept	What the excerpt says
Benchmark reactions	Agreed-on sets of reactions that provide central thermochemical data
Measurement strategy	Measure only the enthalpy changes of benchmark reactions, not every possible reaction
Construction method	Use Hess's law to algebraically construct any reaction from benchmarks and combine their enthalpies

Note: The excerpt ends mid-sentence and does not provide the complete definition of formation reactions or detailed examples of their structure.

Energy and Formation Reactions

Energy

🧭 Overview

🧠 One-sentence thesis

The enthalpy change of any chemical reaction can be calculated using tabulated enthalpies of formation by subtracting the sum of reactants' formation enthalpies from the sum of products' formation enthalpies.

📌 Key points (3–5)

Formation reactions: special benchmark reactions that produce exactly one mole of a substance from its constituent elements in their standard states.
Enthalpies of formation: the enthalpy changes for formation reactions, which serve as tabulated reference data for calculating any reaction's enthalpy change.
Products-minus-reactants method: a shortcut formula that eliminates the need to write out all formation reactions explicitly.
Common confusion: formation reactions may require fractional coefficients on the reactant side to produce exactly one mole of product (not the usual whole-number coefficients).
Energy units: energy is measured in joules (J) or kilojoules (kJ); in nutrition, the Calorie (capital C) is actually a kilocalorie.

🧪 Formation reactions as benchmarks

🧪 What makes a reaction a formation reaction

Formation reactions: chemical reactions that form one mole of a substance from its constituent elements in their standard states.

Standard states mean:
- Elements appear as they naturally exist (e.g., O₂ as a diatomic molecule, not O).
- Proper phase at normal temperatures (typically room temperature).
Exactly one mole of product must be formed.
Coefficients on the reactant side may be fractional to satisfy the one-mole requirement.

Example: The formation reaction for water is H₂(g) + ½O₂(g) → H₂O(ℓ), not 2H₂(g) + O₂(g) → 2H₂O(ℓ), because the latter produces two moles.

✅ Recognizing valid formation reactions

Criterion	Valid	Invalid example
Product amount	Exactly 1 mole	2HCl(g) produced instead of 1
Reactants	Elements in standard states	CaO(s) + CO₂ (compounds, not elements)
Element form	Diatomic if natural (O₂, H₂, Cl₂)	12O(g) instead of 6O₂(g)

Don't confuse: A reaction that produces one mole of product is not automatically a formation reaction if the reactants are compounds rather than elements.

🔢 Writing formation reactions

Start with the formula of the substance.
Identify its constituent elements.
Write elements in their standard states (diatomic molecules where applicable).
Balance to produce exactly one mole of product (fractional coefficients allowed).

Example: For C₂H₆(g), the formation reaction is 2C(s) + 3H₂(g) → C₂H₆(g).

🔥 Enthalpies of formation

🔥 Definition and notation

Enthalpy of formation: the enthalpy change for a formation reaction.

Notation: ΔHf (the subscript f indicates "formation").
Units: kJ/mol (understood to be per one mole of substance formed).
Key fact: By definition, the enthalpy of formation of any element in its standard state is exactly zero.
- Example: H₂(g) → H₂(g) has ΔHf = 0 (no change).

📊 Using tabulated data

Enthalpies of formation are measured and tabulated for a wide variety of substances.
The excerpt provides Table 7.1 with ΔHf values for many compounds.
These values serve as reference data; you don't need to measure every possible reaction.
Phase matters: H₂O(g), H₂O(ℓ), and H₂O(s) have different ΔHf values.

Example: From the table, ΔHf for CO₂(g) = −393.51 kJ/mol; for CH₄(g) = −74.87 kJ/mol.

🧮 Calculating reaction enthalpies

🧮 Hess's law approach

Any chemical reaction can be written as a combination of formation reactions.
Formation reactions for products are written normally; for reactants, they are reversed (sign changes).
Multiply each formation reaction by the coefficient in the balanced equation.
Combine the ΔHf values accordingly.

Example: For 2NO₂(g) → N₂O₄(g), write the reverse formation of NO₂ (multiply by 2, change sign) and the formation of N₂O₄ (keep sign), then add.

⚡ Products-minus-reactants shortcut

The excerpt states: "the enthalpy change of any chemical reaction is equal to the sum of the enthalpies of formation of the products minus the sum of the enthalpies of formation of the reactants."

Formula (in words):

Multiply each product's ΔHf by its coefficient (number of moles).
Sum all products' contributions.
Multiply each reactant's ΔHf by its coefficient.
Sum all reactants' contributions.
Subtract the reactants' total from the products' total.

Don't confuse: The mol units cancel out during multiplication, so the final answer is in energy units (kJ) only, not kJ/mol.

Example: For a reaction with products and reactants, you look up each ΔHf in the table, multiply by coefficients, then compute (sum of products) − (sum of reactants).

⚙️ Energy fundamentals

⚙️ What is energy?

Energy: the ability to do work.

Work (w) is defined as force (F) operating over a distance (Δx).
In SI units: force in newtons (N), distance in metres (m), so work is in N·m.
One N·m is redefined as one joule (J).

📏 Energy units

Unit	Definition	Context
Joule (J)	1 N·m	Primary SI unit; warms ~0.25 g water by 1°C
Kilojoule (kJ)	1,000 J	Common for chemical reactions
Calorie (cal)	4.184 J	Older unit, still used
Kilocalorie (kcal or Cal)	1,000 cal = 4,184 J	Nutrition labels (capital C)

Don't confuse: A food "Calorie" (capital C) is actually a kilocalorie, not a small calorie.

Example: A food label showing 38 Cal means 38 kcal = 38,000 cal = about 159,000 J.

🔒 Conservation of energy

An isolated system does not allow energy or matter to transfer in or out (approximated by a closed, insulated thermos).
The law of conservation of energy states that the total energy of an isolated system does not change.
Energy is said to be conserved (does not increase or decrease in an isolated system).

🍎 Nutrition application

🍎 Calories in food

Nutrition uses the Calorie (capital C), which equals 1 kilocalorie.
A 2,000 Cal daily diet is actually 2,000,000 cal or over 8,000,000 J.

🥗 Macronutrient energy content

Macronutrient	Energy per gram
Protein	4 Cal/g
Carbohydrate	4 Cal/g
Fat	9 Cal/g

On a 2,000 Cal diet of only proteins/carbs: need ~500 g of food (~1 lb).
On a 2,000 Cal diet of only fats: need ~220 g of food (less than ½ lb).
Water has no caloric value (but is important for hydration).

⚖️ Weight management

Gaining weight: consuming more calories than the body uses; ~3,500 extra Cal = ~1 lb gained.
Losing weight: expending 3,500 more Cal than ingested = ~1 lb lost.
The excerpt emphasizes: "maintaining an ideal body weight is a straightforward matter of thermochemistry."

Stoichiometry Calculations Using Enthalpy

🧭 Overview

🧠 One-sentence thesis

Energy changes in balanced chemical equations can be treated as stoichiometric equivalences, allowing calculations that relate enthalpy changes to amounts of reactants or products just like mole-to-mole conversions.

📌 Key points (3–5)

Energy as an equivalence: the enthalpy change in a thermochemical equation relates to the molar amounts shown by coefficients, creating conversion factors between energy and moles.
Units matter: energy is expressed in kJ (not kJ/mol) because it refers to the specific molar amounts in the balanced equation.
Bidirectional calculations: you can start with moles and find energy released/absorbed, or start with energy and find amounts of substances.
Common confusion: the energy value relates to the number of moles indicated by the coefficient in the equation, not to one mole of every substance.
Real application: highly energetic reactions like the thermite reaction release enough heat to melt iron for welding purposes.

🔗 Energy-mole equivalences in thermochemical equations

🔗 What the equivalence means

A thermochemical equation provides an equivalence between the enthalpy change and the molar amounts of substances as indicated by their coefficients.

Just as balanced equations give mole-to-mole ratios, they also give energy-to-mole ratios.
The energy value corresponds to the exact stoichiometric amounts shown in the equation.
Example: if an equation shows 2 mol of hydrogen reacting with −570 kJ, then 2 mol of hydrogen is equivalent to 570 kJ of energy released.

📏 Why the unit is kJ, not kJ/mol

The energy change refers to the specific number of moles shown by the coefficient, not per mole.
This answers the question: "What amount of reactants or products does the energy refer to?"
The answer: it relates to the number of moles as indicated by the substance's coefficient in the balanced equation.

🧮 Calculating energy from amounts of substances

🧮 Converting moles to energy

Use the thermochemical equation to construct a conversion factor between moles and kilojoules.
The excerpt shows: if you know how many moles react, multiply by the energy-to-mole ratio to find energy released or absorbed.
Example: given 8.22 mol of hydrogen and knowing the equation relates a certain number of moles to −184.6 kJ, calculate energy using the conversion factor.

⚖️ Converting grams to energy

First convert grams to moles (using molar mass).
Then use the thermochemical equation to convert moles to energy.
The excerpt demonstrates: starting with 222.4 g of nitrogen, convert to moles, then apply the energy equivalence from the balanced equation.
Don't confuse: the thermochemical equation relates energy to moles, so mass must be converted to moles first.

🔄 Calculating amounts from energy

🔄 Starting with energy to find mass

The process works in reverse: start with kilojoules and use the equivalence to find moles, then convert to grams if needed.
The excerpt shows: given 558 kJ of energy supplied, use the conversion factor to find moles of product, then convert to grams using molar mass.
This is described as "start with an amount of energy" rather than starting with substance amounts.

🔁 Bidirectional flexibility

Energy can be treated like any other stoichiometric quantity.
You can move between energy ↔ moles ↔ grams using appropriate conversion factors.
The key is recognizing that the balanced equation provides the equivalence needed for these conversions.

🔥 Real-world application: the thermite reaction

🔥 What the thermite reaction is

A highly energetic reaction between aluminum metal and iron(III) oxide.
Produces iron metal and aluminum oxide.
Releases so much energy that the iron product becomes liquid (iron normally melts at 1,536°C).

🛠️ Practical uses

Application	Purpose
Civilian welding	Re-weld broken locomotive axles and railroad tracks
Metal separation	Cut through metal when a torch doesn't work
Military incendiary devices	Start fires
Military weapon disabling	Melt holes in artillery barrels

The liquid iron can fill spaces between metal parts and weld them together after cooling.
The excerpt emphasizes this is still used today for various welding and cutting purposes.

Enthalpy and Chemical Reactions

🧭 Overview

🧠 One-sentence thesis

Every chemical reaction occurs with a concurrent change in energy, which we express through enthalpy change to account for conditions like pressure, volume, and temperature.

📌 Key points (3–5)

Core principle: every chemical reaction occurs with a concurrent change in energy.
What enthalpy is: a definition of energy that holds when certain conditions (pressure, volume, temperature) are specified.
Why enthalpy matters: conditions like pressure, volume, and temperature affect the energy content of a system, so we need a standardized way to express energy changes.
Common confusion: energy changes in reactions depend on conditions—enthalpy provides a consistent framework similar to how standard temperature and pressure standardize gas measurements.

🔥 Real-world application: Thermite reactions

🔥 What thermite reactions are

A reaction between aluminum and iron(III) oxide that produces iron metal and aluminum oxide.
The reaction releases so much energy that the iron product comes off as a liquid (iron normally melts at 1,536°C).

🛠️ Civilian uses

Welding metal parts: liquid iron fills spaces between metal parts and welds them together after cooling.
Railroad repair: used to re-weld broken locomotive axles that cannot be easily removed and to weld railroad tracks together.
Metal separation: can separate thin pieces of metal when a torch doesn't work.

⚔️ Military uses

Incendiary devices: thermite mixtures with additional components are used as devices that start fires.
Disabling weapons: can melt holes in enemy artillery barrels, rendering them unusable.

⚡ Energy changes in chemical reactions

⚡ The fundamental concept

Every chemical reaction occurs with a concurrent change in energy.

This is not optional or conditional—it is a fundamental principle.
We must learn how to properly express these energy changes.

📏 Why conditions matter

Pressure, volume, and temperature affect the energy content of a system.
These factors were already seen in:
- The study of gases (Chapter 6).
- The definition of work and heat.
Without accounting for conditions, energy measurements would be inconsistent.

🎯 What enthalpy provides

Enthalpy change (ΔH): a definition of energy that holds when certain conditions are specified.

Similar to how standard temperature and pressure standardize gas measurements, enthalpy standardizes energy change measurements.
It allows consistent comparison of energy changes across different reactions.
Don't confuse: enthalpy is not just "energy"—it is energy defined under specified conditions.

🧪 Measuring enthalpy changes

🧪 Experimental measurement

The excerpt states that enthalpy changes are measured experimentally.
The specific methods are introduced but not detailed in this excerpt.

📊 Stoichiometry and energy

📊 Using energy in calculations

The energy change of a chemical reaction can be used in stoichiometry calculations.
Balanced thermochemical equations imply equivalences between moles of substances and energy (kilojoules).

📝 Example equivalence pattern

From a balanced thermochemical equation, you can write:
- 1 mol of reactant A ⇔ 1 mol of reactant B ⇔ 1 mol of product C ⇔ X kJ
This allows calculation of energy absorbed or released for any given amount of substance.

🔢 Types of calculations

The excerpt includes exercises for:

Calculating kilojoules given off or absorbed when a certain number of moles react.
Calculating mass of substance needed to generate or consume a specific amount of energy.
Example: "How much energy is given off when 100.0 g of glucose react?" or "What mass of substance is decomposed by 256 kJ?"

Work and Heat

🧭 Overview

🧠 One-sentence thesis

Work and heat are two distinct forms of energy transfer—work occurs when a gas changes volume against external pressure, while heat transfers energy due to temperature differences—and both can be quantified using specific equations.

📌 Key points (3–5)

Work definition for gases: work equals negative external pressure times the change in volume (final minus initial).
Heat definition: energy transfer between objects due to temperature difference; measured in joules.
Heat calculation: heat depends on mass, temperature change, and specific heat capacity of the substance.
Common confusion: the sign convention—expanding gas does work (loses energy, negative sign), while contracting gas has work done on it (gains energy, positive sign).
Specific heat matters: substances with lower specific heat require less energy to change temperature by the same amount.

⚙️ Work in gas systems

⚙️ What work means for gases

Work for a gas system: the energy involved when a gas expands or contracts against an external pressure.

When a gas expands, it pushes against external pressure and does work on the surroundings.
The equation is: work = negative external pressure times change in volume.
Written in words: work = −P_ext × ΔV, where ΔV = V_final − V_initial.

📐 Volume change and sign convention

ΔV is positive when gas expands (V_final > V_initial) → work is negative → system loses energy.
ΔV is negative when gas contracts (V_final < V_initial) → work is positive → system gains energy.
The negative sign in the equation ensures this convention: expanding gas does work (energy out), contracting gas has work done on it (energy in).
Example: A gas expands from 3.44 L to 6.19 L against 1.26 atm external pressure → ΔV = +2.75 L → work is negative (energy leaving the system).

🔢 Units for work

Original units	Conversion	Final units
Litre·atmospheres (L·atm)	1 L·atm = 101.32 J	Joules (J)

Volume changes are typically in litres; pressure in atmospheres.
The product gives L·atm, which must be converted to joules for standard energy units.

🔥 Heat and temperature

🔥 What heat is

Heat: the transfer of energy from one body to another due to a difference in temperature.

Heat flows from hotter to colder objects.
If energy transfers into your hands, the object feels hot; if energy transfers out of your hands, the object feels cold.
Heat is also measured in joules, like work.

🌡️ Heat calculation formula

The amount of heat (q) is given by: q = m × c × ΔT

m = mass of the substance.
c = specific heat capacity (energy needed per gram per degree to change temperature).
ΔT = temperature change (final temperature minus initial temperature).

Don't confuse: ΔT can be in degrees Celsius or kelvins—a change in temperature has the same numerical value in both scales.

🧪 Specific heat capacity

Specific heat capacity (c): the amount of energy needed to change the temperature of one gram of a substance by one degree.

Units: J/(g·°C) or J/(g·K).
Higher specific heat → more energy needed to change temperature (e.g., water at 4.184 J/(g·°C)).
Lower specific heat → less energy needed (e.g., gold at 0.129 J/(g·°C)).
Specific heat is a physical property characteristic of each substance.

Substance	Specific Heat (J/(g·°C))
Water	4.184
Iron	0.449
Gold	0.129
Mercury	0.139
Aluminum	0.900

Example: 25.0 g of Fe increases from 22°C to 76°C → ΔT = 54°C → q = 25.0 g × 0.449 J/(g·°C) × 54°C = 606 J (energy going into the system).

🔄 Sign conventions and energy flow

➕ Positive heat and work

Positive q: energy is added to the system (temperature increases).
Positive work: energy is added to the system (gas is compressed).

➖ Negative heat and work

Negative q: energy leaves the system (temperature decreases).
Negative work: energy leaves the system (gas expands and does work on surroundings).

🔁 Solving for unknowns

The heat equation q = m × c × ΔT has four variables.
If you know any three, you can solve for the fourth using algebra.
Example: Given q, m, and ΔT → solve for specific heat c by dividing both sides by m and ΔT.
Example: Given q, c, and ΔT → solve for mass m by dividing both sides by c and ΔT.

Hess's Law

Hess’s Law

🧭 Overview

🧠 One-sentence thesis

Hess's law allows us to calculate enthalpy changes for difficult-to-perform reactions by algebraically combining simpler chemical equations and their known enthalpy values.

📌 Key points (3–5)

What Hess's law does: enables combining chemical equations algebraically and combining their enthalpy changes the same way.
Why it matters: some reactions are extremely difficult to perform directly, but we can calculate their enthalpy changes by combining other reactions.
Two key corollaries: (1) reversing a reaction changes the sign of ΔH; (2) multiplying a reaction by a factor multiplies ΔH by the same factor.
Common confusion: when reversing or scaling reactions, you must apply the same operation to both the chemical equation and its ΔH value.
How it works: treat chemical equations like algebraic equations—substances appearing on both sides cancel out, just like spectator ions.

🧮 Treating chemical equations algebraically

🧮 Combining equations like algebra

Chemical equations can be treated like algebraic equations, with the arrow acting like an equals sign.
You can combine equations by putting all reactants together and all products together.
Substances appearing on both sides of the arrow cancel out (similar to canceling spectator ions in ionic equations).

✂️ Cancellation rules

If the same substance appears on both sides, it cancels completely.
If different amounts appear on both sides, cancel the smaller amount from both sides.
Example from the excerpt: 2CO₂(g) appears on both sides → cancels completely; 2 mol O₂ on reactant side and 1 mol O₂ on product side → 1 mol O₂ cancels from each side, leaving 1 mol O₂ on reactant side.

🎯 Why this is useful

The excerpt gives a concrete scenario:

Problem: Carbon combustion to make carbon monoxide (C + ½O₂ → CO) is extremely difficult to perform directly.
Reality: Given the opportunity, carbon reacts to make carbon dioxide instead (C + O₂ → CO₂).
Solution: By combining two feasible reactions algebraically, we can generate the equation for the difficult reaction and calculate its enthalpy change.

🔄 The two corollaries of Hess's law

🔄 Corollary 1: Reversing reactions

If a chemical reaction is reversed, the sign on ΔH is changed.

When you flip a reaction (products become reactants and vice versa), change the sign of the enthalpy change.
Example from the excerpt: The combustion of CO has a certain ΔH; when reversed (to have CO as a product instead of reactant), the sign on ΔH changes.
Don't confuse: This is not about the magnitude—only the sign flips (positive becomes negative, negative becomes positive).

✖️ Corollary 2: Multiplying reactions

If a multiple of a chemical reaction is taken, the same multiple of the ΔH is taken as well.

If you multiply all coefficients in a reaction by a factor, multiply ΔH by the same factor.
Example from the excerpt: The reaction to make CO₂ from C(s) and O₂(g) has ΔH = −393.5 kJ; when the reaction is taken two times, the enthalpy change becomes 2 × (−393.5 kJ) = −787.0 kJ.

🧪 Working through a Hess's law calculation

🧪 Step 1: Identify what you need

Start with the target reaction (the one you want to find ΔH for).
Look at the given reactions and their known ΔH values.
Determine which reactions contain the substances you need, and on which side they appear.

🧪 Step 2: Modify the given reactions

The excerpt's detailed example shows:

If a substance is on the wrong side: Reverse the reaction (and change the sign of ΔH).
If the coefficient is wrong: Multiply or divide the entire reaction and its ΔH.
Goal: manipulate each given reaction so that when combined, unwanted substances cancel and only the target reaction remains.

🧪 Step 3: Combine and cancel

Add all the modified reactions together.
Cancel substances that appear on both sides.
Verify that what remains is exactly the target reaction.

🧪 Step 4: Add the enthalpy changes

Sum all the ΔH values from the modified reactions.
The result is the ΔH for the target reaction.
Example from the excerpt: Three reactions were combined with ΔH values; the final ΔH was the sum of the three modified ΔH values.

💡 Why Hess's law is powerful

💡 Calculating unmeasurable reactions

Hess's law is very powerful. It allows us to combine equations to generate new chemical reactions whose enthalpy changes can be calculated, rather than directly measured.

Some reactions are impractical or impossible to perform in isolation.
Instead of direct measurement, we use known enthalpy changes from feasible reactions.
By algebraic combination, we obtain the enthalpy change for the difficult reaction.

💡 The underlying principle

The excerpt emphasizes that when chemical equations are combined algebraically, their enthalpies can be combined in exactly the same way.
This parallelism (equation manipulation = enthalpy manipulation) is the core of Hess's law.
Don't confuse: You are not measuring new reactions; you are calculating their ΔH from known data.

Light

🧭 Overview

🧠 One-sentence thesis

Light behaves both as a wave (characterized by wavelength and frequency) and as a particle of energy (the photon), with its energy proportional to its frequency.

📌 Key points (3–5)

Wave properties: Light has a wavelength (distance between corresponding points in adjacent cycles) and frequency (number of cycles per second).
Speed relationship: The speed of light is constant (approximately 3.00 × 10⁸ m/s), so wavelength and frequency are inversely related—as one increases, the other decreases.
Particle properties: Light also acts as packets of energy called photons, with energy proportional to frequency through Planck's constant.
Common confusion: Light is not just a wave or just a particle—it exhibits both behaviors; energy depends on frequency, not amplitude (unlike most waves).
The electromagnetic spectrum: Visible light (400–700 nm) is only one small region of a much wider range of possible wavelengths and frequencies.

🌊 Wave characteristics of light

📏 Wavelength and frequency definitions

Wavelength (λ): the distance between corresponding points in two adjacent light cycles.

Frequency (ν): the number of cycles of light that pass a given point in one second.

Wavelength is measured in units of length (metres, centimetres, nanometres, etc.).
Frequency is measured in per second (s⁻¹), also called hertz (Hz).
These are the two fundamental descriptors when treating light as a wave.

⚡ The speed of light relationship

The speed of any wave equals its wavelength times its frequency. For light traveling through a vacuum (or air, to a very good approximation):

speed = wavelength × frequency

or: c = λ × ν

The speed of light (c) is a universal constant: 2.9979 × 10⁸ m/s (approximately 3.00 × 10⁸ m/s).
Because c is constant, wavelength and frequency are inversely related: when one increases, the other must decrease.
Example: If you know the wavelength is 5.55 × 10⁻⁷ m, you can calculate frequency by dividing the speed of light by the wavelength, giving approximately 5.40 × 10¹⁴ s⁻¹.

Don't confuse: This inverse relationship is unique to light because its speed is constant; for other waves with variable speeds, the relationship differs.

🔋 Particle characteristics of light

💡 Light as energy packets

Light also behaves like a package of energy. The key insight:

For light, energy is proportional to frequency (not amplitude, as with most waves).
Each "package" of light energy is called a photon.

Photon: the particle-type name for a light wave, reflecting its behavior as a discrete packet of energy.

🧮 Energy-frequency relationship

The mathematical relationship between energy (E) and frequency (ν) is:

E = h × ν

where:

E is the energy of the light
ν is the frequency
h is Planck's constant: 6.626 × 10⁻³⁴ J·s

Planck's constant is a fundamental constant of the universe (like the speed of light), with unusual units (joule-seconds) that make the algebra work out correctly.

Example: Light with frequency 1.55 × 10¹⁰ s⁻¹ has energy of approximately 1.03 × 10⁻²³ J—an extremely small amount for a single photon.

Don't confuse: Unlike most waves where energy relates to amplitude (height), light's energy depends only on frequency; higher frequency means higher energy per photon.

🌈 The electromagnetic spectrum

📊 Range of light properties

Property	Range
Wavelength	From very long to very short
Frequency	From very low to very high
Energy	From very low to very high

Electromagnetic spectrum: the entire range of possible wavelengths, frequencies, and energies for light.

👁️ Visible light and beyond

Visible light: the region we can see with our eyes, with wavelengths between approximately 400 nm and 700 nm.
Light exists with much longer and much shorter wavelengths than visible light.
Different regions of the spectrum have different labels (though the excerpt notes these are all forms of light with varying properties).
The borders between regions are approximate, not sharp boundaries.

Why it matters: Understanding that visible light is just one small part of a much larger spectrum helps explain phenomena like electron microscopes (which use electrons with wavelengths around 0.5–1 nm, much shorter than visible light's 400–700 nm, allowing 600–700 times greater magnification).

Quantum Numbers for Electrons

🧭 Overview

🧠 One-sentence thesis

Quantum mechanics explains that electrons in atoms can have only certain quantized energies and are described by four quantum numbers that determine their energy, spatial distribution, and spin.

📌 Key points (3–5)

Why quantum numbers exist: Electrons in atoms have only certain fixed (quantized) energies, not random values, which explains why excited gases emit only specific colours of light (line spectra).
Four quantum numbers describe each electron: principal (n), angular momentum (ℓ), magnetic (mℓ), and spin (ms) quantum numbers together define an electron's state.
Each quantum number has restrictions: n must be a positive integer; ℓ ranges from 0 to n − 1; mℓ ranges from −ℓ to +ℓ; ms is either +½ or −½.
Common confusion—orbitals vs. shells: A shell is all electrons with the same n; a subshell is electrons with the same n and ℓ; an orbital is a specific orientation defined by mℓ.
Why it matters: These quantum numbers explain atomic structure, electron arrangement, and the unique line spectra of each element.

🌈 Light spectra and the discovery of quantization

🔥 Continuous vs. line spectra

Continuous spectrum: a full rainbow of all colours produced when a hot object glows and its light passes through a prism.

Line spectrum: only certain specific colours (lines) of light emitted when electricity passes through a gas and the light is separated by a prism.

Hot objects emit light across all wavelengths → continuous spectrum.
Electrified gases emit light at only certain wavelengths → line spectrum.
Every element has its own unique line spectrum, like a fingerprint.
Don't confuse: A continuous spectrum shows all colours; a line spectrum shows gaps and only discrete lines.

🔬 Hydrogen's simple pattern

Hydrogen gas has a particularly simple line spectrum that follows a predictable mathematical equation.
The equation involves a variable n that takes values 3, 4, 5, 6, and so on.
For a long time, scientists could describe the pattern but could not explain why it existed.

⚛️ Bohr's model and the birth of quantization

💡 Bohr's 1913 proposal

Niels Bohr suggested that the electron in a hydrogen atom could not have any random energy.
Instead, the electron has only certain fixed energy values indexed by the number n (now called a quantum number).

Quantized: quantities that can have only certain specific values, not a continuous range.

Bohr proposed that the electron occupies specific orbits, each with a fixed energy.
Energy changes between orbits can also have only certain values (like steps on a staircase—both the height of each step and the spacing between steps are fixed).

🌟 Why line spectra appear

Bohr suggested that the energy of emitted light equals the difference between two electron energy states:
- Energy of light = change in electron energy.
Because only certain energy differences are possible, only certain frequencies (and wavelengths) of light are emitted.
This explains why hydrogen's spectrum has discrete lines rather than a continuous rainbow.
Example: An electron drops from a higher energy orbit to a lower one → it emits light of a specific colour corresponding to that exact energy difference.

🚧 Limitations of Bohr's ideas

Bohr's model worked well for hydrogen but could not be applied to other atoms.
Later, quantum mechanics generalized Bohr's ideas to all atoms.

🧬 Quantum mechanics and the four quantum numbers

🌊 The quantum-mechanical model

Quantum mechanics treats electrons as if they behave like waves, not just particles.
It predicts:
- Quantized energies for electrons in all atoms (not just hydrogen).
- An organized arrangement of electrons within atoms.
Electrons are no longer thought of as randomly distributed or restricted to fixed orbits.
Instead, electrons are grouped into shells, subshells, and orbitals that explain chemical behaviour.

🔢 Four quantum numbers describe each electron

In the quantum-mechanical model, the state of an electron is described by four quantum numbers (not just one as Bohr predicted):

Quantum number	Symbol	What it describes	Restrictions
Principal	n	Energy level (shell)	Any positive integer: 1, 2, 3, 4, …
Angular momentum	ℓ	Shape of electron distribution (subshell)	Any integer from 0 to n − 1
Magnetic	mℓ	Orientation of electron distribution (orbital)	Any integer from −ℓ to +ℓ
Spin	ms	Spin state of the electron	Either +½ or −½

🏠 Shells, subshells, and orbitals

🏠 Electron shells (principal quantum number n)

Electron shell: all electrons in the same atom that have the same principal quantum number n.

The principal quantum number n largely determines the energy of an electron.
n can be 1, 2, 3, 4, and so on (any nonzero positive integer).
Higher n means higher energy and farther from the nucleus (on average).

📦 Subshells (angular momentum quantum number ℓ)

Subshell: electrons within a shell that have the same value of ℓ.

For a given n, ℓ can be any integer from 0 to n − 1.
Example: If n = 3, then ℓ can be 0, 1, or 2.
The ℓ quantum number has a minor effect on energy but strongly affects the spatial shape of the electron's distribution.

Letter notation for subshells:

ℓ value	Subshell letter
0	s
1	p
2	d
3	f

Instead of saying "ℓ = 1," chemists say "p subshell."

🧭 Orbitals (magnetic quantum number mℓ)

Orbital: a specific orientation of an electron's distribution in space, designated by a particular value of mℓ.

For any value of ℓ, there are (2ℓ + 1) possible values of mℓ.
mℓ ranges from −ℓ to +ℓ in integer steps.
Example: If ℓ = 1, then mℓ can be −1, 0, or +1 → three orbitals in the p subshell.
Example: If ℓ = 2, then mℓ can be −2, −1, 0, +1, or +2 → five orbitals in the d subshell.
The mℓ quantum number dictates the orientation of the orbital in three-dimensional space.
It has no effect on energy unless the electrons are in a magnetic field (hence the name "magnetic" quantum number).

Summary table:

ℓ	Number of orbitals	Possible mℓ values
0 (s)	1	0
1 (p)	3	−1, 0, +1
2 (d)	5	−2, −1, 0, +1, +2
3 (f)	7	−3, −2, −1, 0, +1, +2, +3

🔄 Spin quantum number (ms)

Spin quantum number (ms): describes the spin state of an electron; can be either +½ or −½.

Electrons behave as if they are spinning (we cannot confirm if they truly spin, but they behave that way).
There are only two possible spin states for an electron.
These are the only allowed values for ms; no other numbers are permitted.

🎨 Shapes of orbitals

🔵 s orbitals (ℓ = 0)

Any s orbital is spherically symmetric (shaped like a sphere).
There is only one s orbital per shell (because mℓ can only be 0 when ℓ = 0).
The electron distribution is the same in all directions from the nucleus.

🥜 p orbitals (ℓ = 1)

Any p orbital has a two-lobed, dumbbell-like shape.
There are three p orbitals in each p subshell (mℓ = −1, 0, +1).
They are normally represented as pointing along the x-, y-, and z-axes of three-dimensional space.
Each p orbital is oriented in a different direction.

🌹 d orbitals (ℓ = 2)

d orbitals are four-lobed rosettes (flower-like shapes).
There are five d orbitals in each d subshell.
They are oriented differently in space.
One d orbital (labelled dz²) has two lobes plus a torus (doughnut shape) instead of four lobes, but it is equivalent to the other orbitals.

📐 Important note

The diagrams of orbitals are estimates of where the electron is likely to be found in space.
They are not fixed surfaces that electrons are stuck on; electrons are distributed in a cloud-like probability pattern.

✅ Allowed vs. not allowed quantum number sets

🧮 Rules for checking validity

To determine if a set of quantum numbers {n, ℓ, mℓ, ms} is allowed, check:

n must be a positive integer (1, 2, 3, …).
ℓ must be an integer from 0 to n − 1 (and cannot be negative).
mℓ must be an integer from −ℓ to +ℓ (absolute value of mℓ ≤ ℓ).
ms must be either +½ or −½ (no other values).

🧪 Example checks

Set {3, 2, 1, +½}:

n = 3 (positive integer ✓)
ℓ = 2 (less than n ✓)
mℓ = 1 (between −2 and +2 ✓)
ms = +½ (allowed ✓)
Result: Allowed.

Set {2, 2, 0, −½}:

n = 2 (positive integer ✓)
ℓ = 2 (not less than n; ℓ must be ≤ 1 when n = 2 ✗)
Result: Not allowed.

Set {3, −1, 0, +½}:

n = 3 (positive integer ✓)
ℓ = −1 (negative; ℓ cannot be negative ✗)
Result: Not allowed.

Set {4, 2, −2, 1}:

ms = 1 (not +½ or −½ ✗)
Result: Not allowed.

Common mistake: Forgetting that ℓ must be strictly less than n, or that ms has only two possible values.

Organization of Electrons in Atoms

🧭 Overview

🧠 One-sentence thesis

The Pauli exclusion principle limits how electrons can be arranged in atoms, leading to a predictable pattern of filling shells and subshells that can be represented by electron configurations.

📌 Key points (3–5)

Pauli exclusion principle: no two electrons in an atom can have the same set of four quantum numbers, which limits how many electrons fit in each subshell.
Filling order: electrons fill the lowest-energy shells and subshells first, though the order becomes complicated for larger atoms (e.g., 4s fills before 3d).
Electron configuration notation: a shorthand that lists shell–subshell labels with superscripts showing the number of electrons (e.g., 1s² 2s² 2p⁶).
Common confusion: the filling order is not always strictly by principal quantum number n—energy overlap means some subshells fill out of numerical order.
Three guiding principles: the aufbau principle (fill lowest energy first), the Pauli exclusion principle (max two electrons per orbital with opposite spins), and Hund's rule (spread electrons across degenerate orbitals before pairing).

🔒 The Pauli exclusion principle

🔒 What it states

Pauli exclusion principle: no two electrons in an atom can have the same set of four quantum numbers.

This is the fundamental rule that governs electron arrangement.
Each electron must differ in at least one quantum number from every other electron in the atom.

🧮 How it limits electrons per subshell

Because quantum numbers are restricted, only a certain number of electrons can occupy each subshell:
- s subshell: maximum 2 electrons
- p subshell: maximum 6 electrons
- d subshell: maximum 10 electrons
- f subshell: maximum 14 electrons
Example: Helium has two electrons, both in the 1s subshell with quantum number sets {1, 0, 0, +½} and {1, 0, 0, −½}—they differ only in spin.

🚫 What happens when a subshell is full

Once a subshell reaches its maximum, additional electrons must go to a different subshell or a higher-numbered shell.
Example: Lithium has three electrons—the first two fill 1s, so the third must go into the 2s subshell because the 1s is full and the n = 1 shell has no other subshells.

📝 Electron configuration notation

📝 How to write it

An electron configuration lists shell and subshell labels with a superscript showing the number of electrons.
Format: shell number + subshell letter + superscript count.
Shells and subshells are listed in order of filling.

🔢 Examples from the excerpt

Element	Number of electrons	Electron configuration
H	1	1s¹
He	2	1s²
Li	3	1s² 2s¹
Be	4	1s² 2s²
C	6	1s² 2s² 2p²
Na	11	1s² 2s² 2p⁶ 3s¹

✂️ Abbreviated electron configuration

Abbreviated electron configuration: uses a noble gas symbol in square brackets to represent the core electrons, then lists remaining electrons explicitly.

Noble gases are elements in the last column of the periodic table.
Example: Lithium can be written as [He] 2s¹ instead of 1s² 2s¹.
For tungsten (74 electrons): [Xe] 6s² 4f¹⁴ 5d⁴ is much shorter than listing all 74 electrons.
Don't confuse: the bracketed symbol represents all the electrons of that noble gas, not just one electron.

🔄 Filling order and energy levels

🔄 The aufbau principle

Aufbau principle (German for "building up"): electrons fill the lowest energy orbitals first.

Start with the lowest possible quantum numbers (lowest n, then lowest ℓ).
Energy increases with the principal quantum number n.
For multi-electron atoms, energy also increases with the angular momentum quantum number ℓ within the same shell.

⚡ Energy overlap in larger atoms

After the 3p subshell is filled, the 4s subshell actually has lower energy than the 3d subshell.
This means filling does not always follow strict numerical order by shell number.
Example: Potassium (K) has 19 electrons—after filling through 3p⁶, the next electron goes into 4s, not 3d.

🗺️ Following the filling order

The excerpt provides a diagram (Figure 8.08) with arrows showing the order: follow the arrows to determine which subshell fills next.
The pattern for most atoms:
- 1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d → 5p → 6s → 4f → 5d → 6p → 7s → 5f → 6d…
Don't confuse: higher shell number does not always mean higher energy—4s fills before 3d.

⚠️ Exceptions to the pattern

Some atoms do not follow the strict filling order.
Example: Silver (Ag) with 47 electrons is predicted to be [Kr] 5s² 4d⁹ but experiments show it is actually [Kr] 5s¹ 4d¹⁰.
An electron moves from a higher-numbered shell to a later-filled subshell to achieve lower overall energy.
You do not need to memorize exceptions, but recognize they exist.

🎯 Electron configuration energy diagrams

🎯 Three principles for filling diagrams

Aufbau principle: fill lowest energy orbitals first.
Pauli exclusion principle: maximum two electrons per orbital, with opposite spins.
Hund's rule: place one electron in each degenerate orbital before pairing them.

🔀 Hund's rule explained

Hund's rule: place one electron into each degenerate orbital first, before pairing them in the same orbital.

Degenerate orbitals: orbitals at the same energy level within a subshell (e.g., the three orbitals in a p subshell).
Spread electrons out across all available orbitals of the same energy before doubling up.
Example: Boron (5 electrons) fills 1s² 2s² 2p¹—the single 2p electron goes into one of the three 2p orbitals.
Example: Carbon (6 electrons) is 1s² 2s² 2p²—the two 2p electrons go into two different 2p orbitals, not paired in one.
Example: Nitrogen (7 electrons) is 1s² 2s² 2p³—each of the three 2p orbitals gets one electron.
Example: Oxygen (8 electrons) is 1s² 2s² 2p⁴—now one 2p orbital has a pair, the other two have one each.

📊 Energy diagram structure

Each line represents an orbital.
Lines at the same height represent a subshell of degenerate orbitals.
Electrons are shown as arrows: ↑ for spin +½, ↓ for spin −½.
Energy increases from bottom to top.

🔑 Key takeaways from the excerpt

🔑 Summary of main ideas

The Pauli exclusion principle limits the number of electrons in subshells and shells.
Electrons in larger atoms fill shells and subshells in a regular (though sometimes non-intuitive) pattern.
Electron configurations provide a shorthand for showing which subshells electrons occupy.
Abbreviated configurations using noble gas symbols simplify notation for larger atoms.
Exceptions to strict filling order occur due to energy considerations.
Energy diagrams follow the aufbau principle, Pauli exclusion principle, and Hund's rule.

Electronic Structure and the Periodic Table

🧭 Overview

🧠 One-sentence thesis

The periodic table's structure directly reflects how electrons fill subshells in atoms, allowing us to predict electron configurations from an element's position.

📌 Key points (3–5)

The periodic table mimics electron filling: the shape of the table follows the order in which subshells (s, p, d, f) are filled with electrons.
Blocks correspond to subshells: the table is divided into s-block (first two columns), p-block (right six columns), d-block (middle ten columns), and f-block (bottom detached section).
Valence electrons determine chemistry: elements in the same column have the same valence shell electron configuration and therefore similar chemical properties.
Common confusion: valence vs. core electrons—valence electrons are in the highest-numbered shell plus any unfilled subshells; core electrons are all the inner ones.
Practical use: you can determine an element's electron configuration solely from its position on the periodic table.

🗺️ How the periodic table reflects electron filling

🗺️ The table mimics subshell filling order

The shape of the periodic table mimics the filling of the subshells with electrons.

Each row and column position corresponds to which subshell is being filled.
The first row (H and He) represents the 1s subshell being filled (1s¹ and 1s²).
The second row starts with Li and Be filling the 2s subshell, then B through Ne filling the 2p subshell.
This pattern continues: 3s (Na, Mg), 3p (Al through Ar), 4s (K, Ca), 3d (Sc through Zn), and so on.

📦 Why the table has its distinctive shape

The number of columns in each section matches the number of electrons each subshell type can hold:
- s subshells hold 2 electrons → 2 columns on the left
- p subshells hold 6 electrons → 6 columns on the right
- d subshells hold 10 electrons → 10 columns in the middle
- f subshells hold 14 electrons → 14-column section at the bottom
The f-block is shown detached to keep the table from being too long and cumbersome, but it could be part of the main body.

🧱 Blocks of the periodic table

🧱 The four blocks and their locations

Block	Location	Subshell being filled	Number of columns
s-block	First two columns (left side)	s subshells	2
p-block	Right-most six columns	p subshells	6
d-block	Middle ten columns	d subshells	10
f-block	Bottom detached section	f subshells	14

🔍 Example: tracking selenium's position

Se (selenium) is in the fourth column of the p-block.
This means its electron configuration should end in p⁴.
Indeed, Se's configuration is [Ar]4s²3d¹⁰4p⁴, as expected.
How to use this: count across the block to determine how many electrons are in that subshell.

🎯 Valence electrons and chemical similarity

🎯 What valence electrons are

Valence electrons: the electrons in the highest-numbered shell, plus any electrons in the last unfilled subshell.

Valence shell: the highest-numbered shell.

Core electrons: the inner electrons (not in the valence shell).

Valence electrons largely control the chemistry of an atom.
Don't confuse: valence electrons are not all outer electrons—they are specifically those in the highest shell and any partially filled subshells.

🔗 Why elements in the same column behave similarly

Elements in the same column have the same valence shell electron configuration.
Example: H, Li, Na, K, Rb, and Cs (first column) all have a single s electron in their valence shell (s¹).
Result: similar valence configurations lead to similar chemical properties.
This is strictly true for s and p blocks; d and f blocks have some exceptions due to irregular filling order, but similarities still exist.

📋 Valence configuration patterns by column

First column (s-block): ns¹
Second column (s-block): ns²
First column of p-block: ns²np¹
Last column of p-block: ns²np⁶
These patterns repeat down each column, explaining why chemistry repeats periodically.

🧮 Predicting electron configurations from position

🧮 The method

Identify which block the element is in (s, p, d, or f).
Count the row to determine the principal quantum number (n).
Count across the block to determine how many electrons are in that subshell.
Build the configuration following the filling order.

💡 Examples from the excerpt

Calcium (Ca): located in the second column of the s-block → expect s² → configuration is [Ar]4s²
Tin (Sn): located in the second column of the p-block → expect p² → configuration is [Kr]5s²4d¹⁰5p²
Titanium (Ti): in the d-block → configuration is [Ar]4s²3d²
Chlorine (Cl): in the p-block → configuration is [Ne]3s²3p⁵

⚠️ Important note about d and f blocks

The excerpt mentions that d and f blocks have exceptions to the order of filling.
Similar valence shells are not absolute in these blocks.
However, many similarities still exist, so chemical similarity is still expected within columns.

Periodic Trends

🧭 Overview

🧠 One-sentence thesis

The periodic table's structure allows us to predict how atomic properties—effective nuclear charge, atomic radius, ionization energy, and electron affinity—change systematically across rows and down columns, making it a uniquely powerful tool for understanding elemental behavior.

📌 Key points (3–5)

What periodic trends are: qualitative patterns in atomic properties based on position on the periodic table; general trends with occasional exceptions.
Effective nuclear charge increases left to right: more protons pull valence electrons tighter across a row; slight increase down a column due to diffuse core electron screening.
Atomic radius trends: atoms get larger going down a column (higher principal quantum number) and smaller going left to right (stronger nuclear pull).
Ionization energy and electron affinity patterns: IE increases across and up; EA magnitude generally increases across; both relate to how tightly electrons are held.
Common confusion: successive ionization energies within one atom show huge jumps when removing an electron from a lower shell, not just from increasing positive charge.

⚛️ Effective nuclear charge

⚛️ What it measures

Effective nuclear charge (Z_eff): the net positive charge felt by valence electrons after accounting for screening by core electrons.

Valence electrons experience attraction from the nucleus but repulsion from inner electrons.
Always less than the actual nuclear charge (number of protons).
Approximated by: Z_eff = Z minus S, where Z is nuclear charge and S is the screening constant (roughly the number of core electrons).
Example: Magnesium (element 12) has electron configuration 1s² 2s² 2p⁶ 3s², so 10 core electrons; Z_eff ≈ 12 − 10 = 2.

📈 How Z_eff changes across and down

Left to right across a period: each element adds one proton and one valence electron, but core electrons stay the same → Z_eff increases.
Top to bottom down a column: same number of valence electrons, but higher principal quantum number means core clouds are more spread out and screen less effectively → Z_eff increases slightly.
Don't confuse: even though elements in the same column have the same valence count, Z_eff still rises slightly going down due to poorer screening.

📏 Atomic radius trends

📏 What atomic radius means

Atomic radius: an estimate of an atom's size, determined experimentally (e.g., X-ray crystallography).

Atoms don't have sharp boundaries, but they behave as if they have a definite radius.

🔽 Down a column: radius increases

Valence shell has a larger principal quantum number (n), so it lies physically farther from the nucleus.
Summarized: as you go down the periodic table, atomic radii increase.

➡️ Across a row: radius decreases

Principal quantum number stays the same, but nuclear charge increases.
Higher effective nuclear charge pulls valence electrons closer.
Summarized: as you go left to right, atomic radii decrease.

Direction	Trend	Reason
Down a column	Radius increases	Higher n, valence shell farther out
Across a row (left to right)	Radius decreases	More protons, tighter grip on electrons

Example: Si is larger than S (Si is to the left); Te is larger than S (Te is below).

⚡ Ionization energy

⚡ What ionization energy measures

Ionization energy (IE): the energy required to remove an electron from a gas-phase atom.

Written as: A(g) → A⁺(g) + e⁻
Always positive (endothermic); energy must be supplied.
Expressed in kJ/mol.

🔽 Down a column: IE decreases

Valence electron is farther from the nucleus, so easier to remove.

➡️ Across a row: IE increases

Electrons are drawn closer in by higher effective nuclear charge, so harder to remove.

🪜 Successive ionization energies

Removing a second, third, etc. electron requires progressively more energy because the ion becomes more positive.
Large jump when a new shell is reached: Example for Mg (1s² 2s² 2p⁶ 3s²):
- First IE removes a 3s electron.
- Second IE removes the other 3s electron (about twice the first).
- Third IE removes a 2p electron—over five times the second IE because it comes from a lower shell.
Don't confuse: the jump isn't just due to higher charge; it's due to breaking into a more stable, lower-energy shell.

🔋 Electron affinity

🔋 What electron affinity measures

Electron affinity (EA): the energy change when a gas-phase atom accepts an electron.

Written as: A(g) + e⁻ → A⁻(g)
Expressed in kJ/mol.
Magnitude indicates how strongly an atom attracts an additional electron.

➡️ Across a row: EA magnitude generally increases

Atoms farther to the right have higher effective nuclear charge, so they attract electrons more strongly.

🔽 Down a column: no definitive trend

EA sometimes increases, sometimes decreases; less predictable than other trends.

Property	Across (left to right)	Down (top to bottom)
Effective nuclear charge	Increases	Increases slightly
Atomic radius	Decreases	Increases
Ionization energy	Increases	Decreases
Electron affinity magnitude	Generally increases	No clear trend

Example: F has higher EA magnitude than C (F is farther right); Br has higher EA magnitude than As (Br is farther right).

🎯 Why periodic trends matter

🎯 Predictive power

The periodic table is the only scientific tool that lets us judge relative properties of a whole class of objects qualitatively.
Trends are general; occasional exceptions exist, but overall patterns hold across rows and columns.
Understanding trends helps predict chemical behavior without needing to memorize individual values for every element.

Lewis Electron Dot Diagrams

🧭 Overview

🧠 One-sentence thesis

Lewis electron dot diagrams provide a simple visual method to represent valence electrons around atomic symbols, enabling us to understand how atoms form chemical bonds by showing only the electrons that participate in bonding.

📌 Key points (3–5)

Purpose: Lewis diagrams use dots around element symbols to represent valence electrons, which are the electrons that interact to form chemical bonds.
Drawing convention: dots are placed around the symbol (right, left, above, below) with no more than two dots per side; the number of dots equals the number of valence electrons.
Periodic pattern: elements in the same column have similar dot diagrams because they share the same valence shell electron configuration.
Common confusion: for ions, the diagram shows the original valence shell (which may be empty for cations), not the new outermost shell after electron loss.
Cation formation: electrons are lost from the highest numbered shell first, not necessarily the last subshell that was filled.

🎯 What Lewis diagrams represent

🔬 Valence electrons only

A Lewis electron dot diagram (or electron dot diagram or a Lewis structure) is a representation of the valence electrons of an atom that uses dots around the symbol of the element.

The diagram shows only valence electrons, not all electrons in the atom.
Valence electrons are the ones in the outermost shell that participate in chemical bonding.
The number of dots directly equals the number of valence electrons.
Example: hydrogen has one valence electron, so its Lewis diagram shows one dot around H.

🎨 Drawing conventions

Dots are arranged to the right, left, above, and below the element symbol.
Maximum two dots per side — no side can have more than two dots.
The order of positions used does not matter (you can start on any side).
When an atom has paired electrons in the same subshell (like 2s²), those two dots are conventionally drawn together on the same side.
Atoms will never have more than eight dots around the symbol (following the periodic table pattern).

📐 Drawing diagrams for neutral atoms

⚛️ Simple examples (H through Ne)

Element	Valence config	Number of dots	Notes
Hydrogen	1s¹	1	Single dot on any side
Helium	1s²	2	Two dots together (paired)
Lithium	2s¹	1	Similar to hydrogen
Beryllium	2s²	2	Two dots together
Boron	2s²2p¹	3	Third dot goes on another side

🔄 Carbon through neon pattern

Carbon (2s²2p²): four valence electrons — two s electrons drawn together, two p electrons on different sides.
Nitrogen (2s²2p³): three p electrons get single dots on three remaining sides.
Oxygen (2s²2p⁴): four p electrons means starting to double up dots on one side.
Fluorine and neon: seven and eight dots respectively.
Convention: for p electrons, place single dots on different sides before pairing them up.

🔁 Periodic table pattern

After neon, the process starts over with sodium (one electron in the n=3 shell).
Elements in the same column have similar Lewis diagrams because they have the same valence shell electron configuration.
Example: all first-column elements (alkali metals) have one dot in their Lewis diagrams.

⚙️ Special cases (d and f electrons)

For atoms with partially filled d or f subshells, these electrons are typically omitted from Lewis diagrams.
Example: iron has valence configuration 4s²3d⁶, but its Lewis diagram shows only the two 4s electrons (two dots).
This simplification focuses on the electrons most likely to participate in typical chemical bonding.

⚡ Lewis diagrams for ions

➕ Cations (positive ions)

Cations have lost electrons compared to the neutral atom.
The diagram shows fewer dots than the neutral atom had.
Key convention: show the original valence shell, even if it's now empty.
Example: Na atom has one valence electron (one dot), but Na⁺ ion has lost that electron (no dots shown around Na⁺).
Don't confuse: even though Na⁺ technically has eight electrons in its n=2 shell now, we don't draw eight dots — we show the original n=3 shell, which is now empty.

🔋 Electron loss order

Electrons are lost from the highest numbered shell first, not necessarily the last subshell filled.
Example: Fe atom (4s²3d⁶) loses its two 4s electrons first to become Fe²⁺, not the 3d electrons, even though the 3d subshell was the last one being filled.
This is an important distinction between filling order and loss order.

➖ Anions (negative ions)

Anions have gained electrons compared to the neutral atom.
The diagram shows more dots than the neutral atom had.
Example: Cl atom versus Cl⁻ ion — the anion has one additional dot representing the extra electron.
The excerpt asks whether Cl⁻ should be larger or smaller than Cl based on electrical charges, highlighting that adding electrons affects ionic size.

Electron Transfer: Ionic Bonds

🧭 Overview

🧠 One-sentence thesis

Atoms transfer electrons to achieve stable eight-electron valence shells, and the resulting opposite charges attract to form ionic bonds.

📌 Key points (3–5)

The octet rule: atoms tend to gain or lose electrons to have eight electrons in their valence shell, which is energetically stable.
How ionic bonds form: electrons transfer from one atom to another, creating oppositely charged ions that attract each other.
Electron balance requirement: the number of electrons lost must equal the number of electrons gained when forming ionic compounds.
Common confusion: atoms don't always stop at one electron transfer—some need multiple atoms to satisfy the octet (e.g., two Na atoms for one O atom).
Bond strength factors: ionic bond strength depends on charge magnitude (larger = stronger) and ion size (smaller = stronger).

⚛️ The octet rule and stability

⚛️ What the octet rule means

The octet rule: the trend that atoms like to have eight electrons in their valence shell.

Having eight electrons in the valence shell is a particularly energetically stable arrangement.
This rule explains why atoms form the ions they do—they gain or lose electrons to reach this stable state.
The octet rule is "a very good rule of thumb" but not always satisfied in all compounds.

🔋 Why atoms stop at certain charges

Sodium (Na) has one valence electron and can lose it to form Na⁺, which then has a complete octet in its new valence shell (n = 2).
Forming Na²⁺ would require removing another electron, but that "requires much more energy than is normally available in chemical reactions."
Example: Na stops at 1+ charge because the Na⁺ ion already satisfies the octet rule.

🔄 How electron transfer creates ionic bonds

🔄 The transfer process

When a Na atom meets a Cl atom:

Na must lose one electron to obtain an octet.
Cl must gain one electron to gain an octet.
One electron transfers from Na to Cl, resulting in Na⁺ and Cl⁻ ions.
Both species now have complete octets and energetically stable electron shells.

⚡ What an ionic bond is

Ionic bond: the attraction between oppositely charged ions, caused by electrons transferring from one atom to another.

From basic physics: opposite charges attract.
This attraction is "one of the main types of chemical bonds in chemistry."
The final formula (e.g., NaCl) is written without listing charges explicitly, following ionic compound conventions.

🧮 Balancing electron transfer

🧮 The conservation requirement

In electron transfer, the number of electrons lost must equal the number of electrons gained.

This is required by the law of conservation of matter.
It explains why ionic compounds have specific ratios of cations to anions.

🔢 Examples of different ratios

Reaction	Electrons transferred	Resulting compound	Why this ratio
Na + Cl	1 electron: Na → Cl	NaCl	One Na loses 1e⁻, one Cl gains 1e⁻
Mg + O	2 electrons: Mg → O	MgO	One Mg loses 2e⁻, one O gains 2e⁻
Na + O	1 electron each from two Na → O	Na₂O	O needs 2e⁻, but each Na supplies only 1e⁻, so two Na atoms are needed
Ca + Cl	1 electron each: Ca → two Cl atoms	CaCl₂	Ca has 2e⁻ to lose, but each Cl needs only 1e⁻, so two Cl atoms are needed

🔍 Don't confuse: one-to-one vs. multiple atoms

Not all ionic compounds are 1:1 ratios.
When one atom needs more electrons than another can supply (or vice versa), multiple atoms participate.
Example: Na₂O requires two Na atoms because one O atom needs two electrons but each Na can donate only one.

💪 Ionic bond strength

💪 What determines lattice energy

Lattice energy: the measured strength of ionic bonding.

Two major characteristics affect strength:

Magnitude of charges: greater charge → stronger ionic bond.
Size of ions: smaller ion → stronger ionic bond (smaller size allows ions to get closer together).

📊 Lattice energy patterns

The excerpt provides a table showing:

LiF has lattice energy 1,036 kJ/mol.
MgO has lattice energy 3,791 kJ/mol (much higher).
MgO is stronger because Mg²⁺ and O²⁻ have higher charges (2+ and 2−) compared to Li⁺ and F⁻ (1+ and 1−).
Compounds with doubly charged ions (like MgF₂ at 2,957 kJ/mol) are stronger than singly charged ions (like NaCl at 786 kJ/mol).

Covalent Bonds

🧭 Overview

🧠 One-sentence thesis

Covalent bonds form when atoms share electrons to fill their valence shells, allowing atoms that cannot easily gain or lose electrons to still participate in stable compound formation.

📌 Key points (3–5)

What covalent bonding is: atoms share electrons rather than transfer them, creating a bond through shared electron pairs.
How to represent covalent bonds: Lewis electron dot diagrams show shared pairs (bonding pairs) and unshared pairs (lone pairs); a dash can represent a shared pair.
Single, double, and triple bonds: atoms can share one, two, or three pairs of electrons depending on what is needed to complete octets.
Common confusion: bonding electrons vs lone electrons—only the shared pairs make the bond; other electrons around an atom are lone pairs that don't participate in bonding.
Why it matters: covalent bonding explains how molecules like H₂, H₂O, and NH₃ form, and it applies to vitamins and many essential compounds.

🔗 What covalent bonds are and why they form

🔗 When covalent bonding happens

Ionic bonding occurs when one atom easily loses electrons and another easily gains them.
However, some atoms won't give up or gain electrons easily, yet they still form compounds.
The solution: atoms share electrons to fill their valence shells.

Covalent bond: a bond formed when electrons are shared between two atoms.

🎯 The octet rule and sharing

Atoms want a complete valence shell (eight electrons for most atoms, two for hydrogen).
Sharing allows each atom to "count" the shared electrons toward its own valence shell.
Example: Two hydrogen atoms each have one electron; by sharing, each can count two electrons (a filled 1s subshell).

🧩 Types of electrons in covalent molecules

🧩 Bonding electron pairs

Bonding electron pair: the pair of electrons that makes the covalent bond.

These are the shared electrons between two atoms.
A single shared pair is called a single bond.
Example: In H₂, the two electrons between the H atoms are the bonding pair.

🧩 Lone electron pairs

Lone electron pairs: pairs of electrons on an atom that do not participate in bonding.

These electrons belong to one atom only and are not shared.
Example: In F₂, each fluorine atom has one bonding pair (the shared pair) and three lone pairs (six electrons that are not shared).
Don't confuse: not all electrons around an atom are involved in bonding—only the shared pairs are bonding pairs.

📐 Drawing Lewis electron dot diagrams

📐 Steps for simple molecules

The excerpt provides a systematic method:

Count total valence electrons (add extra for negative charges, subtract for positive charges).
Write the central atom surrounded by surrounding atoms.
Put a pair of electrons between the central atom and each surrounding atom.
Complete the octets around surrounding atoms (except hydrogen, which needs only two).
Put remaining electrons, if any, around the central atom.
Check that every atom has a full valence shell.

📐 Identifying central and surrounding atoms

Central atom: the atom in the center of the molecule.
Surrounding atoms: the atoms making bonds to the central atom.

The central atom is usually written first in the formula (exception: H₂O).
Example: In NH₃, nitrogen is the central atom and the three hydrogen atoms are surrounding atoms.

📐 Example: BF₄⁻

Central atom: B; surrounding atoms: four F atoms; extra electron from the negative charge.
Total valence electrons: 3 (from B) + 7×4 (from F) + 1 (extra) = 32.
After placing pairs between B and each F, and completing octets around F atoms, all 32 electrons are used and every atom has a full valence shell.

🔗 Multiple bonds

🔗 When single bonds are not enough

Sometimes following the standard steps leaves the central atom with fewer than eight electrons.
Solution: atoms can share more than one pair of electrons.

🔗 Double bonds

Double bond: a bond in which two pairs of electrons are shared between two atoms.

Example: In formaldehyde (CH₂O), carbon and oxygen share two pairs of electrons to give carbon a complete octet.
Example: In CO₂, carbon forms a double bond with each oxygen atom, so carbon has eight electrons around it.

🔗 Triple bonds

Triple bond: a bond in which three pairs of electrons are shared between two atoms.

Example: Elemental nitrogen (N₂) has a triple bond—three pairs of electrons shared between the two nitrogen atoms.
Example: Acetylene (C₂H₂) has a triple bond between the two carbon atoms.
Note: Acetylene is an example of a molecule with two central atoms (both carbons).

🧪 Covalent bonding in compounds and ions

🧪 Building molecules with multiple atoms

More than two atoms can participate in covalent bonding, but any given covalent bond is between two atoms only.
Example: Water (H₂O) forms when an oxygen atom makes a covalent bond with each of two hydrogen atoms; oxygen ends up with a complete octet, and each hydrogen has two electrons.
Example: Ammonia (NH₃) forms when nitrogen (which has three unpaired electrons) shares electrons with three hydrogen atoms.

🧪 Polyatomic ions

Polyatomic ions are held together internally by covalent bonds.
However, because they carry a charge, they participate in ionic bonding with other ions.
This means both major types of bonding (covalent and ionic) can occur at the same time in a compound.

🍎 Real-world application: Vitamins and minerals

🍎 Vitamins

Vitamin: a nutrient that our bodies need in small amounts but cannot synthesize, so it must be obtained from the diet.

The word comes from "vital amine," though not all vitamins contain an amine group.
All vitamins are covalently bonded molecules.
Examples: vitamin A (retinol), vitamin C (ascorbic acid), vitamin E (tocopherol).
The B complex vitamins are a group of water-soluble vitamins that participate in cell metabolism.
Deficiency diseases (e.g., scurvy, rickets) can develop if a diet lacks a vitamin, but supplements can correct deficiencies.

🍎 Minerals

Mineral: any chemical element other than carbon, hydrogen, oxygen, or nitrogen that is needed by the body.

Minerals needed in quantity: sodium, potassium, magnesium, calcium, phosphorus, sulfur, chlorine.
Trace elements: minerals needed in tiny quantities (manganese, iron, cobalt, nickel, copper, zinc, molybdenum, selenium, iodine).
Most minerals are consumed in ionic form, not as elements or covalent molecules.
Like vitamins, minerals are available as supplements.

Nutrient type	Bonding type	Examples
Vitamins	Covalent molecules	Retinol (A), ascorbic acid (C), tocopherol (E), B complex
Minerals	Ionic form	Sodium, potassium, calcium, iron, iodine

Other Aspects of Covalent Bonds

🧭 Overview

🧠 One-sentence thesis

The polarity of covalent bonds—determined by electronegativity differences—affects molecular properties, and bond energies can be used to estimate the energy changes in chemical reactions.

📌 Key points (3–5)

Nonpolar vs polar covalent bonds: equal sharing of electrons creates nonpolar bonds; unequal sharing (due to different electronegativities) creates polar bonds.
Electronegativity scale: a unitless scale that measures how strongly atoms attract electrons; the difference between two atoms' electronegativities determines bond type.
Common confusion: not all covalent bonds between different elements are significantly polar—small electronegativity differences produce essentially nonpolar bonds, while very large differences produce ionic bonds.
Bond energy: the approximate amount of energy needed to break a covalent bond; breaking bonds requires energy (endothermic), while forming bonds releases energy (exothermic).
Why it matters: bond polarity influences melting point, boiling point, and solubility; bond energies allow estimation of reaction energy changes.

⚖️ Nonpolar vs polar covalent bonds

⚖️ Nonpolar covalent bonds

Nonpolar covalent bond: the equal sharing of electrons in a covalent bond.

Occurs when both atoms attract the bonding electrons by the same amount.
Example: H₂ molecule—both H atoms have one proton, so each nucleus attracts the electrons equally; the electron pair is equally shared.
No partial charges develop on either atom.

⚖️ Polar covalent bonds

Polar covalent bond: a covalent bond between different atoms that attract the shared electrons by different amounts and cause an imbalance of electron distribution.

Occurs when one atom attracts the bonding electrons more strongly than the other.
The more attractive atom takes on a partial negative charge (δ−); the other atom takes on a partial positive charge (δ+).
Example: HF molecule—the F atom has nine protons (nine times the attraction of H's one proton), so electrons remain closer to F; F becomes δ− and H becomes δ+.
Technically, any covalent bond between two different elements is polar, but the degree of polarity varies.

🔍 Representing polarity

Partial charge notation: δ− on the more electronegative atom, δ+ on the less electronegative atom.
Dipole arrow: shows the flow of electron density; the "+" end marks the electropositive area, and the arrowhead points toward the more electronegative atom.

🔢 Electronegativity and bond classification

🔢 What electronegativity measures

Electronegativity: a scale for judging how much atoms of any element attract electrons.

Unitless number; higher number = stronger attraction for electrons.
Used to determine the polarity of covalent bonds.

📊 Judging bond type by electronegativity difference

The difference between the electronegativities of two bonded atoms determines the bond type:

Electronegativity Difference	Bond Type
0	Nonpolar covalent
0–0.4	Slightly polar covalent
0.4–1.9	Definitely polar covalent
>1.9	Likely ionic

Example: C–H bond has a difference of 2.5 − 2.1 = 0.4, so it is slightly polar covalent.
Example: O–H bond has a difference of 3.5 − 2.1 = 1.4, so it is definitely polar covalent.
Don't confuse: a bond may be so slightly imbalanced that it is essentially nonpolar, or so polar that an electron actually transfers, forming a true ionic bond.

🌡️ How polarity affects properties

Polar molecules may have higher melting and boiling points than expected.
Polarity influences solubility in various substances (e.g., water or hexane).

💥 Bond energy and breaking/forming bonds

💥 What bond energy is

Bond energy: the approximate amount of energy needed to break a covalent bond.

The exact amount depends on the molecule, but the approximate amount is similar if the atoms in the bond are the same.
Bond energies are average values; exact values vary slightly among molecules but should be close to the listed values.

💥 Breaking bonds (endothermic)

Covalent bonds always require energy to be broken.
Bond breaking is always an endothermic process (ΔH is positive).
Example: breaking a bond absorbs energy from the surroundings.

💥 Forming bonds (exothermic)

When making a covalent bond, energy is always given off.
Bond making is always an exothermic process (ΔH is negative).
Example: forming a bond releases energy to the surroundings.

📈 Trends in bond energies

From the bond energy table, several trends are clear:

Multiple bonds are stronger: for the same two elements, a double bond is stronger than a single bond, and a triple bond is stronger than a double bond.
Energy increases are not exact multiples:
- For carbon-carbon bonds, energy increases somewhat less than double or triple the C–C single bond energy.
- For nitrogen-nitrogen bonds, energy increases at a rate greater than the multiple of the N–N single bond energy.
Example: C–C single bond = 348 kJ/mol, C=C double bond = 611 kJ/mol (not exactly double), C≡C triple bond = 837 kJ/mol (not exactly triple).

🧮 Estimating reaction energy changes

🧮 Using bond energies to estimate ΔH

Bond energies can be used to estimate the energy change of a chemical reaction by combining:

Energy required to break bonds (endothermic, positive).
Energy released when forming bonds (exothermic, negative).

🧮 Step-by-step process

Example: 2H₂ + O₂ → 2H₂O

Identify bonds broken: two H–H bonds and one O=O double bond.
Calculate energy for breaking: 2(436 kJ/mol) + 498 kJ/mol = +1,370 kJ/mol.
Identify bonds formed: four O–H single bonds.
Calculate energy for forming: 4(−463 kJ/mol) = −1,852 kJ/mol.
Combine: +1,370 + (−1,852) = −482 kJ/mol.

The actual ΔH is −572 kJ/mol; the estimate is off by about 16%, which is reasonable because bond energies are averages, not exact values.

🧮 Why estimates differ from actual values

Bond energies are average values across many molecules.
The exact bond energy varies slightly depending on the molecular environment.
A 16% difference is considered reasonable for estimation purposes.

Violations of the Octet Rule

🧭 Overview

🧠 One-sentence thesis

The octet rule, while useful, has three well-known types of violations—odd-electron molecules, electron-deficient molecules, and expanded valence shell molecules—that are stable despite not having eight electrons around every atom.

📌 Key points (3–5)

The octet rule has exceptions: some stable compounds violate the rule but are still chemically valid.
Three violation types: odd-electron molecules (odd total electrons), electron-deficient molecules (fewer than eight electrons), and expanded valence shell molecules (more than eight electrons).
Location matters: expanded valence shell molecules only form with central atoms in the third row or beyond of the periodic table.
Common confusion: violations don't mean the octet rule is useless—it's still a valuable guideline with known exceptions.
Reactivity note: odd-electron molecules tend to be very chemically reactive even though they are stable.

🔢 Odd-electron molecules

🔢 What they are

Odd-electron molecules: stable compounds with an odd number of electrons in their valence shells.

With an odd total number of electrons, at least one atom must violate the octet rule (you can't distribute an odd number evenly to give every atom eight).
These molecules are stable but typically very chemically reactive.

🧪 Examples from the excerpt

NO, NO₂, and ClO₂ are stable odd-electron compounds.
In NO: the oxygen atom has an octet, but the nitrogen atom has only seven electrons in its valence shell.
Example: ClO has 6 + 7 = 13 valence electrons total, making it impossible for both atoms to have eight electrons each.

⚗️ Electron-deficient molecules

⚗️ What they are

Electron-deficient molecules: stable compounds with less than eight electrons around an atom in the molecule.

These compounds have fewer than eight electrons around at least one atom, yet remain stable.
The excerpt emphasizes that this is the second type of violation.

🧲 Common examples

The most common examples involve beryllium and boron covalent compounds.
Beryllium: can form two covalent bonds, resulting in only four electrons in its valence shell.
Boron: commonly makes only three covalent bonds, resulting in only six valence electrons around the B atom.
Example: BF₃ has boron with six valence electrons instead of eight.

🌐 Expanded valence shell molecules

🌐 What they are

Expanded valence shell molecules: compounds with more than eight electrons assigned to their valence shell.

These molecules have a central atom surrounded by more than eight electrons.
The third violation type—having "too many" electrons rather than too few.

🗺️ Where they can form

Location requirement: only central atoms in the third row of the periodic table or beyond can form these molecules.
Why: these atoms have empty d orbitals in their valence shells that can participate in covalent bonding.
Atoms in the second row cannot form expanded valence shell molecules because they lack these d orbitals.

🧪 Examples from the excerpt

PF₅: the phosphorus atom makes five covalent bonds, giving it formally 10 electrons in its valence shell.
SF₆: the central sulfur atom makes six covalent bonds to six surrounding fluorine atoms.
XeF₂: the xenon atom has an expanded valence shell with more than eight electrons around it.

🎯 Why violations matter

🎯 The rule is still useful

The excerpt emphasizes that violations do not mean the octet rule is useless.
The octet rule remains important and useful in chemical bonding; these are simply known exceptions.
Don't confuse: "violations exist" does not equal "the rule is invalid"—as with many rules, there are exceptions.

⚡ Chemical behavior

Odd-electron molecules are noted as very chemically reactive, even though they are stable compounds.
The excerpt distinguishes between stability (the compound exists) and reactivity (how readily it undergoes chemical reactions).

Molecular Shapes and Polarity

🧭 Overview

🧠 One-sentence thesis

The shape of a molecule can be predicted from the number of electron groups around its central atom using VSEPR theory, and the overall polarity depends on both individual bond dipoles and the three-dimensional arrangement of atoms.

📌 Key points (3–5)

VSEPR principle: electron pairs repel each other and arrange themselves as far apart as possible to minimize repulsion.
Electron group vs molecular geometry: electron group geometry describes how all electron pairs (bonding and nonbonding) are arranged; molecular geometry describes how the atoms themselves are positioned.
Multiple bonds count as one group: a double or triple bond is treated as a single electron group when predicting shape.
Common confusion: a molecule can have polar bonds but still be nonpolar overall if the bond dipoles cancel out due to symmetry.
Polarity from vectors: molecular polarity is the vector sum of all individual bond dipoles, not just their presence.

🔬 VSEPR Theory and Electron Groups

🔬 What VSEPR means

Valence shell electron pair repulsion (VSEPR): the principle that electron pairs, being negatively charged, repel each other to get as far away from each other as possible.

This repulsion determines the three-dimensional arrangement of electron groups around a central atom.
The excerpt emphasizes that VSEPR applies to small molecules with a single central atom.

🧩 Two types of electron groups

Electron groups: any type of bond (single, double, or triple) and lone electron pairs.

When counting electron groups, remember that a multiple bond (double or triple) counts as only one electron group.
Example: a molecule with one double bond and two single bonds has three electron groups total, not four.

🔍 Electron group geometry vs molecular geometry

Electron group geometry: how electron groups (bonding and nonbonding electron pairs) are arranged.

Molecular geometry: how the atoms in a molecule are arranged.

The two geometries are related but not always identical.
The actual shape of the molecule is dictated by the positions of the atoms, not the electron pairs.
Example: GeF₂ has a trigonal planar electron group geometry (three electron groups) but a bent molecular geometry (only two atoms bonded).

📐 Common Molecular Shapes

📐 Two electron groups: linear

When there are two electron groups around the central atom, they orient 180° apart.
The molecular shape is linear.
Example: BeH₂ and CO₂ both have linear shapes.

🔺 Three electron groups: trigonal planar or bent

Three electron groups orient themselves 120° apart in a plane, forming an equilateral triangle.
If all three groups are bonded to atoms, the shape is trigonal planar (e.g., BF₃).
If only two groups are bonded to atoms, the shape is bent or angular (e.g., GeF₂).
Don't confuse: the electron group geometry is still trigonal planar, but the molecular geometry is bent when one group is a lone pair.

🧊 Four electron groups: tetrahedral, trigonal pyramidal, or bent

Four electron groups orient themselves in the shape of a tetrahedron.
If all four groups are bonded to atoms, the molecular shape is tetrahedral (e.g., CH₄).
If three groups are bonded to atoms, the shape is trigonal pyramidal (e.g., NH₃).
If two groups are bonded to atoms, the shape is bent (e.g., H₂O).
If only one group is bonded to another atom, the molecule is linear (only two atoms total).

🎨 Drawing conventions

The excerpt describes a standard convention for displaying three-dimensional molecules on paper:
- Straight lines: bonds in the plane of the page.
- Solid wedged line: bond coming out of the plane toward the reader.
- Dashed wedged line: bond going away from the reader into the plane.

🔢 Summary table

Number of Electron Groups	Number of Surrounding Atoms	Molecular Shape
any	1	linear
2	2	linear
3	3	trigonal planar
3	2	bent
4	4	tetrahedral
4	3	trigonal pyramidal
4	2	bent

⚡ Molecular Polarity and Dipole Vectors

⚡ What determines molecular polarity

Molecular polarity: determined from both the polarity of the individual bonds and the shape of the molecule.

Each bond's dipole moment can be treated as a vector quantity, having both magnitude and direction.
The overall molecular polarity is the vector sum of all individual bond dipoles.
This means you cannot determine polarity just by knowing whether bonds are polar; you must also consider how they are arranged in space.

🧭 Tail-to-head method for vector sum

The excerpt describes a step-by-step method to find the net molecular dipole:

Draw the Lewis electron dot diagram and determine the molecular shape.
Draw dipole arrows for all polar covalent bonds, starting at the more electropositive atom and ending at the more electronegative atom.
Connect the dipole arrows tail-to-head (the tail of one arrow to the head of the next).
Draw a new line connecting the tail of the first vector to the head of the last vector—this is the net molecular dipole.
Superimpose the net molecular dipole arrow onto the molecule.

Example: For water (H₂O), the bent shape means the two H–O bond dipoles do not cancel; they add up to a net dipole pointing from the hydrogen side toward the oxygen.

📊 Vector component method (alternative)

The excerpt also describes an alternative approach:

Draw the Lewis diagram and determine the molecular shape.
Draw dipole arrows for all polar bonds.
Separate angled dipole arrows into horizontal and vertical vector components.
Superimpose the vector components onto the molecule.
Cancel out any vector components that are equal in magnitude and pointing in opposite directions.
The remaining vector components show the net molecular dipole.

This method is useful when dipole arrows are at angles, making it easier to see which components cancel.

❌ Polar bonds but nonpolar molecule

Some molecules contain polar bonds yet have no net molecular dipole moment.
This happens when the bond dipoles are symmetrically arranged and cancel each other out.
Example: CO₂ is linear with two C=O bonds; the dipoles point in opposite directions (180° apart) and cancel, so CO₂ is nonpolar overall.
Don't confuse: the presence of polar bonds does not guarantee a polar molecule; shape matters.

Valence Bond Theory and Hybrid Orbitals

Valence Bond Theory and Hybrid Orbitals Jessie A. Key

🧭 Overview

🧠 One-sentence thesis

Valence bond theory explains covalent bonding through the overlapping of atomic orbitals, and hybridization allows atoms like carbon to mix their orbitals mathematically to form the correct number and geometry of bonds observed in real molecules.

📌 Key points (3–5)

Core mechanism: Covalent bonds form when valence atomic orbitals overlap, creating electron pair density between nuclei that holds atoms together.
Two bond types: Sigma bonds (σ) result from head-on orbital overlap with cylindrical symmetry; pi bonds (π) result from sideways overlap of p orbitals.
Hybridization solves a problem: Carbon's unhybridized orbitals cannot explain molecules like methane (CH₄), so mathematical mixing of s and p orbitals creates hybrid orbitals with the right number and geometry.
Common confusion: The number of atomic orbitals mixed always equals the number of hybrid orbitals produced (e.g., one s + three p → four sp³ hybrids).
Geometry follows hybridization: sp³ gives tetrahedral (109.5°), sp² gives trigonal planar (120°), and sp gives linear (180°) arrangements.

🔬 How valence bond theory works

🔬 Orbital overlap creates bonds

Valence bond theory: atoms in a covalent bond share electron density through the overlapping of their valence atomic orbitals.

Electrons are not in fixed positions; they exist as probability distributions called atomic orbitals.
When two atoms approach, their orbitals can overlap, creating a region of electron pair density between the nuclei.
Both nuclei attract this shared electron pair simultaneously, holding the atoms together.
Example: Two hydrogen atoms form H₂ when their 1s orbitals overlap at an optimal distance of 74 pm, balancing attractive and repulsive forces.

🔗 Sigma vs pi bonds

Bond Type	How It Forms	Electron Density Location	Example
Sigma (σ)	Head-on overlap of orbitals	Along the internuclear axis (cylindrical symmetry)	H-H bond in H₂; any single bond
Pi (π)	Sideways overlap of p orbitals	On opposite sides of the internuclear axis	Second/third bonds in double/triple bonds

In molecules with double or triple bonds, one bond is always sigma and the rest are pi.
Don't confuse: A double bond = 1 σ + 1 π; a triple bond = 1 σ + 2 π.

🧬 Why hybridization is needed

❓ The methane problem

Carbon's electron configuration (1s² 2s² 2p²) shows only two unpaired electrons in the 2p orbitals.
Yet methane (CH₄) has four equivalent C-H bonds.
Unhybridized carbon orbitals cannot explain this bonding pattern.

🎯 Linus Pauling's solution (1931)

Hybridization: mathematical mixing of atomic orbitals to produce hybrid orbitals.

The 2s and 2p orbitals are averaged mathematically to create new hybrid orbitals.
Key rule: The number of atomic orbitals hybridized equals the number of hybrid orbitals generated.
These hybrid orbitals are "degenerate" (equal in energy) and arrange in space according to VSEPR theory.

🔀 Three main hybridization types

🔀 sp³ hybridization (tetrahedral)

What mixes: One 2s + three 2p orbitals → four sp³ hybrid orbitals.
Geometry: Tetrahedral with 109.5° bond angles.
Orbital shape: Unsymmetrical propeller shape with one larger lobe (used for bonding) and one smaller lobe.
Example: Carbon in methane (CH₄) uses four sp³ orbitals to form four equivalent C-H sigma bonds.
All four orbitals arrange as far apart as possible following VSEPR.

🔺 sp² hybridization (trigonal planar)

What mixes: One 2s + two 2p orbitals → three sp² hybrid orbitals.
What's left: One unhybridized 2p orbital remains.
Geometry: Trigonal planar with 120° bond angles.
Example: Carbon in ethene (C₂H₄) uses three sp² orbitals for sigma bonds (two C-H and one C-C).
The unhybridized 2p orbital on each carbon forms the pi bond of the C=C double bond.
Don't confuse: The double bond uses both hybridized (for σ) and unhybridized (for π) orbitals.

➖ sp hybridization (linear)

What mixes: One 2s + one 2p orbital → two sp hybrid orbitals.
What's left: Two unhybridized 2p orbitals remain.
Geometry: Linear with 180° bond angle.
Example: Carbon in ethyne (C₂H₂) uses two sp orbitals for sigma bonds (one C-H and one C-C).
The two remaining unhybridized 2p orbitals on each carbon form the two pi bonds of the C≡C triple bond.

📐 Summary table of hybridizations

Hybridization	Orbitals Mixed	Hybrid Orbitals Formed	Geometry	Bond Angle	Unhybridized p Orbitals	Example
sp³	1s + 3p	4 sp³	Tetrahedral	109.5°	0	CH₄
sp²	1s + 2p	3 sp²	Trigonal planar	120°	1	C₂H₄
sp	1s + 1p	2 sp	Linear	180°	2	C₂H₂

The excerpt notes that other hybridizations are possible for explaining bonding in most real molecules.
The geometry follows VSEPR: hybrid orbitals arrange to minimize repulsion.

Molecular Orbitals

Molecular Orbitals Jessie A. Key

🧭 Overview

🧠 One-sentence thesis

Molecular orbital theory explains bonding by combining atomic orbitals mathematically to form new molecular orbitals that are delocalized over the entire molecule, allowing us to predict bond strength and molecular stability through bond order calculations.

📌 Key points (3–5)

What MO theory does: generates new molecular orbitals by mathematically combining atomic orbitals (LCAO method), creating bonding and antibonding orbitals.
Bonding vs antibonding orbitals: bonding orbitals concentrate electron density between nuclei (lower energy, stabilizing); antibonding orbitals have a node between nuclei (higher energy, destabilizing).
Bond order calculation: measures bond strength by comparing bonding and antibonding electrons; whole numbers correspond to single/double bonds, zero means no bond.
Common confusion: atomic orbitals are localized to one atom, but molecular orbitals are delocalized over the entire molecule.
Frontier orbitals (HOMO/LUMO): the highest occupied and lowest unoccupied molecular orbitals are key to understanding molecular spectroscopy and chemical reactivity.

🔬 Core MO theory concepts

🔬 What molecular orbital theory adds

Valence bond theory cannot explain all bonding patterns, so MO theory complements it.
MO theory uses a mathematical process called linear combination of atomic orbitals (LCAO) to generate new molecular orbitals.
Key difference from atomic orbitals: molecular orbitals represent electron density spread out over more than one atom (delocalized), not confined to a single atom.

📋 Filling molecular orbitals

Molecular orbitals follow similar rules to atomic orbitals:

Aufbau principle: fill from lowest to highest energy.
Pauli exclusion principle: maximum two electrons of opposite spin per orbital.
The number of molecular orbitals generated equals the number of atomic orbitals combined.
Combined atomic orbitals should have similar energy levels.

⚛️ Bonding and antibonding orbitals

⚛️ Bonding molecular orbitals

Bonding molecular orbital: formed by constructive combination where atomic orbital wave functions reinforce (add to) each other, resulting in lower energy.

Electron density concentrates between the two nuclei.
Electrons are stabilized by attractions to both nuclei.
These electrons hold atoms together with a covalent bond.
Example: In hydrogen molecule (H₂), the sigma 1s orbital is the bonding orbital.

💥 Antibonding molecular orbitals

Antibonding molecular orbital: formed by destructive combination where wave functions cancel each other, resulting in higher energy (denoted by asterisk *).

Creates a nodal plane (node): an area of zero electron density between the two nuclei.
This node is destabilizing toward the bond.
Example: In H₂, the sigma star 1s orbital is the antibonding orbital.
Don't confuse: antibonding orbitals are not "bad"—they're just higher energy and destabilize bonds when filled.

🔢 Bond order and stability

🔢 Calculating bond order

Bond order: a measure used to evaluate the strength of a covalent bond.

The formula uses the number of electrons in bonding versus antibonding orbitals.

Interpretation of bond order values:

Bond Order	Meaning	Example
1	Single bond	H₂, Li₂
2	Double bond	O₂
0	No bond; atoms exist separately	He₂ (unstable)
Fractions	Partial bond character	Between single and double

🧪 Example: Hydrogen molecule

H₂ has two electrons in the bonding sigma 1s orbital.
Zero electrons in the antibonding sigma star 1s orbital.
Bond order = 1, meaning a single bond.
The bonding orbital is lower in energy than the original atomic orbitals, explaining why H₂ molecules are more stable than separate hydrogen atoms.

🧪 Example: Dilithium (Li₂)

Both 1s orbitals combine to form bonding and antibonding orbitals (both filled).
The 2s orbitals also combine, creating bonding and antibonding orbitals.
Valence electrons fill from bottom up.
Bond order = 1 (single bond).
Important: atomic orbitals of similar energy combine; 1s does not combine with 2s.

🌐 Molecular orbitals from p atomic orbitals

🌐 Two types of p orbital overlap

Head-to-head overlap:

Results in sigma (σ) bonding and antibonding molecular orbitals.
Electron density centered along the internuclear axis.
Greater overlap makes the bonding orbital most stable (lowest energy) and antibonding least stable (highest energy).

Sideways overlap:

Results in pi (π) molecular orbitals.
Electron density on opposite sides of the internuclear axis.
Generates four π molecular orbitals: two lower-energy degenerate bonding orbitals and two higher-energy antibonding orbitals.

🔄 Energy ordering variations

For O₂, F₂, and Ne₂: sigma 2p orbitals are lower in energy than pi 2p orbitals.
For B₂, C₂, and N₂: interactions between 2s and 2p atomic orbitals swap the ordering—pi 2p orbitals become lower in energy than sigma 2p.
This difference is important for correctly predicting electron configurations and bond orders.

🔀 Heteronuclear diatomic molecules

When two different atoms bond, their atomic orbital energy levels may differ.
The same molecular orbital diagram framework can still estimate electron configuration and bond order.

🎯 Frontier molecular orbitals

🎯 HOMO and LUMO definitions

Highest Occupied Molecular Orbital (HOMO): the molecular orbital with the highest energy that contains electrons.

Lowest Unoccupied Molecular Orbital (LUMO): the lowest energy molecular orbital that does not contain electrons.

Together called frontier molecular orbitals.

🔬 Why frontier orbitals matter

In spectroscopy:

When molecules absorb energy, a HOMO electron typically transitions to the LUMO excited-state orbital.
This transition can be observed in ultraviolet-visible (UV-Vis) spectroscopy experiments.

In chemical reactions:

One reactant molecule may donate HOMO electrons to the LUMO of another reactant.
A new bonding molecular orbital forms by combining reactant HOMO and LUMO.
Understanding frontier orbital energy levels provides insight into molecular reactivity.

Example: Frontier orbitals help chemists predict which molecules will react and how they will interact.

Properties of Liquids

🧭 Overview

🧠 One-sentence thesis

Liquids exhibit characteristic behaviors including evaporation at temperatures below boiling, surface tension, and capillary action, which distinguish them from gases and solids.

📌 Key points (3–5)

Evaporation mechanism: liquid particles with enough energy at the surface can enter the gas phase even below the boiling point.
Vapor vs gas terminology: material in the gas phase below boiling point is called "vapor," while "gas" is reserved for other conditions.
General liquid properties: liquids fill containers from bottom to top, have high density, and low compressibility compared to gases.
Common confusion: glass appears to flow but is actually a solid—liquids flow under small forces and don't return to original shape, while solids (including glass) do return to their original shape when force is removed.
Surface phenomena: the excerpt introduces surface tension and capillary action as properties all liquids share.

🌡️ Phase characteristics and liquid behavior

🌡️ How liquids differ from gases and solids

Phase	Shape	Density	Compressibility
Gas	Fills entire container	Low	High
Liquid	Fills container from bottom to top	High	Low
Solid	Rigid	High	Low

Liquids have high density like solids but flow to fill containers from the bottom up.
Unlike gases, liquids are not easily compressed.
This combination of properties makes liquids distinct from both other phases.

🧊 The glass misconception: solid vs liquid

Urban legend claim: glass is an extremely thick liquid that flows over time (supposedly evidenced by old windows being thicker at bottom).
Why it's wrong:
- Old windows had variable thickness due to manufacturing standards, not flow.
- Thicker parts were intentionally placed at bottom for structural support.
- Key distinction: liquids flow when small force is applied, even if slowly; solids may deform but return to original shape when force is removed.
Evidence glass is solid: telescope lenses still focus light decades after manufacture—wouldn't work if the material flowed.
Don't confuse: deformation under force (which solids can do temporarily) with actual flow (which only liquids do).

💨 Evaporation and vapor formation

💨 What evaporation is

Evaporation: the formation of a gas from a liquid at temperatures below the boiling point.

Not all liquid particles have the same energy—some have enough energy to escape into the gas phase.
Only particles at the surface of the liquid can evaporate (they need to be at the boundary to escape).
This happens even when the liquid is not boiling.

🌫️ Vapor vs gas terminology

Vapor: the term used for material in the gas phase when it comes from a liquid below its boiling point.
Gas: this term is reserved for other conditions (the excerpt indicates the definition continues beyond what is provided).
Example: water evaporating from a puddle at room temperature produces water vapor, not water gas.
The distinction is temperature-dependent: below boiling point → vapor; at or above certain conditions → gas.

🫧 Surface properties of liquids

🫧 Universal liquid properties

The excerpt states that "all liquids have" certain properties, using water as the most familiar example.
Two key surface phenomena mentioned:
- Surface tension: a property all liquids share (origin to be explained).
- Capillary action: another universal liquid property (origin to be explained).
These properties arise from the behavior of liquid particles, particularly those at the surface versus those in the bulk liquid.

⚡ Energy and particle behavior

Liquid particles have varying amounts of energy.
A "certain portion" of particles have enough energy to enter the gas phase.
The surface location is critical—only surface particles can actually evaporate because they are at the liquid-air boundary.
This energy distribution explains why evaporation occurs continuously at temperatures below boiling.

Solids

🧭 Overview

🧠 One-sentence thesis

Solids maintain their shape and can be classified into amorphous or crystalline types, with crystalline solids further divided into ionic, molecular, covalent network, and metallic categories based on their bonding and resulting properties.

📌 Key points (3–5)

Two main categories: Solids are either amorphous (no long-term structure) or crystalline (regular, repeating 3D structure).
Four types of crystalline solids: Ionic, molecular, covalent network, and metallic—each with distinct bonding and properties.
Shape and density: Unlike liquids and gases, solids maintain their shape, are not easily compressed, and have relatively high densities.
Common confusion: Not all solids have the same properties—melting points, hardness, conductivity, and appearance vary widely depending on the type of bonding.
Why bonding matters: The type of intermolecular or intramolecular forces determines physical properties like melting point, hardness, and electrical conductivity.

🧱 General properties of solids

🧱 What defines a solid

A solid is like a liquid in that particles are in contact with each other, but intermolecular forces are strong enough to hold the particles in place.

Solids maintain their shape—they do not fill containers like gases or adopt container shapes like liquids.
They cannot be easily compressed and have relatively high densities.
At low enough temperatures, all substances except helium become solids.
The temperature at which a substance becomes solid varies widely: hydrogen solidifies at 20 K (−253°C), while carbon requires over 3,900 K (3,600°C).

🎨 Variable properties across solids

Solids demonstrate a wide range of properties:

Property	Examples of variation
Malleability	Metals can be beaten into sheets; NaCl shatters when struck
Hardness	Sodium and potassium are soft; diamond is very hard
Appearance	Most metals are shiny and silvery; sulfur is yellow; ionic compounds have varied colors
Conductivity	Solid metals conduct electricity and heat; ionic solids do not (in solid state)
Transparency	Some solids are opaque; others are transparent
Solubility	Some dissolve in water; others do not

Don't confuse: The wide variation in properties is not random—it depends on the type of bonding and structure within the solid.

🔷 Amorphous vs. crystalline solids

🔷 Amorphous solids

An amorphous solid is a solid with no long-term structure or repetition.

Examples: glass and many plastics.
Composed of long chains of molecules with no order from one molecule to the next.
There is only one type of amorphous solid.

💎 Crystalline solids

A crystalline solid is a solid that has a regular, repeating three-dimensional structure.

Example: NaCl crystal has a regular 3D array of Na⁺ and Cl⁻ ions.
There are several different types of crystalline solids, classified by the identity of the units that compose the crystal.

⚡ Types of crystalline solids

⚡ Ionic solids

An ionic solid is a crystalline solid composed of ions (even if the ions are polyatomic).

Structure and bonding:

Ions alternate in three dimensions in a repeating pattern (e.g., Na⁺ and Cl⁻ in NaCl).
Held together by attraction of opposite charges—a very strong force.

Properties:

High melting points (e.g., NaCl melts at 801°C) due to strong ionic attractions.
Very brittle: displacement of about 1 × 10⁻¹⁰ m moves ions next to same-charge ions, causing repulsion and breakage.
Do not conduct electricity in solid state.
Do conduct electricity in liquid state and when dissolved in solvent.

Why these properties? The strong electrostatic attraction between opposite charges requires high energy to break, explaining high melting points. Brittleness results from the need to break very strong attractions and the repulsion that occurs when like charges align.

🧊 Molecular solids

A molecular solid is a crystalline solid whose components are covalently bonded molecules.

Structure and bonding:

Molecules line up in a regular pattern (like ionic crystals, but with molecules instead of ions).
Held together by intermolecular forces between molecules.

Properties:

Melt at lower temperatures than ionic solids.
Softer than ionic solids.
Example: ice—water molecules line up in a regular pattern with hydrogen bonding between molecules.

Why these properties? Intermolecular forces between molecules are typically less strong than ionic bonds, so less energy is needed to melt them.

Don't confuse: The covalent bonds within each molecule are strong, but the forces between molecules are weaker—it's the intermolecular forces that determine melting point and hardness.

🔗 Covalent network solids

Covalent network solids are composed of atoms covalently bonded together in a seemingly never-ending fashion.

Structure and bonding:

Each piece is essentially one huge molecule.
Covalent bonding extends throughout the entire crystal.
Examples: diamond (carbon) and silicon dioxide (SiO₂).

Properties:

Very hard (diamond is the hardest known substance).
High melting points (diamond: over 3,500°C; SiO₂: around 1,650°C).
Generally poor conductors of electricity.
Variable thermal conductivity: diamond is one of the most thermally conductive substances; SiO₂ is about 100 times less conductive.

Why these properties? The network of covalent bonds throughout the sample must all be broken to melt the solid or deform it, requiring enormous energy.

🪙 Metallic solids

A metallic solid is a solid with the characteristic properties of a metal: shiny and silvery in color and a good conductor of heat and electricity.

Structure and bonding:

Exhibits metallic bonding: sharing of s valence electrons by all atoms in the sample.
Can be hammered into sheets and pulled into wires.

Properties:

Good conductors of heat and electricity.
Shiny and silvery appearance.
Malleable and ductile.
Metals easily lose valence electrons, explaining why metallic elements usually form cations.

Why these properties? The sharing of valence electrons throughout the sample explains conductivity. The mobile electrons allow atoms to slide past each other without breaking bonds, explaining malleability.

📊 Comparison of crystalline solid types

Type	Bonding	Melting point	Hardness	Conductivity (solid)	Example
Ionic	Electrostatic attraction between ions	High	Brittle	No (yes when liquid/dissolved)	NaCl
Molecular	Intermolecular forces	Low	Soft	No	Ice (H₂O)
Covalent network	Covalent bonds throughout	Very high	Very hard	Generally no	Diamond, SiO₂
Metallic	Metallic bonding (shared electrons)	Variable	Variable	Yes	Silver (Ag)

🔬 Identifying solid types

🔬 Prediction strategy

To predict the type of crystal:

Metal + nonmetal → ionic solid (e.g., MgO)
Pure metal → metallic solid (e.g., Ag)
Covalently bonded molecules → molecular solid (e.g., CO₂, I₂)
Polyatomic ions → ionic solid (e.g., Ca(NO₃)₂)
Extended covalent network → covalent network solid (e.g., diamond, SiO₂)

Example: CO₂ is a covalently bonded molecular compound, so in the solid state it forms molecular crystals (visible in dry ice).

Don't confuse: The type of bonding within a unit (covalent, ionic) versus the forces between units determines the solid type—CO₂ has covalent bonds within molecules but intermolecular forces between molecules.

Phase Transitions: Melting, Boiling, and Subliming

🧭 Overview

🧠 One-sentence thesis

Phase changes between solid, liquid, and gas states are isothermal processes that require specific amounts of energy without changing temperature, and these energy requirements can be calculated using enthalpy values.

📌 Key points (3–5)

What phase changes are: transitions between solid, liquid, and gas states that occur at characteristic temperatures and require energy input or release.
Isothermal nature: during a phase change, all energy goes into changing the phase (breaking or forming intermolecular forces), not into changing temperature—the substance stays at the same temperature until the transition is complete.
Energy direction: melting, boiling, and sublimation are endothermic (require energy input, positive ΔH); solidification, condensation, and deposition are exothermic (release energy, negative ΔH).
Common confusion: pressure affects boiling point significantly (so "normal boiling point" is defined at exactly 1 atm), but melting point is a characteristic value for pure substances.
Molecular picture: solids have particles stuck in place; liquids have particles in contact but mobile; gases have particles separated with mostly empty space.

🧊 Solid-liquid transitions

🔥 Melting (fusion)

Melting: the process of a solid becoming a liquid.

Occurs at a characteristic temperature called the melting point for any pure substance.
Requires energy input to overcome intermolecular forces holding particles in fixed positions.
The opposite process is solidification (liquid becoming solid), which releases the same amount of energy.

⚡ Enthalpy of fusion

Enthalpy of fusion (ΔH_fus): the amount of energy needed to change a substance from solid to liquid at its melting point, measured in kilojoules per mole.

Always tabulated as a positive number.
For melting (endothermic): ΔH is positive.
For solidification (exothermic): ΔH is negative (same magnitude, opposite sign).
Example: Water at 0°C has ΔH_fus = 6.01 kJ/mol.

🔬 Molecular changes during melting

In a solid: particles are stuck in place because intermolecular forces cannot be overcome by particle energy.
At melting point: particles gain enough energy to move around each other but not enough to separate completely.
In a liquid: particles remain in contact but can slide past one another, explaining why liquids take the shape of their container (under gravity).

💨 Liquid-gas transitions

🌡️ Boiling and condensation

Boiling (vaporization): the process of a liquid becoming a gas.

Condensation: the process of a gas becoming a liquid.

Unlike melting, boiling is noticeably affected by surrounding pressure because gases are strongly pressure-dependent.
Normal boiling point: the temperature at which a liquid changes to gas when surrounding pressure is exactly 1 atm (760 torr).
Unless specified otherwise, assume boiling point refers to 1 atm pressure.

⚡ Enthalpy of vaporization

Enthalpy of vaporization (ΔH_vap): the amount of energy required to convert a liquid to a gas at its normal boiling point, measured in kilojoules per mole.

Always tabulated as a positive number.
For boiling (endothermic): ΔH is positive.
For condensation (exothermic): ΔH is negative (same magnitude, opposite sign).
Example: Water at 100°C has ΔH_vap = 40.68 kJ/mol.

🔬 Molecular changes during boiling

In a liquid: particles are in contact and able to move around each other.
At boiling point: particles gain enough energy to completely separate from each other.
In a gas: particles go their own way in space, separated from one another.
Most of the gas volume is empty space—only about one one-thousandth of the volume is actually occupied by matter.
This explains why gases can be compressed and why they fill their containers.

❄️ Direct solid-gas transitions

🌫️ Sublimation and deposition

Sublimation: the solid phase transitioning directly to the gas phase without going through a liquid phase.

Deposition: the reverse process, a gas directly becoming a solid.

Sublimation is also isothermal, like other phase changes.
Has a measurable energy change called the enthalpy of sublimation (ΔH_sub).

🧮 Relationship between enthalpies

The enthalpy of sublimation equals the sum of fusion and vaporization enthalpies:

ΔH_sub = ΔH_fus + ΔH_vap

Because of this relationship, ΔH_sub is not always tabulated separately—it can be calculated from the other two values.

🧊 Common examples of sublimation

Dry ice (solid CO₂): sublimes at −77°C, bypassing the liquid phase entirely (hence "dry").
Ice cubes in freezers: slowly get smaller over time because solid water very slowly sublimes.
Freezer burn: occurs when foods like meat slowly lose solid water content through sublimation (the food is still safe but looks unappetizing).
Don't confuse: freezer burn is not an actual burn; it's water loss through sublimation.

🌡️ Energy and temperature behavior

🔄 Isothermal phase changes

Isothermal process: a process that occurs at constant temperature.

All phase changes are isothermal.
During a phase change, energy goes exclusively to changing the phase, not to changing temperature.
The substance stays at the same temperature throughout the entire phase transition.
Only after all of the substance has completed the phase change does additional energy go into changing temperature.

📊 Heating curves

Heating curve: a plot of temperature versus the amount of heat added, showing the relationship between phase changes and enthalpy.

Key features of a heating curve:

Sloped regions: temperature increases as heat is added (kinetic energy increases).
Flat (horizontal) regions: temperature remains constant during phase changes.
- At melting point: heat breaks intermolecular forces of the solid instead of increasing kinetic energy.
- At boiling point: heat breaks intermolecular forces of the liquid instead of increasing kinetic energy.
After each phase change completes, temperature rises again until the next phase change.

🧪 Chemical equations for phase changes

Phase changes can be represented by chemical equations using phase labels:

Example for melting ice: H₂O(s) → H₂O(ℓ)
No chemical change occurs, only a physical change.
Phase labels are crucial: (s) for solid, (ℓ) for liquid, (g) for gas.

🧮 Calculating energy changes

📐 Conversion steps

To calculate energy for a phase change:

Convert mass to moles using molar mass.
Multiply moles by the appropriate enthalpy value (ΔH_fus or ΔH_vap).
Determine sign: positive for endothermic (melting, boiling, sublimation), negative for exothermic (solidification, condensation, deposition).

📋 Example calculation pattern

For melting 45.7 g of H₂O at 0°C:

Convert grams to moles: 45.7 g ÷ 18.0 g/mol = 2.54 mol
Multiply by ΔH_fus: 2.54 mol × 6.01 kJ/mol = 15.3 kJ
Since melting is endothermic, the answer is positive: +15.3 kJ

For condensation (exothermic), the same calculation magnitude would have a negative sign.

Intermolecular Forces

🧭 Overview

🧠 One-sentence thesis

The phase a substance adopts depends on the balance between particle energy (mainly temperature) and the strength of intermolecular forces holding particles together.

📌 Key points (3–5)

What determines phase: the balance between particle energy and intermolecular forces—stronger forces favor liquid or solid; weaker forces and higher energy favor gas.
Three types of intermolecular forces: dispersion forces (present in all substances), dipole-dipole interactions (in polar molecules), and hydrogen bonding (strongest, in molecules with H bonded to N, O, or F).
Common confusion: hydrogen bonding vs ordinary dipole-dipole—hydrogen bonding requires a specific bond (H to N, O, or F) and is unusually strong, creating a distinct category.
How temperature affects phase: as temperature increases, substances progress from solid → liquid → gas because particle energy overcomes intermolecular forces.
Why size and polarity matter: larger molecules have stronger dispersion forces; polar molecules have stronger interactions than nonpolar ones of similar mass.

🔗 The three types of intermolecular forces

🌀 Dispersion forces (London dispersion forces)

Dispersion force: an interaction caused by the instantaneous position of an electron in a molecule, which temporarily makes part of the molecule negatively charged and the rest positively charged.

Present in all substances with electrons.
The interaction is fleeting: the electron moves, and the imbalance shifts constantly, but molecules can still attract each other through these temporary charges.
Strength increases with more electrons: larger molecules have stronger dispersion forces, which partially explains why smaller molecules are gases and larger ones are liquids or solids at the same temperature.
Mass also plays a role.

Example: Smaller molecules like helium are gases because they have few electrons and weak dispersion forces; larger molecules remain liquid or solid at the same temperature.

⚡ Dipole-dipole interactions

Dipole-dipole interactions: attractions between the oppositely charged ends of polar molecules, which have partial charges.

Only occur in polar molecules (molecules with a permanent dipole moment).
Generally stronger than dispersion forces if all other factors are equal.
The oppositely charged ends of polar molecules attract each other.

Example: CH₂Cl₂ (polar, molar mass 85 g/mol) has a boiling point of 313 K (40°C), significantly higher than CF₄ (nonpolar, molar mass 88 g/mol) with a boiling point of 145 K (−128°C), even though CF₄ has slightly higher mass.

Don't confuse: A molecule can have polar bonds but still be nonpolar overall if the bond dipoles cancel out (e.g., CF₄); only molecules with a net permanent dipole experience dipole-dipole interactions.

🔵 Hydrogen bonding

Hydrogen bonding: an unusually strong form of dipole-dipole interaction found in molecules with an H atom bonded to an N, O, or F atom.

Specific requirement: the H must be covalently bonded to N, O, or F.
These covalent bonds are very polar, and the dipole-dipole interaction between them is strong enough to create a new category of intermolecular force.
Strongest of the three types of intermolecular forces.

💧 Why water is unusual

Water (H₂O, molar mass only 18 g/mol) has relatively high melting and boiling points.
Boiling point of H₂O: 373 K (100°C).
Boiling point of H₂S (similar molecule): 233 K (−60°C).
H₂O experiences hydrogen bonding; H₂S does not.
The strong attraction between H₂O molecules requires additional energy to separate them in the condensed phase, raising the boiling point.

🧊 Other effects of hydrogen bonding in water

Solvent ability: hydrogen bonding helps water dissolve many substances.
High heat capacity: more energy needed to change temperature.
Expansion when freezing: molecules line up in a way that creates extra space between them, increasing volume in the solid state—this is why ice is less dense than liquid water.

Don't confuse: Not all molecules with H atoms experience hydrogen bonding—only those where H is bonded to N, O, or F. For example, H₂S has H atoms but does not experience hydrogen bonding because H is bonded to S, not N, O, or F.

🔄 How intermolecular forces determine phase

⚖️ The balance between energy and forces

If forces are strong enough: the substance is a liquid or (if even stronger) a solid.
If forces are weak and sufficient energy is present: particles separate, and the gas phase is preferred.
Temperature is the main variable: it determines particle energy, so it controls which phase is stable at any given point.

📈 Phase progression with increasing temperature

Temperature range	Preferred phase	Why
Low temperatures	Solid	Most substances are solid (only helium predicted to be liquid at absolute zero)
Moderate temperatures	Liquid	Substances with weak interactions become liquid as temperature increases
High temperatures	Gas	Particles have enough energy to overcome intermolecular forces and separate

Sublimation: substances with very weak intermolecular forces become gases directly from solid.
General progression: all substances go from solid → liquid → gas as temperature increases (assuming chemical bonds don't decompose from high temperature).

Don't confuse: The same substance can be in different phases at different temperatures; phase is not a fixed property but depends on the balance between energy and intermolecular forces.

🧪 Comparing intermolecular forces in practice

🔍 Identifying the strongest force

To identify the most significant intermolecular force in a substance:

Check for hydrogen bonding first: Is there an H atom bonded to N, O, or F? If yes, hydrogen bonding is the strongest force.
Check for polarity: Is the molecule polar (permanent dipole)? If yes and no hydrogen bonding, dipole-dipole interactions are strongest.
Default to dispersion forces: All substances have dispersion forces; if the molecule is nonpolar and has no hydrogen bonding, dispersion forces are the most significant.

Example comparisons from the excerpt:

C₃H₈: C–H bonds are only minimally polar → dispersion forces.
CH₃OH: H bonded to O → hydrogen bonding.
H₂S: Bent molecule with permanent dipole, but no H bonded to N/O/F → dipole-dipole interaction.
HF: H bonded to F → hydrogen bonding.
HCl: Polar molecule, but H bonded to Cl (not N/O/F) → dipole-dipole interactions.

📊 Why these distinctions matter

Boiling points: Stronger intermolecular forces → higher boiling point (more energy needed to separate molecules).
Phase at room temperature: Stronger forces → more likely to be liquid or solid.
Physical properties: Hydrogen bonding explains water's unusual properties (high boiling point, solvent ability, expansion when freezing).

Colligative Properties of Solutions

🧭 Overview

🧠 One-sentence thesis

Colligative properties depend only on the number of dissolved solute particles in a solution—not their chemical identity—and they predictably alter vapor pressure, boiling point, freezing point, and osmotic pressure in ways proportional to solute concentration.

📌 Key points (3–5)

What colligative properties are: solution properties that depend on the number of solute particles, not what those particles are.
Four main colligative properties: vapor pressure depression, boiling point elevation, freezing point depression, and osmotic pressure.
Concentration units matter: mole fraction is used for vapor pressure; molality for boiling/freezing point changes; molarity for osmotic pressure.
Common confusion: the calculations give the change in boiling or freezing point, not the final temperature—you must add or subtract from the pure solvent's value.
Real-world importance: antifreeze, IV fluids, road salt, and biological cell function all depend on colligative properties.

🔢 Mole fraction and concentration units

🔢 What mole fraction is

Mole fraction of component i (χᵢ): the number of moles of that component divided by the total number of moles in the sample.

Always a number between 0 and 1 (inclusive).
Has no units—it's just a ratio.
The sum of all mole fractions in a mixture equals 1.
Example: if a solution contains 0.137 mol of one substance and 0.576 mol of another, the total is 0.713 mol, so the mole fraction of the first is 0.137 ÷ 0.713 = 0.192.

📐 Why different concentration units

Mole fraction is used for vapor pressure calculations (Raoult's law).
Molality (moles of solute per kilogram of solvent) is used for boiling point elevation and freezing point depression.
Molarity (moles of solute per liter of solution) is used for osmotic pressure.
Don't confuse: each colligative property has its own preferred concentration unit because of how the property is defined.

💨 Vapor pressure depression

💨 How vapor pressure changes

Vapor pressure depression: solutions have a lower vapor pressure than the pure solvent, and the amount of lowering depends on the fraction of solute particles (assuming the solute is nonvolatile).

Raoult's law: P_soln = χ_solv × P*_solv
- P_soln = vapor pressure of the solution
- χ_solv = mole fraction of the solvent
- P*_solv = vapor pressure of the pure solvent at that temperature
The excerpt explains this by saying solute particles occupy positions at the surface where solvent particles would otherwise evaporate, so fewer solvent molecules can escape into the vapor phase.

🧪 Example scenario

Example: 12.0 g of naphthalene (C₁₀H₈) mixed with 45.0 g of benzene (C₆H₆). If pure benzene has a vapor pressure of 95.3 torr, the solution's vapor pressure drops to about 86.5 torr because the mole fraction of benzene is now less than 1.

🌡️ Boiling point elevation

🌡️ Why boiling points rise

Boiling point elevation: because a solution has lower vapor pressure than the pure solvent, it requires a higher temperature for the vapor pressure to reach 1.00 atm (the definition of normal boiling point).

The change in boiling point is calculated as: ΔTb = Kb × m
- ΔTb = change in boiling point (in °C)
- Kb = boiling point elevation constant (characteristic of the solvent)
- m = molality of the solution
Important: this equation gives the change, not the new boiling point. You must add ΔTb to the pure solvent's boiling point.

📊 Boiling point elevation constants

Solvent	Normal Boiling Point (°C)	Kb (°C/m)
Acetic acid (HC₂H₃O₂)	117.90	3.07
Benzene (C₆H₆)	80.10	2.53
Carbon tetrachloride (CCl₄)	76.8	4.95
Water (H₂O)	100.00	0.512

🧪 Example scenario

Example: a 2.50 m solution of dichlorobenzene in CCl₄. The change is ΔTb = 4.95 × 2.50 = 12.4°C. The new boiling point is 76.8 + 12.4 = 89.2°C.

❄️ Freezing point depression

❄️ Why freezing points drop

Freezing point depression: the freezing point of a solution is lower than that of the pure solvent because solute particles interfere with solvent particles coming together to form a solid.

The change in freezing point is calculated as: ΔTf = Kf × m
- ΔTf = change in freezing point (in °C)
- Kf = freezing point depression constant (characteristic of the solvent)
- m = molality of the solution
Important: this equation gives the change. You must subtract ΔTf from the pure solvent's freezing point because freezing points always go down.

📊 Freezing point depression constants

Solvent	Normal Freezing Point (°C)	Kf (°C/m)
Acetic acid (HC₂H₃O₂)	16.60	3.90
Benzene (C₆H₆)	5.51	4.90
Cyclohexane (C₆H₁₂)	6.4	20.2
Naphthalene (C₁₀H₈)	80.2	6.8
Water (H₂O)	0.00	1.86

🧊 Real-world applications

Antifreeze in car radiators uses solutions with lower freezing points so engines can operate below 0°C.
Road salt and other compounds lower the freezing point of water, preventing ice formation on sidewalks and roads for safety.
Example: a 1.77 m solution of CBr₄ in benzene has ΔTf = 4.90 × 1.77 = 8.67°C, so the new freezing point is 5.51 − 8.67 = −3.16°C.

🧬 Osmotic pressure

🧬 What osmosis is

Osmosis: the tendency for solvent molecules to move through a semipermeable membrane from a dilute solution to a concentrated solution until concentrations are equalized.

A semipermeable membrane allows certain small molecules (like water) to pass but not others (like large solute particles).
The excerpt describes a system where two solutions of different concentrations are separated by such a membrane; over time, solvent moves to the more concentrated side.
The pressure difference created by the different liquid column heights is the osmotic pressure (Π).

🧬 Calculating osmotic pressure

The equation is: Π = MRT
- Π = osmotic pressure (in atm)
- M = molarity of the solution
- R = ideal gas law constant (0.08206 L·atm/mol·K)
- T = absolute temperature (in kelvins)
This equation resembles the ideal gas law.
Example: a 0.333 M solution of glucose at 25°C (298 K) has Π = 0.333 × 0.08206 × 298 = 8.14 atm, equivalent to an 84 m tall column of water.

🩸 Biological importance

Cell walls are semipermeable membranes, so osmotic pressure is critical in biological systems.
IV fluids must have approximately the same osmotic pressure as blood serum (isotonic) to avoid damaging red blood cells.
- Hypotonic solution (lower concentration than blood): water enters cells, causing them to swell.
- Hypertonic solution (higher concentration than blood): water leaves cells, causing them to shrink and collapse.
Seawater has higher osmotic pressure than body fluids. Drinking it pulls water out of your cells, causing dehydration and cell death even though you're consuming liquid.
Osmotic pressure may also help transport water to the tops of tall trees (in addition to capillary action).

⚠️ Don't confuse

Osmotic pressure is not about phase changes—it's about solvent movement through a membrane.
The other three colligative properties (vapor pressure, boiling point, freezing point) all involve phase changes.

Concentrations as Conversion Factors

🧭 Overview

🧠 One-sentence thesis

Concentration units can be used as conversion factors in stoichiometry problems to relate amounts of solute, solution volume, and reactant quantities through balanced chemical equations.

📌 Key points (3–5)

Core skill: Concentration definitions (e.g., 0.887 M = 0.887 mol/L) can be rearranged and used as conversion factors in calculations.
Basic conversions: Use concentration to convert between moles of solute and volume of solution, then extend to mass using molar mass.
Stoichiometry integration: Combine concentration conversion factors with balanced chemical equations to relate volumes of different solutions.
Common confusion: Remember that concentration can be written as a reciprocal depending on what you're solving for—units must cancel correctly.
Real application: Titration experiments use these conversions to determine unknown concentrations by measuring volumes of reacting solutions.

🔄 Using concentration as a conversion factor

🔄 The basic principle

Concentration as a conversion factor: the definition of a concentration unit (e.g., molarity = mol/L) provides a ratio that relates amount of solute to volume of solution.

Instead of using concentration only as a definition to rearrange, treat it as a conversion factor between two different types of units.
The reciprocal of the concentration can also be used, depending on which units need to cancel.
Example: If a solution is 0.887 M NaCl, this means 0.887 mol/L, so to find moles in 0.108 L, multiply 0.108 L × (0.887 mol / 1 L) = moles of NaCl.

🔁 Writing the reciprocal

When converting from moles to volume, flip the concentration ratio.
Example: To find litres of 2.35 M CuSO₄ needed for 4.88 mol of CuSO₄, use 4.88 mol × (1 L / 2.35 mol) = litres.
Don't confuse: The concentration stays the same number; you're just choosing which form (mol/L or L/mol) makes the units cancel.

🧮 Multi-step conversions with concentration

🧮 From volume to mass of solute

First step: Use concentration to convert volume of solution to moles of solute.
Second step: Use molar mass to convert moles to grams.
Example: For 0.765 L of 1.93 M NaOH, first find moles: 0.765 L × (1.93 mol/L) = moles. Then convert to mass: moles × (40.0 g/mol) = grams of NaOH.

🔗 Combining with balanced equations

Start with moles (or mass converted to moles) of one reactant.
Use the balanced chemical equation to find moles of another reactant or product.
Then use concentration to find the volume of solution needed.
Example: If 1.25 mol of AgNO₃ reacts according to 2AgNO₃ + CaCl₂ → products, first find moles of CaCl₂ needed using the 2:1 ratio, then convert moles of CaCl₂ to litres using its concentration (0.555 M).

🧪 Starting from mass of a reactant

Convert mass to moles using molar mass.
Use the balanced equation to relate moles of one substance to another.
Use concentration to find volume of solution.
Example: Given 3.66 g of Ag reacting with Al(NO₃)₃, convert grams Ag to moles Ag, use the balanced equation (3Ag + Al(NO₃)₃ → products) to find moles of Al(NO₃)₃, then convert to litres using 0.0995 M.

🧪 Titration and solution-to-solution problems

🧪 What is titration

Titration: a precisely measured experiment in which one solution is carefully added to another reactant until the reaction is complete, used to determine the amount of a substance in a sample.

An aliquot is a precisely measured sample of solution.
A burette is a precisely measured tube used to deliver the titrant solution.
The student measures the volume of titrant needed to completely react with the analyte.

🧪 Relating two solutions

You can use concentration and volume of one solution to find concentration or volume of another solution through the balanced equation.
Steps:
1. Convert volume of known solution to moles using its concentration.
2. Use the balanced equation to find moles of the other reactant.
3. Use the volume of the other solution to calculate its concentration (or vice versa).
Example: A student adds 9.04 mL of 0.1074 M Na₂C₂O₄ to 10.00 mL of FeCl₃ solution. First, find moles of Na₂C₂O₄ added (convert 9.04 mL to L, multiply by 0.1074 M). Then use the balanced equation (2FeCl₃ + 3Na₂C₂O₄ → products) to find moles of FeCl₃. Finally, divide moles of FeCl₃ by 0.01000 L to get its concentration.

🔍 Working backwards to find unknown concentration

Measure the volume of the unknown solution (the aliquot).
Add a solution of known concentration until the reaction is complete; measure this volume.
Calculate moles of the known solution added.
Use stoichiometry to find moles of the unknown substance.
Divide by the aliquot volume to find the unknown concentration.
Don't confuse: The volume of titrant added is different from the volume of the original sample—use the correct volume for each calculation.

🔢 Other concentration units

🔢 Percentage by mass (m/m)

The excerpt shows that concentration units other than molarity can also be conversion factors.
A 3.00% m/m H₂O₂ solution means 3.00 g of H₂O₂ per 100 g of solution.
Example: To find the mass of 3.00% m/m H₂O₂ solution needed to react with 0.355 mol of MnO₄⁻, first use the balanced equation (2MnO₄⁻ + 5H₂O₂ → products) to find moles of H₂O₂, then convert moles to grams using molar mass of H₂O₂, then convert grams of H₂O₂ to grams of solution using the percentage: grams H₂O₂ × (100 g solution / 3.00 g H₂O₂).

🔢 Three-step conversion with percentage

First conversion: Use stoichiometry (balanced equation) to relate moles of one substance to moles of another.
Second conversion: Use molar mass to convert moles to grams of solute.
Third conversion: Use the percentage concentration definition to convert grams of solute to grams of solution.
The definition of percentage concentration provides the conversion factor just like molarity does.

Quantitative Units of Concentration

🧭 Overview

🧠 One-sentence thesis

Concentration can be expressed quantitatively through several common units—molarity, molality, mass percentage, and parts-based measures—each requiring careful attention to whether the denominator is solution volume, solvent mass, or total mass.

📌 Key points (3–5)

Why quantitative units matter: qualitative terms are insufficient; specific units allow precise calculation of solute amounts in solutions.
Molarity vs molality: molarity uses liters of solution as the denominator; molality uses kilograms of solvent.
Mass-based units: mass percentage, parts per thousand (ppth), parts per million (ppm), and parts per billion (ppb) express concentration as ratios of masses.
Common confusion—ionic solutions: the concentration of individual ions may differ from the salt concentration (e.g., 1 M CaCl₂ yields 2 M Cl⁻ ions).
Unit conversions are essential: mass must be converted to moles for molarity/molality; volume often needs conversion from mL to L.

🧪 Molarity and molality

🧪 Molarity (M)

Molarity (M): the number of moles of solute divided by the number of liters of solution.

Formula in words: molarity equals moles of solute divided by liters of solution.
The denominator is the total solution volume, not the solvent volume alone.
Spoken as "molar" (e.g., 0.48 M is "zero point forty-eight molar").
If solute mass is given, convert to moles first using molar mass before calculating molarity.

Example from the excerpt: 0.24 mol of NaOH in 0.500 L of solution gives 0.48 M concentration (0.24 divided by 0.500).

🧪 Molality (m)

Molality (m): the number of moles of solute per kilogram of solvent.

Formula in words: molality equals moles of solute divided by kilograms of solvent.
The denominator is the solvent mass, not the solution mass or volume.
Mathematical manipulation is the same as with molarity.
Don't confuse: molarity uses solution volume (L); molality uses solvent mass (kg).

📊 Mass-based concentration units

📊 Mass percentage (% m/m)

Mass percentage: (mass of solute divided by mass of solution) multiplied by 100%.

Also called "percentage composition by mass."
Both masses must be in the same unit.
Commonly seen on commercial product labels.

Example from the excerpt: 87.9 g of Fe in a 113 g sample gives (87.9 / 113) × 100% = 77.8% Fe.

📊 Parts per thousand, million, and billion

Unit	Definition	Use case
Parts per thousand (ppth)	(mass of solute / mass of solution) × 1,000	Moderate dilution
Parts per million (ppm)	(mass of solute / mass of solution) × 1,000,000	Low concentration
Parts per billion (ppb)	(mass of solute / mass of solution) × 1,000,000,000	Very low concentration

Each unit is used for progressively lower concentrations.
The two masses must be in the same unit; conversions may be necessary.

Example from the excerpt: 0.6 g of Pb in 277 g of solution gives (0.6 / 277) × 1,000 = 2.2 ppth.

🔢 Solving concentration problems

🔢 Finding concentration when amount and volume are known

Substitute known values into the definition.
Ensure units match: convert mL to L, grams to moles as needed.

Example from the excerpt: 32.7 g of NaOH dissolved to make 445 mL of solution.

Convert 445 mL to 0.445 L.
Convert 32.7 g NaOH to moles: 32.7 g ÷ 40.0 g/mol = 0.818 mol.
Molarity = 0.818 mol ÷ 0.445 L = 1.84 M.

🔢 Finding amount of solute when concentration and volume are known

Rearrange the definition: moles = molarity × liters.
Multiply the concentration by the volume.

Example from the excerpt: 0.108 L of 0.887 M NaCl solution contains 0.887 M × 0.108 L = 0.0958 mol of solute.

🔢 Finding volume when concentration and amount are known

Rearrange the definition: volume = moles ÷ molarity.
The unknown quantity must be by itself in the numerator.

Example from the excerpt: To obtain 0.222 mol from a 2.33 M NaNO₃ solution, volume = 0.222 mol ÷ 2.33 M = 0.0953 L (or 95.3 mL).

🔢 Using density to find mass

When concentration is in ppm or ppb and volume is given, use density to convert volume to mass first.

Example from the excerpt: 240.0 mL of H₂O with density 1.00 g/mL has mass = 240.0 mL × 1.00 g/mL = 240.0 g. Then use the ppm definition to find solute mass.

⚛️ Ionic solutions and ion concentration

⚛️ Individual ion concentration vs salt concentration

When an ionic compound dissolves, ions separate and may have different concentrations than the original salt.
The concentration of each ion depends on the number of that ion per formula unit.

Example from the excerpt:

1 M NaCl solution → 1 M Na⁺ and 1 M Cl⁻ (one of each ion per formula unit).
1 M CaCl₂ solution → 1 M Ca²⁺ but 2 M Cl⁻ (two Cl⁻ ions per formula unit).

⚛️ Total ion concentration

Total ion concentration is the sum of all individual ion concentrations.

Example from the excerpt:

1 M NaCl: total ion concentration = 1 M + 1 M = 2 M.
1 M CaCl₂: total ion concentration = 1 M + 2 M = 3 M.

Don't confuse: the salt concentration with the individual ion concentrations—always account for the stoichiometry of the formula unit.

Colligative Properties of Ionic Solutes

🧭 Overview

🧠 One-sentence thesis

Ionic solutes produce greater-than-expected colligative effects because they separate into multiple ions when dissolved, requiring the van't Hoff factor to correctly predict solution properties.

📌 Key points (3–5)

Why ionic solutes differ: they separate into multiple particles (ions) when dissolved, increasing the total particle count beyond what molecular solutes produce.
The van't Hoff factor (i): represents the number of particles each formula unit breaks into; it must be included in colligative property calculations for ionic compounds.
Ideal vs actual factors: the ideal van't Hoff factor works well only in dilute solutions (less than 0.001 M); at higher concentrations, ion interactions reduce the actual factor below the ideal.
Common confusion: a 1 M NaCl solution has a net particle concentration of 2 M (not 1 M) because each formula unit produces two ions.
Historical significance: the greater-than-expected impact on colligative properties was key evidence that ionic compounds separate into ions in solution.

🧪 Why ionic solutes behave differently

🔬 Ion separation increases particle count

When ionic compounds dissolve, they break apart into individual ions rather than staying as intact molecules.
This separation increases the total number of dissolved particles beyond the initial solute concentration.
Example: NaCl dissolves as NaCl(s) → Na⁺(aq) + Cl⁻(aq), producing two particles per formula unit.

📈 Impact on colligative properties

The increased total number of particles dissolved in solution increases the impact on the resulting colligative property.

A 1 M NaCl solution actually has a net particle concentration of 2 M.
The observed colligative property (freezing point depression, boiling point elevation, etc.) will be twice as large as expected for a 1 M molecular solution.
Don't confuse: the molarity of the salt (1 M) with the total particle concentration (2 M for NaCl).

🔢 The van't Hoff factor

📐 Definition and purpose

The van't Hoff factor (i): the number of particles each solute formula unit breaks apart into when it dissolves.

For molecular solutes, we tacitly assume i = 1 (no separation).
For ionic solutes, i equals the number of ions produced.
This factor must be incorporated into colligative property equations.

📊 Ideal van't Hoff factors for common compounds

Compound	van't Hoff factor (i)	Why
NaCl, KBr, LiNO₃	2	One cation + one anion
CaCl₂, Mg(C₂H₃O₂)₂	3	One cation + two anions (or vice versa)
FeCl₃	4	One cation + three anions
Al₂(SO₄)₃	5	Two cations + three anions

Example: Sr(OH)₂ dissolves as Sr²⁺(aq) + 2OH⁻(aq), producing three ions total, so i = 3.
Example: Fe(NO₃)₃ produces one Fe³⁺ and three NO₃⁻ ions, so i = 4.

⚠️ Ideal vs actual factors

The "ideal" van't Hoff factor assumes complete separation with no interactions between ions.
This is correct only for dilute solutions (less than 0.001 M).
At concentrations greater than 0.001 M, ions of opposite charge interact enough that the net ion concentration is less than expected.
The actual van't Hoff factor is thus less than the ideal one, sometimes significantly.
The excerpt notes that ideal factors will be used for calculations.

🧮 Revised calculation equations

🌡️ Modified colligative property formulas

The van't Hoff factor is incorporated into standard colligative property equations:

Freezing point depression: ΔTf = i × Kf × m
Boiling point elevation: ΔTb = i × Kb × m
Osmotic pressure and vapor pressure: similarly modified with the i factor

Where:

i = van't Hoff factor
Kf or Kb = freezing/boiling point constant
m = molality

🧊 Worked example: freezing point

For a 1.77 m solution of NaCl in water:

NaCl has i = 2 (produces Na⁺ and Cl⁻)
ΔTf = 2 × 1.86 °C/m × 1.77 m = 6.59°C
This is the change (decrease) in freezing point
New freezing point = 0.00°C - 6.59°C = -6.59°C

♨️ Worked example: boiling point

For a 0.887 m solution of CaCl₂ in water:

CaCl₂ has i = 3 (produces Ca²⁺ and 2 Cl⁻)
The calculation yields a boiling point of 101.36°C (an increase of 1.36°C above water's normal 100°C).

🍝 Practical application: salting pasta water

🧂 The common claim

Many recipes call for salting water before cooking pasta.
Some argue that salt raises the boiling point, cooking pasta faster.
The excerpt examines whether this claim has scientific merit.

🔍 Testing the claim

To raise the boiling point by 1.0°C (assuming this would noticeably speed cooking):

Calculation shows approximately 1 lb (nearly 1 cup) of salt would be needed for 4 L of water.
In practice, people add only a few pinches or perhaps one-fourth teaspoon—far less than required.
The small amount of salt added does not significantly raise the boiling point.

🤔 Why people actually add salt

Taste: adding salt adds a little salt flavor to the pasta (though most salt remains in the water).
Habit: recipes tell us to add salt, so we do, even without strong scientific or culinary justification.
Don't confuse: the colligative effect explanation (which requires large amounts of salt) with the actual reasons people salt pasta water (flavor and tradition).

Some Definitions

🧭 Overview

🧠 One-sentence thesis

Solutions are mixtures in which a solute dissolves in a solvent according to the "like dissolves like" rule, and the amount of dissolved solute can be described qualitatively (dilute, concentrated, saturated) or quantitatively (concentration, solubility).

📌 Key points (3–5)

Solvent vs solute: the major component (by mass or moles) is the solvent; the minor component is the solute.
Concentration terminology: dilute and concentrated are qualitative (relative) terms; precise measurements require quantitative units.
Solubility limits: solubility is the maximum amount of solute that can dissolve in a given amount of solvent at a specific temperature; solutions can be unsaturated, saturated, or supersaturated.
Common confusion: "saturated" does not mean "concentrated"—a saturated solution of a sparingly soluble substance can still be very dilute.
Predicting solubility: "like dissolves like"—solutes dissolve in solvents when they experience the same types of intermolecular forces.

🧪 Solvent and solute

🧪 What defines solvent and solute

Solvent: the major component of a solution (by mass or by moles).

Solute: the minor component of a solution (by mass or by moles).

The distinction is based on which component has the greater presence.
The overall phase of the solution matches the phase of the solvent.
Example: dissolving 1.00 g of sucrose in 100.0 g of water → water is the solvent (majority), sucrose is the solute (minority).

🌊 Solutions exist in all phase combinations

Solute phase	Solvent phase	Example
Solid	Liquid	Salt water (NaCl in H₂O)
Gas	Liquid	Soda water (CO₂ in H₂O)
Gas	Gas	Air (O₂ in N₂)

In all cases, the solution takes the phase of the solvent.

📏 Describing how much solute is present

📏 Concentration (general concept)

Concentration: how much solute is dissolved in a given amount of solvent.

This is a fundamental concept for understanding solutions.
Can be described qualitatively or quantitatively.

🔤 Qualitative terms: dilute and concentrated

Dilute: a solution that has very little solute.

Concentrated: a solution that has a lot of solute.

Problem: these terms are qualitative—they describe "more or less" but not exactly how much.
They are relative and imprecise.
For precise work, quantitative units of concentration are needed (mentioned but not detailed in this excerpt).

🚫 Don't confuse dilute/concentrated with saturated/unsaturated

Dilute/concentrated refer to the relative amount of solute.
Saturated/unsaturated refer to whether the solution has reached its maximum capacity for that particular solute.
A saturated solution can be dilute if the solute has very low solubility.

🧊 Solubility and saturation

🧊 Solubility: the maximum amount

Solubility: the maximum amount of solute that can be dissolved in a given amount of solvent.

Usually expressed as grams of solute per 100 g of solvent at a given temperature.
Solubilities vary widely between different solutes.

Solute	Solubility (g per 100 g H₂O at 25°C)
AgCl	0.00019
CaCO₃	0.0006
KBr	70.7
NaCl	36.1
NaNO₃	94.6

Example: NaCl can dissolve up to 36.1 g per 100 g of water, while AgCl can dissolve only 0.00019 g per 100 g of water.

🔄 Saturated, unsaturated, and supersaturated

Saturated: the maximum amount of solute has been dissolved in a given amount of solvent.

Unsaturated: less than the maximum amount of solute is dissolved.

Supersaturated: more than the maximum amount of solute is dissolved (unstable condition).

Important distinction: A solution of 0.00019 g AgCl per 100 g H₂O is saturated but also dilute (very little solute). A solution of 36.1 g NaCl in 100 g H₂O is saturated but concentrated (lots of solute).
Supersaturated solutions are created by heating the solvent, dissolving extra solute, then cooling slowly and carefully.
Supersaturated solutions are not stable—given an opportunity (e.g., adding a crystal), the excess solute will precipitate out.

🔗 Why solutes dissolve: "like dissolves like"

🔗 Intermolecular interactions determine solubility

Whether a solute dissolves in a solvent depends on intermolecular interactions.
The relevant forces include:
- London dispersion forces
- Dipole-dipole interactions
- Hydrogen bonding
Key finding from experiments: if solute molecules experience the same intermolecular forces as the solvent, the solute will likely dissolve in that solvent.

🧲 The "like dissolves like" rule

"Like dissolves like": a general rule for predicting whether a solute is soluble in a given solvent.

Polar solutes dissolve in polar solvents.
Nonpolar solutes dissolve in nonpolar solvents.
Example: NaCl (very polar, composed of ions) dissolves in water (very polar) but not in oil (generally nonpolar).
Example: Nonpolar wax dissolves in nonpolar hexane but not in polar water.
Example: I₂ (nonpolar) would be more soluble in CCl₄ (nonpolar) than in H₂O (polar).
Example: C₃H₇OH (experiences hydrogen bonding) would be more soluble in H₂O (also experiences hydrogen bonding) than in CCl₄.

⚠️ Caution: a general rule, not absolute

"Like dissolves like" is a general rule, not an absolute statement.
It must be applied with care—there are exceptions.

Dilutions and Concentrations

🧭 Overview

🧠 One-sentence thesis

Dilution and concentration change the amount of solvent in a solution while keeping the amount of solute constant, and the relationship M₁V₁ = M₂V₂ allows calculation of new concentrations or volumes.

📌 Key points (3–5)

Dilution vs concentration: dilution adds solvent (decreases solute concentration); concentration removes solvent (increases solute concentration).
What stays constant: the amount of solute does not change during dilution or concentration—only the solvent amount changes.
The dilution equation: M₁V₁ = M₂V₂ relates initial and final molarity and volume; volumes must use the same units.
Common confusion: the word "concentration" has two meanings—the general property (amount of solute per solvent) and the specific process (removing solvent to increase concentration).
Practical use: medical and pharmaceutical workers routinely dilute stock solutions to prepare correct dosages for patients.

🔄 Core processes

💧 What dilution means

Dilution: the addition of solvent, which decreases the concentration of the solute in the solution.

You are making the solution less concentrated by adding more solvent.
The solute amount stays the same; only the total volume increases.
Example: if 25.0 mL of solution is diluted to 72.8 mL, then 72.8 − 25.0 = 47.8 mL of solvent must be added.

🔥 What concentration means

Concentration: the removal of solvent, which increases the concentration of the solute in the solution.

You are making the solution more concentrated by removing solvent (usually by evaporating or boiling).
The solute amount stays the same; the total volume decreases.
Don't confuse: "concentration" as a process (removing solvent) vs "concentration" as a property (how much solute is present per amount of solvent).

🧮 The dilution equation

📐 Deriving the relationship

Molarity is defined as moles of solute divided by volume of solution.
Moles of solute = molarity × volume, or using shorthand: moles = M × V.
Because the amount of solute does not change before and after dilution or concentration, the product MV must be the same before and after.
This gives the dilution equation: M₁V₁ = M₂V₂, where subscript 1 represents initial conditions and subscript 2 represents final conditions.

🔢 Using the equation

The volumes must be expressed in the same units (e.g., both in mL or both in L).
It does not matter which set of conditions is labelled 1 or 2, as long as the conditions are paired together properly.
The equation gives only the initial and final conditions, not the amount of change; the amount of change is determined by subtraction.
Example: if 25.0 mL of a 2.19 M solution are diluted to 72.8 mL, then (2.19 M)(25.0 mL) = M₂(72.8 mL), so M₂ = 0.752 M.

🧪 Solving for different unknowns

What you know	What you solve for	Rearrangement
M₁, V₁, M₂	Final volume V₂	V₂ = M₁V₁ / M₂
M₁, V₁, V₂	Final concentration M₂	M₂ = M₁V₁ / V₂
M₂, V₂, V₁	Initial concentration M₁	M₁ = M₂V₂ / V₁

Example: a 0.885 M solution of KBr with initial volume 76.5 mL has water added until concentration is 0.500 M; the new volume is (0.885 M)(76.5 mL) / (0.500 M) = 135.4 mL.

💉 Real-world application: IV solutions

🏥 Preparing medical solutions

In a hospital emergency room, a physician may order an intravenous (IV) delivery of a specific concentration (e.g., 100 mL of 0.5% KCl).
An aide does not take a pre-made bag; instead, the aide must make the proper solution from a sterile IV bag and a more concentrated sterile solution called a stock solution.
The aide uses a syringe to draw up some stock solution, inject it into the waiting IV bag, and dilute it to the proper concentration—this requires a dilution calculation.

🧪 Example calculation

If the stock solution is 10.0% KCl and the final volume and concentration need to be 100 mL and 0.50%, respectively:
- (10.0%)(V₁) = (0.50%)(100 mL)
- V₁ = 5.0 mL of stock solution is needed.
The addition of the stock solution affects the total volume of the diluted solution, but the final concentration is likely close enough even for medical purposes.

⚠️ Importance of accuracy

Medical and pharmaceutical personnel are constantly dealing with dosages that require concentration measurements and dilutions.
It is an important responsibility: calculating the wrong dose can be useless, harmful, or even fatal.

🔬 Concentration by evaporation

🌡️ Removing solvent

Concentrating solutions involves removing solvent, usually by evaporating or boiling.
Assumption: the heat of boiling does not affect the solute.
The dilution equation is used in these circumstances as well.

📊 Example calculation

If 665 mL of a 0.875 M KBr solution are boiled gently to concentrate the solute to 1.45 M:
- (0.875 M)(665 mL) = (1.45 M)(V₂)
- V₂ = 401 mL final volume.
The solution has been concentrated by removing 665 − 401 = 264 mL of solvent.

Acid-Base Titrations

🧭 Overview

🧠 One-sentence thesis

Titrations are quantitative chemical reactions between acids and bases that allow scientists to determine the exact amount of an unknown substance by carefully measuring how much of a known reagent is needed to complete the reaction.

📌 Key points (3–5)

What a titration is: a quantitative reaction where one reagent (titrant) with known concentration reacts with an unknown amount of substance (analyte) to determine its quantity.
How to know when it's done: the equivalence point is reached when the reaction is complete, and indicators change color to signal this moment.
Key equipment: a burette (precisely calibrated tube) is used to add the titrant drop by drop while measuring the exact volume used.
The calculation process: use the volume and concentration of titrant to find moles, then use the balanced equation to convert to moles of analyte, then to mass.
Common confusion: the titrant is the known reagent being added; the analyte is the unknown substance being measured—either can be an acid or base.

🧪 Core titration concepts

🔬 What is a titration?

Titration: performing chemical reactions quantitatively to determine the exact amount of a reagent.

A titration is not just mixing chemicals—it's a precise measurement technique.
The method works for any reaction with a known balanced equation, though acid-base reactions are most common.
One substance has a known concentration (titrant), the other has an unknown amount (analyte).

🎯 Titrant vs analyte

Component	Definition	Characteristics
Titrant	The reagent with known concentration	Added from the burette; amount can be precisely measured
Analyte	The substance with unknown concentration or amount	Usually dissolved in solution; what you're trying to measure

Don't confuse: Either an acid or a base can be the titrant—it's not always the acid.
The analyte is usually (but not always) dissolved in solution before the titration begins.

📍 Equivalence point

Equivalence point: the moment when the reaction is complete.

This is when exactly enough titrant has been added to react with all of the analyte.
At this point, you stop adding titrant and record the volume used.
The equivalence point is the key measurement that allows you to calculate the unknown quantity.

🔧 Equipment and detection

🧴 The burette

Burette: a precisely calibrated volumetric delivery tube used to add titrant.

Has markings to measure exactly how much solution has been added.
Allows drop-by-drop addition for precise control.
The volume reading from the burette is essential for the calculation.

🎨 Indicators

Indicator: a substance that changes color depending on the acidity or basicity of the solution.

Indicators show when the equivalence point has been reached.
Different indicators change colors at different acidity levels.
Choosing the correct indicator is important for accurate results.
Only a small amount is added so it doesn't interfere with the reaction.

🧮 Performing titration calculations

📊 The calculation steps

The excerpt provides a systematic approach:

Calculate moles of titrant: multiply concentration (M) by volume (L)
Use the balanced equation: convert moles of titrant to moles of analyte using stoichiometry
Convert to mass: multiply moles of analyte by its molar mass

💡 Example walkthrough

The excerpt shows: 25.66 mL of 0.1078 M HCl titrated an unknown NaOH sample.

Step 1: Find moles of HCl

Volume = 0.02566 L (convert mL to L)
Moles = concentration × volume = (calculation shown in excerpt)

Step 2: Use balanced equation HCl + NaOH → NaCl + H₂O

The 1:1 ratio means moles of NaOH = moles of HCl

Step 3: Convert to mass

Mass = moles × molar mass of NaOH (40.00 g/mol)

⚠️ Important calculation details

Always convert volume to liters before calculating moles.
The balanced chemical equation determines the mole ratio between titrant and analyte.
Different reactions have different stoichiometric ratios (e.g., 2HNO₃ + Ca(OH)₂ has a 2:1 ratio).
Don't confuse: the mole ratio from the equation is critical—it's not always 1:1.

Strong and Weak Acids and Bases and Their Salts

🧭 Overview

🧠 One-sentence thesis

Acids and bases differ fundamentally in their degree of ionization—strong acids and bases dissociate 100% in solution while weak ones do not—and this difference determines whether their salts produce acidic, basic, or neutral solutions.

📌 Key points (3–5)

Strong vs weak definition: Strong acids/bases dissociate 100% into ions; weak acids/bases dissociate less than 100%.
Very few strong acids and bases exist: Only those listed in Table 12.1 are strong; all others are weak.
Salt hydrolysis rule: Salts from strong acids/bases don't affect pH; salts from weak acids/bases do hydrolyze and change solution pH.
Common confusion: Don't assume all acids/bases behave the same—a weak acid may be 1% or 99% ionized but is still classified as weak, not strong.
Predicting salt behavior: If an ion comes from a weak acid, the salt is basic; if from a weak base, the salt is acidic; if both ions come from strong acids/bases, the salt is neutral.

🔬 Defining strong and weak acids and bases

💪 Strong acids

Strong acid: An acid that dissociates 100% into ions in solution.

When HCl dissolves in water, it completely breaks apart: HCl → H⁺(aq) + Cl⁻(aq) with 100% conversion.
The excerpt lists very few strong acids in Table 12.1: HCl, HBr, HI, HNO₃, H₂SO₄, HClO₃, HClO₄.
If an acid is not in this table, it is weak.

🌊 Weak acids

Weak acid: An acid that does not dissociate 100% into ions.

HC₂H₃O₂ (acetic acid) is an example: HC₂H₃O₂ → H⁺(aq) + C₂H₃O₂⁻(aq) proceeds only about 5%.
Because the reaction doesn't go to completion, it's better written as an equilibrium: HC₂H₃O₂ ⇄ H⁺(aq) + C₂H₃O₂⁻(aq).
A weak acid may be 1% ionized or 99% ionized—it's still classified as weak, not strong.

💪 Strong bases

Strong base: A base that is 100% ionized in solution.

All strong bases are OH⁻ compounds.
Table 12.1 lists the strong bases: LiOH, NaOH, KOH, RbOH, CsOH, Mg(OH)₂, Ca(OH)₂, Sr(OH)₂, Ba(OH)₂.
Example: Ca(OH)₂ → Ca²⁺(aq) + 2OH⁻(aq) proceeds 100% to products.

🌊 Weak bases

Weak base: A base that is less than 100% ionized in solution.

Any base not listed in Table 12.1 is weak.
NH₃ is a weak base—it doesn't contain OH⁻ ions in its formula and acts by accepting protons.
Bases based on mechanisms other than OH⁻ release will be weak.

🧪 How salts affect solution acidity

🧂 Neutral salts

Neutral salt: A salt whose ions do not affect the acidity or basicity of the solution.

NaCl is an example: it separates into Na⁺ and Cl⁻ ions.
The Na⁺ ion would form NaOH if it hydrolyzed, but NaOH is a strong base (100% ionized), so the net effect is zero.
The Cl⁻ ion would form HCl if it hydrolyzed, but HCl is a strong acid (100% ionized), so the net effect is zero.
Rule: If both ions derive from strong acids or strong bases, the salt is neutral.

🔵 Basic salts

Basic salt: A salt that makes the solution basic because one of its ions hydrolyzes to produce OH⁻ ions.

NaC₂H₃O₂ (sodium acetate) is an example.
The Na⁺ ion doesn't affect pH (comes from strong base NaOH).
The C₂H₃O₂⁻ ion hydrolyzes: C₂H₃O₂⁻(aq) + H₂O → HC₂H₃O₂ + OH⁻(aq).
This happens because HC₂H₃O₂ is a weak acid—any chance a weak acid has to form, it will.
The OH⁻ ions produced make the solution basic.
Rule: If an ion derives from a weak acid, it will make the solution basic.

🔴 Acidic salts

Acidic salt: A salt that makes the solution acidic because one of its ions hydrolyzes to produce H₃O⁺ (or H⁺) ions.

NH₄Cl is an example.
The Cl⁻ ion doesn't affect pH (comes from strong acid HCl).
The NH₄⁺ ion hydrolyzes: NH₄⁺(aq) + H₂O → NH₃(aq) + H₃O⁺(aq).
This happens because NH₃ is a weak base—it will form when it can, just like a weak acid will.
The H₃O⁺ ions produced make the solution acidic.
Rule: If an ion derives from a weak base, it will make the solution acidic.

📋 General rules for predicting salt behavior

Ion origin	Effect on solution	Reason
Strong acid or strong base	No effect (neutral)	Ion doesn't hydrolyze; any product would immediately re-ionize
Weak acid	Makes solution basic	Ion hydrolyzes to form the weak acid, releasing OH⁻
Weak base	Makes solution acidic	Ion hydrolyzes to form the weak base, releasing H₃O⁺

Don't confuse: The behavior depends on where the ion comes from, not what it is. For example, Cl⁻ comes from HCl (strong acid), so it won't hydrolyze; but C₂H₃O₂⁻ comes from HC₂H₃O₂ (weak acid), so it will hydrolyze.

🧮 Applying the concepts

🔍 Identifying strong vs weak

Example from the excerpt:

HCl: listed in Table 12.1 → strong acid
Mg(OH)₂: listed in Table 12.1 → strong base
C₅H₅N: nitrogen acts as proton acceptor (base), but no OH⁻ in formula and not in Table 12.1 → weak base
HNO₂: not listed in Table 12.1 → weak acid

🔍 Identifying salt type

Example from the excerpt:

KCl: K⁺ from KOH (strong base), Cl⁻ from HCl (strong acid) → neutral salt
KNO₂: K⁺ from KOH (strong base), NO₂⁻ from HNO₂ (weak acid) → basic salt (the NO₂⁻ will hydrolyze)
NH₄Br: NH₄⁺ from NH₃ (weak base), Br⁻ from HBr (strong acid) → acidic salt (the NH₄⁺ will hydrolyze)

⚠️ Special cases

Some salts have ions from both weak acids and weak bases.
The overall effect depends on which ion exerts more influence.
The excerpt notes these cases exist but does not cover them in detail.

Brønsted-Lowry Acids and Bases

🧭 Overview

🧠 One-sentence thesis

The Brønsted-Lowry definition expands acid-base chemistry beyond water by focusing on proton transfer, where acids donate protons and bases accept them, creating conjugate acid-base pairs in every reaction.

📌 Key points (3–5)

Core definition shift: Brønsted-Lowry acids are proton donors (PD) and bases are proton acceptors (PA), independent of water.
Broader than Arrhenius: This definition covers Arrhenius acids/bases but also applies to non-aqueous reactions and explains bases like ammonia that lack OH⁻ in their formula.
Amphiprotic substances: Water and some other substances can act as either acid or base depending on the reaction partner.
Conjugate pairs: Every Brønsted-Lowry reaction involves two conjugate acid-base pairs that differ by one proton.
Common confusion: Don't assume bases must contain OH⁻ ions—bases can generate OH⁻ through proton acceptance (hydrolysis) or simply accept protons without producing OH⁻ at all.

🔄 Core definitions and scope

🔬 What Brønsted-Lowry adds

The Arrhenius definition limits acids and bases to aqueous solutions and the H⁺/OH⁻ relationship. The 1923 Brønsted-Lowry definitions (proposed independently by Johannes Brønsted and Thomas Lowry) provide a more general framework:

Brønsted-Lowry acid: any species that can donate a proton (H⁺) to another molecule.

Brønsted-Lowry base: any species that can accept a proton from another molecule.

In short: acid = proton donor (PD); base = proton acceptor (PA).
This definition is independent of water and applies to a wider range of chemical reactions.

✅ How it covers Arrhenius

The Brønsted-Lowry definition includes all Arrhenius cases:

In the prototypical reaction HCl + NaOH → NaCl + H₂O, the H⁺ ion is the proton donor (Brønsted-Lowry acid) and OH⁻ is the proton acceptor (Brønsted-Lowry base).
Thus H⁺ is an acid by both definitions, and OH⁻ is a base by both definitions.

💧 Water and amphiprotic behavior

💧 Ammonia as a base without OH⁻

Ammonia (NH₃) is a base even though its formula contains no OH⁻ ions. Instead:

NH₃ reacts with water: NH₃ + H₂O → NH₄⁺ + OH⁻
NH₃ acts as a Brønsted-Lowry base (proton acceptor), and H₂O acts as a Brønsted-Lowry acid (proton donor).
This reaction with water is called hydrolysis; we say NH₃ hydrolyzes to make NH₄⁺ and OH⁻ ions.

Example: When ammonia dissolves in water, it accepts a proton from water, generating OH⁻ as a product—not because ammonia contains OH⁻, but because it triggers proton transfer.

🔁 Amphiprotic substances

Amphiprotic: a substance that can act as either a proton donor or a proton acceptor, depending on the other reactant.

Water is the most common amphiprotic substance.
In the ammonia reaction above, water donates a proton (acts as acid).
When HCl dissolves in water: HCl(g) + H₂O(ℓ) → H₃O⁺(aq) + Cl⁻(aq), water accepts a proton (acts as base).
Don't confuse: the same molecule can switch roles depending on what it reacts with.

🔗 Conjugate acid-base pairs

🔗 What conjugate pairs are

Consider the ammonia hydrolysis reaction at equilibrium (both forward and reverse reactions occur):

NH₃ + H₂O ⇄ NH₄⁺ + OH⁻

Forward: NH₃ (base) accepts a proton from H₂O (acid).
Reverse: NH₄⁺ (acid) donates a proton to OH⁻ (base).
Both directions are Brønsted-Lowry acid-base reactions.

Conjugate acid-base pair: two species that differ by one proton; one is the acid, the other is the base.

In this reaction, there are two conjugate pairs:

NH₃ (base) and NH₄⁺ (conjugate acid)
H₂O (acid) and OH⁻ (conjugate base)

🧩 How to identify conjugate pairs

The conjugate acid has one more H⁺ than the base.
The conjugate base has one fewer H⁺ than the acid.
Every Brønsted-Lowry acid-base reaction can be labeled with two conjugate acid-base pairs.

Example: In the reaction (CH₃)₃N + H₂O ⇄ (CH₃)₃NH⁺ + OH⁻:

Pair 1: H₂O (acid) and OH⁻ (conjugate base)
Pair 2: (CH₃)₃N (base) and (CH₃)₃NH⁺ (conjugate acid)

🏠 Practical context

🏠 Household acids and bases

Many common household products are acids or bases:

Product type	Example	Chemical identity
Pool cleaner	Muriatic acid	HCl(aq)
Kitchen	Vinegar	Acetic acid, HC₂H₃O₂(aq)
Medicine	Vitamin C	Ascorbic acid, HC₆H₇O₆
Cleaning products	Ammonia	NH₃ (base)
Soaps	Various	Contain Brønsted-Lowry bases that accept protons from water, forming excess OH⁻ (one reason soap solutions are slippery)
Drain cleaner	Lye	NaOH or KOH (extremely caustic)

⚠️ Safety note

Lye-based drain cleaners are extremely dangerous because lye (NaOH or KOH) can attack body tissues. Safer alternatives use peroxide compounds instead. Always avoid touching solid drain cleaner or spilling the solution.

Arrhenius Acids and Bases

🧭 Overview

🧠 One-sentence thesis

Arrhenius acids and bases are defined by their ability to increase H⁺ or OH⁻ ion concentrations in water, and they react together in neutralization reactions to produce water and salts.

📌 Key points (3–5)

Arrhenius acid definition: a compound that increases H⁺ ion concentration in aqueous solution.
Arrhenius base definition: a compound that increases OH⁻ ion concentration in aqueous solution.
Neutralization reaction: acids and bases react to form water and a salt (an ionic compound).
Common confusion: not all compounds with OH in the formula are bases—the OH must be present as the OH⁻ ion in an ionic compound.
Historical context: this was the first chemical definition of acids and bases, proposed by Svante Arrhenius in 1884.

🔬 Defining Arrhenius acids

🔬 What an Arrhenius acid is

Arrhenius acid: a compound that increases the H⁺ ion concentration in aqueous solution.

The H⁺ ion is a bare proton, but in water it actually exists as the hydronium ion (H₃O⁺).
H⁺ and H₃O⁺ are often used interchangeably in chemical equations.
Classic Arrhenius acids can be thought of as ionic compounds where H⁺ is the cation.

📝 Examples of Arrhenius acids

Common Arrhenius acids include:

HCl (hydrochloric acid)
HNO₃ (nitric acid)
H₂SO₄ (sulfuric acid)
HC₂H₃O₂ or CH₃COOH (acetic acid)
H₃PO₄ (phosphoric acid)

⚠️ Recognizing acids

Look for H⁺ ions paired with an anion (negative ion).
Example: HNO₃ is an ionic compound between H⁺ and NO₃⁻, so it is an Arrhenius acid.
Don't confuse: CH₃OH (methanol) has OH in the formula but is not a base—it's an organic compound, not an ionic compound with OH⁻.

🧪 Defining Arrhenius bases

🧪 What an Arrhenius base is

Arrhenius base: a compound that increases the OH⁻ ion concentration in aqueous solution.

Ionic compounds containing the OH⁻ ion are classic Arrhenius bases.
The key is that OH must be present as the hydroxide ion (OH⁻), not just as part of a molecular formula.

🔍 Recognizing bases vs non-bases

Base example: Mg(OH)₂ contains Mg²⁺ cations and OH⁻ ions, so it is an Arrhenius base.
Not a base: CH₃OH has OH in the formula, but the remaining part is not a recognizable cation—this is methanol, an organic compound, not a base.
The distinction: you must recognize the compound as ionic with OH⁻ as the anion.

🎨 Properties of acids and bases

🎨 Common acid properties

Acids share several observable characteristics:

Turn litmus (a plant extract) red
React with some metals to produce H₂ gas
React with carbonate and hydrogen carbonate salts to release CO₂ gas
Have a sour, sharp taste when ingested
The word "acid" comes from the Latin acidus, meaning "sour"

🎨 Common base properties

Bases also have distinctive properties:

Feel slippery to the touch
Turn litmus blue
Have a bitter flavor if ingested

⚗️ Neutralization reactions

⚗️ What happens when acids and bases react

Neutralization reaction: the reaction between an acid and a base that produces water and a salt.

General equation:

acid + base → H₂O + salt

Salt (in chemistry): any ionic compound made by combining an acid with a base.

⚗️ How to balance neutralization equations

The stoichiometry depends on:

The number of H⁺ ions in the acid
The number of OH⁻ ions in the base

Example: H₂SO₄ + KOH → H₂O + salt

H₂SO₄ has two H⁺ ions, so it needs two OH⁻ ions to react
This makes two H₂O molecules
The remaining ions (K⁺ and SO₄²⁻) form the salt potassium sulfate (K₂SO₄)
Balanced equation: H₂SO₄ + 2KOH → 2H₂O + K₂SO₄

🧂 What is a salt?

A salt is the ionic compound formed from the cation of the base and the anion of the acid.
Example: HCl + Mg(OH)₂ produces MgCl₂ (magnesium chloride) as the salt.
The salt is what remains after the H⁺ and OH⁻ combine to form water.

Autoionization of Water

🧭 Overview

🧠 One-sentence thesis

Water molecules can simultaneously act as both acids and bases in a self-ionization process, maintaining a constant product of hydrogen and hydroxide ion concentrations equal to 1.0 × 10⁻¹⁴ in all aqueous solutions.

📌 Key points (3–5)

Autoionization process: A small fraction of water molecules (about 6 in 10⁸) act as acids and bases with each other, producing H⁺ and OH⁻ ions.
The constant product: In any aqueous solution, the product [H⁺][OH⁻] always equals 1.0 × 10⁻¹⁴ (the autoionization constant Kw).
Inverse relationship: As [H⁺] increases, [OH⁻] must decrease proportionally to maintain the constant product, and vice versa.
Common confusion: The concentration of an acid or base is not always the same as [H⁺] or [OH⁻]—you must account for the number of ions per formula unit.
Strong vs weak: Strong acids/bases are 100% ionized, but weak acids/bases require knowing the percent ionization to calculate [H⁺] or [OH⁻].

💧 The autoionization process

💧 What happens in pure water

Autoionization of water: the process where some H₂O molecules act as acids and other H₂O molecules act as bases within the same sample.

Only a tiny fraction participates: about 6 in 10⁸ molecules.
Water acts as both acid (donating H⁺) and base (accepting H⁺) simultaneously.
In pure water, this produces equal concentrations: [H⁺] = [OH⁻] = 1.0 × 10⁻⁷ M.

⚖️ Why this matters

This dual behavior explains why water is neither purely acidic nor purely basic—it's neutral.
The process establishes a baseline for understanding all aqueous solutions.

🔢 The autoionization constant (Kw)

🔢 The fundamental relationship

Autoionization constant of water (Kw): the product of [H⁺] and [OH⁻] concentrations, which always equals 1.0 × 10⁻¹⁴ for aqueous solutions.

Mathematical expression: [H⁺][OH⁻] = 1.0 × 10⁻¹⁴

This holds true for any aqueous solution—acidic, basic, or neutral.
If you know one concentration, you can calculate the other by dividing Kw by the known value.

🔄 The inverse relationship

When [H⁺] goes up, [OH⁻] must go down to keep the product constant.
When [OH⁻] goes up, [H⁺] must go down.

Solution type	[H⁺]	[OH⁻]	Product
Acidic	> 1.0 × 10⁻⁷ M	< 1.0 × 10⁻⁷ M	1.0 × 10⁻¹⁴
Neutral	= 1.0 × 10⁻⁷ M	= 1.0 × 10⁻⁷ M	1.0 × 10⁻¹⁴
Basic	< 1.0 × 10⁻⁷ M	> 1.0 × 10⁻⁷ M	1.0 × 10⁻¹⁴

Example: If [H⁺] is 1.0 × 10⁻⁴ M, then [OH⁻] = (1.0 × 10⁻¹⁴) ÷ (1.0 × 10⁻⁴) = 1.0 × 10⁻¹⁰ M.

🧪 Calculating concentrations from acids and bases

🧪 Accounting for multiple ions

Don't confuse the concentration of the compound with the concentration of H⁺ or OH⁻ ions.
You must look at the chemical formula to see how many ions are released per formula unit.

Example: A 0.0044 M solution of Ca(OH)₂ has two OH⁻ ions per formula unit, so [OH⁻] = 2 × 0.0044 M = 0.0088 M. Then [H⁺] = (1.0 × 10⁻¹⁴) ÷ 0.0088 = 1.1 × 10⁻¹² M.

💪 Strong acids and bases

Strong acids and bases are 100% ionized by definition.
[H⁺] or [OH⁻] can be determined directly from the compound's concentration (accounting for the number of ions per formula unit).

🌊 Weak acids and bases

Weak acids and bases are not 100% ionized.
You must know the percent ionization before calculating [H⁺] or [OH⁻].

Example: A 0.0788 M solution of HC₂H₃O₂ that is 3.0% ionized has [H⁺] = 0.030 × 0.0788 M = 2.4 × 10⁻³ M. Then [OH⁻] = (1.0 × 10⁻¹⁴) ÷ (2.4 × 10⁻³) = 4.2 × 10⁻¹² M.

Don't assume weak acids/bases behave like strong ones—the percent ionization makes a significant difference in the final concentrations.

Buffers

🧭 Overview

🧠 One-sentence thesis

Buffers resist dramatic pH changes by containing pairs of weak acids or bases with their salts, which react with added strong acids or bases to maintain relatively stable pH levels.

📌 Key points (3–5)

What a buffer is: a solution that resists sudden changes in pH when strong acids or bases are added.
Buffer composition: must contain either a weak acid plus its salt OR a weak base plus its salt (not strong acids/bases).
How buffers work: the weak acid/base and its salt react with added H⁺ or OH⁻ ions to prevent dramatic pH shifts.
Common confusion: strong acid + strong base combinations do NOT make buffers; only weak acid/base pairs with their salts work.
Buffer capacity: buffers work only for limited amounts of added acid/base; more dissolved solute means larger capacity.

🧪 What buffers are and why they matter

🧪 The problem buffers solve

Strong acids and bases can produce large amounts of H⁺ or OH⁻ ions very quickly.
Very small amounts can change pH dramatically.
Example: 1 mL of stomach acid (approximated as 0.1 M HCl) added to bloodstream would drop pH from about 7.4 to about 4.7 without a correcting mechanism—a pH not conducive to continued living.
The body needs a mechanism to minimize such dramatic pH changes.

🛡️ Buffer definition and composition

Buffer: a solution that resists dramatic changes in pH.

Buffers must be composed of specific pairs:

Either: weak acid + salt derived from that weak acid
Or: weak base + salt derived from that weak base

Valid buffer examples from the excerpt:

HC₂H₃O₂ (weak acid) + NaC₂H₃O₂ (its salt)
NH₃ (weak base) + NH₄Cl (its salt)
H₃PO₄ + NaH₂PO₄

Invalid combinations:

HCl + NaCl (strong acid, not weak)
NH₃ + NaOH (NaOH is a strong base, not a salt of the weak base)

⚙️ How buffers work mechanically

⚙️ When strong base is added

The added OH⁻ ions react with the weak acid component.
Example with HC₂H₃O₂/NaC₂H₃O₂ buffer:
- OH⁻ ions react with HC₂H₃O₂ in an acid-base reaction
- Rather than making the solution basic, the OH⁻ ions react to make H₂O
- pH does not change much

⚙️ When strong acid is added

The added H⁺ ions react with the anion from the salt.
Example with HC₂H₃O₂/NaC₂H₃O₂ buffer:
- Because HC₂H₃O₂ is a weak acid, it is not ionized much
- If lots of H⁺ and C₂H₃O₂⁻ ions are present, they come together to make HC₂H₃O₂
- Rather than making the solution acidic, the added H⁺ ions react to make molecules of weak acid

⚙️ Weak base buffers work similarly

Example with NH₃/NH₄Cl buffer:

NH₃ molecules can react with excess H⁺ ions introduced by strong acids
NH₄⁺ ions can react with OH⁻ ions introduced by strong bases

🔬 Buffer capacity and limitations

🔬 What capacity means

Buffer capacity: the amount of strong acid or base a buffer can neutralize before losing its buffering ability.

Buffers work well only for limited amounts of added strong acid or base.
Once either solute is completely reacted, the solution is no longer a buffer.
Rapid changes in pH may occur after capacity is exceeded.

🔬 What affects capacity

Buffers with more solute dissolved to start with have larger capacities.
Example: Two solutions with same concentrations—one with H₃PO₄/Na₃PO₄, another with HCN/NaCN—the first should have larger capacity (implied by the question structure in the excerpt).

🩸 Biological buffer systems

🩸 Blood buffering

Human blood has a buffering system to minimize extreme pH changes.
One buffer is based on HCO₃⁻ and H₂CO₃ (another way to write CO₂ in aqueous solution).
With this buffer present, even if stomach acid entered the bloodstream directly, the pH change would be minimal.

🩸 Cellular buffering

Inside many body cells, there is a buffering system based on phosphate ions.
The complete phosphate buffer system uses four substances: H₃PO₄, H₂PO₄⁻, HPO₄²⁻, and PO₄³⁻.

🔍 Identifying valid buffers

🔍 Decision table

Combination	Buffer?	Reason
HCHO₂ + NaCHO₂	Yes	Weak acid (formic acid) + its salt (formate ion)
HCl + NaCl	No	HCl is a strong acid, not weak
CH₃NH₂ + CH₃NH₃Cl	Yes	Weak base (methylamine, like NH₃) + its salt
NH₃ + NaOH	No	NaOH is a strong base, not a salt of the weak base
H₃PO₄ + NaH₂PO₄	Yes	Weak acid + its salt

🔍 Key distinction

Don't confuse: A buffer requires a weak acid or base paired with its salt.
Strong acids/bases cannot form buffers because they are already fully ionized and cannot moderate pH changes through the buffer mechanism.

The pH Scale

🧭 Overview

🧠 One-sentence thesis

The pH scale provides a logarithmic way to express hydrogen ion concentration in aqueous solutions, allowing chemists to quickly classify solutions as acidic, basic, or neutral and calculate related ion concentrations.

📌 Key points (3–5)

What pH measures: pH is the negative logarithm of hydrogen ion concentration [H⁺], usually ranging from 0 to 14.
How to classify solutions: pH < 7 is acidic, pH = 7 is neutral, pH > 7 is basic.
Logarithmic nature: each pH unit represents a 10-fold change in [H⁺] concentration.
Common confusion: the relationship between pH and pOH—they always sum to 14 in aqueous solutions, allowing easy conversion between them.
Significant figures rule: for pH values, only the digits after the decimal point determine significant figures in the calculated concentration.

🔢 Understanding pH definition and scale

🔢 What pH represents

pH: a logarithmic function of [H⁺] concentration.

pH is defined as the negative logarithm of the hydrogen ion concentration.
The scale typically ranges from 0 to 14, though values outside this range are possible.
It provides a compact way to express very small or very large ion concentrations.

📏 The pH classification system

pH Range	Classification	Meaning
pH < 7	Acidic	Higher hydrogen ion concentration
pH = 7	Neutral	Equal hydrogen and hydroxide ion concentrations
pH > 7	Basic	Lower hydrogen ion concentration

Example: milk of magnesia with pH = 10.5 is basic; wine with pH = 3.0 is acidic; pure water with pH = 7 is neutral.
Most common food items listed in the excerpt are acidic (lemon juice pH = 2.2, vinegar pH = 2.9, coffee pH = 5.0).

🔁 Logarithmic relationships and calculations

📊 The logarithmic scale property

A solution with pH 1.0 has 10 times the [H⁺] of a solution with pH 2.0.
A solution with pH 2.0 has 10 times the [H⁺] of a solution with pH 3.0.
This pattern continues throughout the scale—each unit change represents a tenfold difference in concentration.
Don't confuse: a small numerical difference in pH (e.g., pH 3 vs pH 4) represents a large difference in actual hydrogen ion concentration.

🧮 Converting between pH and [H⁺]

To find [H⁺] from pH: use the expression that involves raising 10 to the negative pH power.
The method varies by calculator—some require entering the negative pH first, others reverse the sequence.
Example: for pH = 4.88, the [H⁺] = 1.3 × 10⁻⁵ M (limited to two significant figures because 4.88 has two digits after the decimal).

🎯 Significant figures in pH calculations

The digits before the decimal point in a logarithm relate to the power of 10.
Only the number of digits after the decimal point determines significant figures in the final concentration answer.
This is different from typical significant figure rules and is specific to logarithmic calculations.

🔄 The pH and pOH relationship

🔄 Defining pOH

pOH: the negative logarithm of [OH⁻] concentration.

pOH is defined similarly to pH but for hydroxide ion concentration.
The "p" notation can be applied to any quantity, always meaning the negative logarithm of that quantity.

⚖️ The pH + pOH = 14 rule

For any aqueous solution: pH + pOH = 14
This relationship makes it simple to determine one value from the other.
Example: if pH = 8.22, then pOH = 14 - 8.22 = 5.78
Once you know either pH or pOH, you can calculate both [H⁺] and [OH⁻].

🔢 Complete calculation workflow

If given pH, calculate pOH by subtracting from 14.
Calculate [H⁺] from pH using the inverse logarithm expression.
Calculate [OH⁻] from pOH using the same type of expression.
Example: for pH = 8.22, pOH = 5.78, [H⁺] = 6.0 × 10⁻⁹ M, [OH⁻] = 1.7 × 10⁻⁶ M.

📋 Practical pH values

📋 Common substances and their pH

The excerpt provides typical pH values showing the wide range in everyday materials:

Highly acidic: stomach acid (pH 1.7), lemon juice (pH 2.2)
Moderately acidic: vinegar (pH 2.9), soda (pH 3.0), wine (pH 3.5), black coffee (pH 5.0)
Near neutral: milk (pH 6.9), pure water (pH 7.0)
Basic: blood (pH 7.4), seawater (pH 8.5), milk of magnesia (pH 10.5), ammonia solution (pH 12.5)
Highly basic: 1.0 M NaOH (pH 14.0)

🍎 Food chemistry observation

Most food items listed are acidic (below pH 7).
This acidity contributes to taste and preservation properties.
Even milk is slightly acidic at pH 6.9, just below neutral.

Chemical Equilibrium

🧭 Overview

🧠 One-sentence thesis

Chemical reactions do not always go to completion but instead reach a dynamic equilibrium where forward and reverse reactions occur at the same rate, balancing each other's progress.

📌 Key points (3–5)

What equilibrium is: the point at which forward and reverse reactions balance each other's progress, so no overall change occurs.
Dynamic, not static: both forward and reverse reactions continue to occur simultaneously at the same rate; reactions do not stop.
How to represent it: use a double arrow (⇄) instead of a single arrow to show both directions are happening.
Common confusion: equilibrium does not mean reactions stop—it means the rates of forward and reverse reactions are equal.
Reversibility: an equilibrium equation can be written in either direction (reactants ⇄ products or products ⇄ reactants).

⚖️ What equilibrium means

⚖️ The balance point

Chemical equilibrium: the point at which the forward and reverse processes balance each other's progress.

It is not "completion"—not all reactants turn into products.
Instead, the forward reaction (reactants → products) and reverse reaction (products → reactants) proceed at the same speed.
Any change made by the forward reaction is undone by the reverse reaction at the same rate.
Example: In a closed container, H₂ + I₂ → 2HI occurs, but simultaneously 2HI → H₂ + I₂ also occurs; when their rates match, equilibrium is reached.

🔄 Dynamic nature

Don't confuse: equilibrium does not mean the reactions have stopped.
Both reactions continue to occur; they are just balanced.
The excerpt emphasizes that equilibrium is dynamic, rather than static.
Think of it like the rowboat analogy: water keeps leaking in and you keep bailing out, but the water level stays constant because both processes happen at the same rate.

🖊️ How to write equilibrium equations

🖊️ The double arrow notation

Use a double arrow (⇄) to show that the reaction goes in both directions.
This replaces the single arrow (→) used for reactions assumed to go to completion.
The equation must still be balanced.
Example: H₂ + I₂ ⇄ 2HI shows that hydrogen and iodine form hydrogen iodide, and hydrogen iodide breaks down back into hydrogen and iodine.

🔁 Reversibility of notation

An equilibrium can be written in either direction.
H₂ + I₂ ⇄ 2HI is the same as 2HI ⇄ H₂ + I₂.
This is only valid when the reaction is at equilibrium.
The choice of which side to write as "reactants" vs "products" is a matter of convention or context.

🧪 Examples from the excerpt

🧪 Hydrogen and iodine

Forward reaction: H₂ + I₂ → 2HI (hydrogen and iodine combine to form hydrogen iodide).
Reverse reaction: 2HI → H₂ + I₂ (hydrogen iodide breaks down).
At equilibrium: H₂ + I₂ ⇄ 2HI (both reactions occur at the same rate).

🧪 Calcium carbonate decomposition

Equilibrium: CaCO₃ ⇄ CaO + CO₂.
Calcium carbonate can decompose into calcium oxide and carbon dioxide, and the reverse can also occur.

🧪 Water formation

Equilibrium: 2H₂ + O₂ ⇄ 2H₂O.
Hydrogen and oxygen can form water, and water can decompose back into hydrogen and oxygen.

The Equilibrium Constant

🧭 Overview

🧠 One-sentence thesis

The equilibrium constant (K_eq) is a characteristic numerical value that relates the concentrations of products and reactants at equilibrium, allowing us to calculate unknown concentrations and predict reaction behavior.

📌 Key points (3–5)

What K_eq represents: a fixed ratio of product concentrations to reactant concentrations at equilibrium for a given reaction at a given temperature.
How to construct K_eq: products over reactants, with each concentration raised to the power of its coefficient in the balanced equation.
Common confusion: equilibrium does not mean reactions stop—both forward and reverse reactions continue at the same rate (dynamic equilibrium).
Different forms: K_eq uses molar concentrations; K_P uses partial pressures for gas-phase reactions; they are related by temperature and change in moles of gas.
Heterogeneous equilibria rule: pure solids and pure liquids do not appear in equilibrium constant expressions.

🔄 Dynamic equilibrium fundamentals

⚖️ What equilibrium means

Chemical equilibrium: the point at which the forward and reverse processes balance each other's progress.

Reactions do not go to completion—both forward and reverse reactions occur simultaneously.
Example: H₂ + I₂ ⇄ 2HI means hydrogen and iodine form HI while HI simultaneously breaks down back into H₂ and I₂.
At equilibrium, the forward reaction rate equals the reverse reaction rate, so no net change occurs.

🔁 Dynamic vs static

Dynamic equilibrium: both reactions continue occurring; they just cancel each other's progress.
Don't confuse: equilibrium does not mean "stopped" or "no reaction"—it means "balanced ongoing reactions."
The double arrow (⇄) represents this two-way process.
Equilibrium can be written in either direction: H₂ + I₂ ⇄ 2HI is the same as 2HI ⇄ H₂ + I₂.

📐 The law of mass action and K_eq construction

📜 Law of mass action

Discovered by Norwegian scientists C. M. Guldberg and P. Waage in the mid-1860s.
Observation: no matter how many reactants you start with, a certain ratio of reactants and products is achieved at equilibrium.
This ratio is constant for a given reaction at a given temperature.

🧮 Building the K_eq expression

For a general reaction: aA + bB ⇄ cC + dD

The equilibrium constant is defined as:

K_eq = [C]^c × [D]^d / [A]^a × [B]^b
[A] means the molar concentration of species A at equilibrium (in molarity, M).
The coefficients from the balanced equation become exponents in the expression.
Common shorthand: "products over reactants."

🔢 What K_eq tells us

Each chemical reaction has its own characteristic K_eq value.
The concentrations at equilibrium are related—they cannot be random values.
Given K_eq and all but one concentration, you can calculate the missing concentration.

🧪 Using K_eq to calculate concentrations

🎯 Simple example

For the equilibrium A ⇄ B with K_eq = 2.0:

K_eq = [B] / [A] = 2.0
If [B] = 4.0 M, then [A] must equal 2.0 M to maintain the ratio.
If [B] = 6.0 M, then [A] must equal 3.0 M.
If [A] is not the correct value, the reaction is not at equilibrium and a net reaction will occur until the ratio equals 2.0.

🔬 More complex calculations

For H₂ + I₂ ⇄ 2HI:

K_eq = [HI]² / ([H₂] × [I₂])
Note that [HI] is squared because of the coefficient 2 in the balanced equation.
Example: If K_eq = 0.40, [HI] = 0.75 M, and [H₂] = 0.20 M, then solving for [I₂] gives 7.0 M.
Some problems require taking square roots, cube roots, or higher roots—make sure you know how to perform these operations on your calculator.

⚗️ Pressure-based equilibrium constants

💨 K_P for gas-phase reactions

For gas-phase reactions: aA(g) + bB(g) ⇄ cC(g) + dD(g)

The pressure-based equilibrium constant is:

K_P = (P_C)^c × (P_D)^d / (P_A)^a × (P_B)^b
P_A is the partial pressure of substance A at equilibrium in atmospheres.
Units are omitted when substituting values.

🔗 Relationship between K_eq and K_P

The two constants are related by:

K_P = K_eq × (RT)^Δn
R is the ideal gas law constant (0.08205 L·atm/mol·K).
T is the absolute temperature in kelvins.
Δn is the change in moles of gas: (moles of gaseous products) minus (moles of gaseous reactants).
If the number of moles of gas is the same in reactants and products, then K_eq = K_P.

🌈 Heterogeneous equilibria

🧊 The rule for mixed phases

Heterogeneous equilibrium: an equilibrium involving more than one phase (solid, liquid, gas).

Critical rule: Do not include the concentrations of pure solids and pure liquids in K_eq expressions.

📝 Example application

For the reaction: 2NaHCO₃(s) ⇄ Na₂CO₃(s) + CO₂(g) + H₂O(ℓ)

This includes all three phases: solid, gas, and liquid.
The K_eq expression is simply: K_eq = [CO₂]
The two solids (NaHCO₃ and Na₂CO₃) and the liquid (H₂O) do not appear in the expression.
Only partial pressures for gases or concentrations in solutions are included.

Shifting Equilibria: Le Chatelier's Principle

Shifting Equilibria: Le Chatelier’s Principle

🧭 Overview

🧠 One-sentence thesis

Le Chatelier's principle states that when a chemical equilibrium is stressed by changing conditions, the reaction shifts in a direction that reduces that stress.

📌 Key points (3–5)

Core principle: If an equilibrium is stressed, the reaction shifts to reduce the stress.
Ways to stress an equilibrium: adding or removing reactants/products, changing pressure (for gases), or changing temperature.
Effect of concentration changes: Adding a substance shifts the equilibrium away from it; removing a substance shifts the equilibrium toward replacing it.
Common confusion: Temperature changes actually alter the K_eq value, while concentration and pressure changes do not change K_eq—the system simply shifts to restore the original equilibrium constant.
Catalysts: They speed up reaching equilibrium but do not change the position or extent of equilibrium.

⚖️ What Le Chatelier's principle means

⚖️ The formal statement

Le Chatelier's principle: If an equilibrium is stressed, then the reaction shifts to reduce the stress.

"Stress" means changing the conditions that the system experiences.
When stressed, the chemical reaction is no longer at equilibrium.
The reaction moves back toward equilibrium in a way that decreases the stress.
This gives experimenters some ability to affect the equilibrium.

🔄 What "shift" means

The reaction is not "over" once equilibrium is established—it can be manipulated.
A shift means the reaction moves toward either reactants or products.
The shift is predictable based on the type of stress applied.

🧪 Concentration changes

➕ Adding reactants or products

Adding a reactant: The equilibrium shifts toward products to reduce the added reactant.
Adding a product: The equilibrium shifts toward reactants to reduce the added product.
Example: For the reaction N₂ + 3H₂ ⇄ 2NH₃, if H₂ is added, the reaction shifts toward products (makes more NH₃).

➖ Removing reactants or products

Removing a reactant: The equilibrium shifts toward reactants to replace what was removed.
Removing a product: The equilibrium shifts toward products to replace the product removed.
Example: For the same reaction, if NH₃ is removed, the reaction shifts toward products to replace the lost NH₃.

📊 Important note about K_eq

When reactants or products are added or removed, the value of K_eq does not change.
The chemical reaction simply shifts in a predictable fashion to reestablish concentrations so that the K_eq expression returns to the correct value.

💨 Pressure changes (gas-phase reactions)

💨 How pressure affects equilibrium

Pressure changes do not markedly affect solid or liquid phases.
Pressure strongly impacts the gas phase.

⬆️ Increasing pressure

A pressure increase shifts equilibrium to the side with fewer moles of gas.
Example: For N₂(g) + 3H₂(g) ⇄ 2NH₃(g), there are 4 mol of gas on the reactant side and 2 mol on the product side, so increasing pressure shifts toward products.

⬇️ Decreasing pressure

A pressure decrease shifts equilibrium to the side with more moles of gas.
Example: For 3O₂(g) ⇄ 2O₃(g), decreasing pressure shifts toward reactants (3 mol vs 2 mol).

⚖️ No effect case

If the number of moles of gas is the same on both sides of the reaction, pressure has no effect.

🌡️ Temperature changes

🌡️ Temperature depends on reaction type

The effect depends on whether the reaction is endothermic or exothermic.
Endothermic: Energy is absorbed (energy acts as a reactant).
Exothermic: Energy is given off (energy acts as a product).

🔥 Increasing temperature

For endothermic reactions: Adding heat is like adding a reactant, so equilibrium shifts toward products.
For exothermic reactions: Adding heat is like adding a product, so equilibrium shifts toward reactants.
Example: For PCl₃ + Cl₂ ⇄ PCl₅ + 60 kJ (exothermic), increasing temperature shifts toward reactants.

❄️ Decreasing temperature

For endothermic reactions: Removing heat is like removing a reactant, so equilibrium shifts toward reactants.
For exothermic reactions: Removing heat is like removing a product, so equilibrium shifts toward products.
Example: For N₂O₄ + 57 kJ ⇄ 2NO₂ (endothermic), decreasing temperature shifts toward reactants.

🔑 Critical difference from other stresses

Unlike concentration and pressure changes, temperature changes do alter the value of K_eq.
The K_eq is dependent on temperature—that is why equilibria shift with temperature changes.

⚡ Catalysts

⚡ What catalysts do

A catalyst is a substance that increases the speed of a reaction.

A catalyst is not a reactant and is not used up.
It affects how fast a reaction proceeds.

⚡ What catalysts do NOT do

A catalyst does not affect the extent or position of a reaction at equilibrium.
It helps a reaction achieve equilibrium faster but does not change where the equilibrium lies.

📋 Summary table of stresses

Stress type	Effect on equilibrium	Effect on K_eq
Add reactant	Shifts toward products	No change
Remove reactant	Shifts toward reactants	No change
Add product	Shifts toward reactants	No change
Remove product	Shifts toward products	No change
Increase pressure (gas)	Shifts toward fewer moles of gas	No change
Decrease pressure (gas)	Shifts toward more moles of gas	No change
Increase temperature	Shifts away from heat (depends on endo/exo)	Changes
Decrease temperature	Shifts toward heat (depends on endo/exo)	Changes
Add catalyst	No shift	No change

Calculating Equilibrium Constant Values

🧭 Overview

🧠 One-sentence thesis

The ICE chart method provides a systematic approach to calculate equilibrium concentrations by tracking initial amounts, changes in concentration, and final equilibrium values through algebraic expressions that satisfy the equilibrium constant.

📌 Key points (3–5)

What the method does: uses initial concentrations and the equilibrium constant (K_eq) to calculate all species' concentrations at equilibrium.
How ICE charts work: organize initial (I), change (C), and equilibrium (E) values in rows, with changes expressed algebraically using a variable x.
Stoichiometry matters: change values must follow the molar ratios from the balanced chemical equation's coefficients.
Common confusion: the variable x represents the amount of reactant consumed, not the final concentration—equilibrium concentrations are expressions like (initial − x) or (initial + 2x).
When algebra gets complex: quadratic equations may arise, yielding two possible x values, but only one will be physically meaningful (non-negative concentrations).

🧮 The ICE chart framework

📋 What ICE stands for

ICE chart: a table organizing Initial concentrations, Change in concentrations, and Equilibrium concentrations for all species in a reaction.

The chart has three rows, one for each stage of the reaction.
Each column represents one chemical species (reactant or product).
The equilibrium row combines initial and change values for each species.

🔢 How to fill each row

Initial row (I):

Enter the starting concentrations of all species.
Products often start at zero if the reaction hasn't begun.

Change row (C):

Use the variable x to represent the unknown amount of change.
Reactants decrease (−x), products increase (+x).
Critical: coefficients from the balanced equation determine the stoichiometric ratio—if the equation shows 2 mol of product per 1 mol of reactant, the change is +2x for the product.

Equilibrium row (E):

Combine initial and change: (initial value) + (change value).
Example: if initial is 1.0 M and change is −x, equilibrium is (1.0 − x) M.
These expressions get substituted into the K_eq formula.

⚖️ Stoichiometric relationships

The excerpt emphasizes that change values "must be in the proper stoichiometric ratio as indicated by the balanced chemical equation."
Example from the excerpt: H₂ + Cl₂ ⇄ 2HCl means if x M of H₂ reacts, x M of Cl₂ also reacts (1:1 ratio), but 2x M of HCl forms (1:2 ratio).
Don't confuse: the variable x itself is not multiplied by coefficients—the coefficients multiply x in the change expressions (−x, −x, +2x).

🧩 Solving for equilibrium concentrations

🔍 Setting up the algebraic equation

Substitute the equilibrium row expressions into the K_eq formula.
The result is an equation with one unknown (x) that can be solved.
Example from excerpt: K_eq = [HCl]² / ([H₂][Cl₂]) becomes 4.0 = (2x)² / [(1.0−x)(1.0−x)].

✅ Simple cases: perfect squares

Sometimes the equation simplifies so you can take square roots of both sides.
The excerpt's example: (2x)² / (1.0−x)² = 4.0 allows taking the square root to get 2x / (1.0−x) = 2.
Solve by rearranging: 2x = 2(1.0−x) → 2x = 2 − 2x → 4x = 2 → x = 0.67.
Then substitute back: equilibrium [H₂] = 1.0 − 0.67 = 0.33 M, [HCl] = 2(0.67) = 1.33 M.

🔢 Complex cases: quadratic equations

Quadratic equation: an algebraic equation with the general form ax² + bx + c = 0, solved using the formula x = [−b ± √(b²−4ac)] / (2a).

When the K_eq expression doesn't simplify, you may get an x² term.
The quadratic formula gives two possible values (using + and − in the numerator).
Key point from excerpt: "one value of x typically makes no sense as an answer and can be discarded as physically impossible."
Example: if one solution is negative but x represents a concentration change, discard the negative value.

🚫 Discarding impossible solutions

Concentrations cannot be negative.
If x = −0.0216 and x represents the final concentration of a product starting at zero, this is physically impossible.
The excerpt's example discards x = −0.0216 and keeps x = 0.0216.

✔️ Verification and final steps

🔍 Checking your answer

Substitute the calculated equilibrium concentrations back into the K_eq expression.
Verify that the result matches the given K_eq value.
The excerpt demonstrates: [HCl]² / ([H₂][Cl₂]) = (1.33)² / (0.33 × 0.33) ≈ 4.0 ✓

📊 Example walkthrough from the excerpt

Species	Initial (M)	Change (M)	Equilibrium (M)
COI₂	0.55	−x	0.55 − x
CO	0	+x	x
I₂	0	+x	x

K_eq = 0.00012 = (x)(x) / (0.55 − x)
Rearranging gives a quadratic: x² + 0.00012x − 0.000066 = 0
Quadratic formula yields x = 0.0216 or x = −0.0216
Discard negative value → equilibrium: [COI₂] = 0.53 M, [CO] = 0.0216 M, [I₂] = 0.0216 M

🎯 Why this method works

The ICE chart ensures you account for stoichiometry systematically.
The algebraic approach handles any initial conditions and K_eq value.
The excerpt states this is "a consistent approach" that makes such calculations "not difficult to do."

Some Special Types of Equilibria

🧭 Overview

🧠 One-sentence thesis

Certain classes of chemical equilibria—weak acids and bases, water autoionization, and slightly soluble salts—each have specialized equilibrium constant expressions (Ka, Kb, Kw, Ksp) that simplify calculations and reveal important chemical behavior.

📌 Key points (3–5)

Weak acids and bases do not ionize 100% in water, so their behavior is described by equilibrium constants Ka and Kb.
Relationship between Ka and Kb: for any conjugate acid-base pair, Ka × Kb = Kw = 1.0 × 10⁻¹⁴.
Autoionization of water establishes the constant Kw, which has no denominator because water is a pure liquid.
Slightly soluble salts are described by solubility product constants (Ksp) that also lack denominators because the solid reactant concentration does not appear.
Common confusion: "insoluble" compounds actually do dissolve slightly and establish equilibria; they are not completely insoluble.

🧪 Weak acids and bases

🧪 What makes an acid or base weak

Strong acids/bases: ionize 100% in water (e.g., HCl → H⁺ + Cl⁻ completely).
Weak acids/bases: dissolve in water but do not ionize completely; an equilibrium exists between the unionized and ionized forms.
Example: HC₂H₃O₂ (acetic acid in vinegar) dissolves but only partially separates into H⁺ and C₂H₃O₂⁻ ions.

📊 Acid dissociation constant (Ka)

Acid dissociation constant (Ka): the equilibrium constant for the dissociation of a weak acid into ions.

The subscript "a" indicates the substance is acting as an acid.
Larger Ka = stronger acid: a higher Ka means more ionization at equilibrium.
Example for acetic acid:
HC₂H₃O₂(aq) ⇄ H⁺(aq) + C₂H₃O₂⁻(aq)
Ka = [H⁺][C₂H₃O₂⁻] / [HC₂H₃O₂] = 1.8 × 10⁻⁵

🔢 Polyprotic acids

Polyprotic acids lose more than one H⁺ ion sequentially, each with its own Ka.
Example: H₃PO₄ loses one H⁺ with Ka = 7.5 × 10⁻³, then H₂PO₄⁻ loses another H⁺ with Ka = 6.2 × 10⁻⁸.
Each ionization step is a separate equilibrium.

🧮 Simplification for small Ka

When Ka is much smaller than the initial acid concentration, the change in concentration (x) is negligible in the denominator.
Example: for 1.00 M HC₂H₃O₂ with Ka = 1.8 × 10⁻⁵, assume (1.00 − x) ≈ 1.00.
This turns a quadratic equation into a simple square root problem: x = √(Ka × [acid]).
After solving, verify that x is indeed small compared to the initial concentration.

🔄 Base dissociation constant (Kb)

Weak bases also have equilibrium constants, labeled Kb.
Key relationship: Ka × Kb = Kw = 1.0 × 10⁻¹⁴ for any conjugate acid-base pair.
You rarely need to look up Kb; calculate it from the Ka of the conjugate acid.
Example: for C₂H₃O₂⁻ (conjugate base of HC₂H₃O₂), Kb = Kw / Ka = (1.0 × 10⁻¹⁴) / (1.8 × 10⁻⁵) ≈ 5.6 × 10⁻¹⁰.

💧 Autoionization of water

💧 Water as both acid and base

Water can act as both proton donor and proton acceptor simultaneously.
Equilibrium:
H₂O(ℓ) + H₂O(ℓ) ⇄ H₃O⁺(aq) + OH⁻(aq)

📐 The Kw expression

Kw (ion product of water): the equilibrium constant for water's autoionization, equal to 1.0 × 10⁻¹⁴ at 25°C.

No denominator: because H₂O is a pure liquid, its concentration does not appear in the expression.
Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴
This is the same Kw that appears in the relationship Ka × Kb = Kw.

🔗 Connection to conjugate pairs

The relationship Ka × Kb = Kw can be rewritten as:
Ka × Kb = [H₃O⁺][OH⁻]
This shows that the product of acid and base strengths for a conjugate pair is always tied to water's autoionization.

🧂 Slightly soluble salts and Ksp

🧂 "Insoluble" is relative

Describing a compound as "insoluble" is misleading; virtually all substances dissolve to some extent.
Slightly soluble salts dissolve only a tiny amount, quickly establishing an equilibrium between solid and dissolved ions.
Example: AgCl(s) ⇄ Ag⁺(aq) + Cl⁻(aq)

📏 Solubility product constant (Ksp)

Solubility product constant (Ksp): the equilibrium constant for a compound normally considered insoluble.

The subscript "sp" stands for "solubility product."
No denominator: because the reactant is a solid, its concentration does not appear in the Ksp expression.
Example for AgCl:
Ksp = [Ag⁺][Cl⁻] = 1.8 × 10⁻¹⁰

🧮 Solving Ksp problems

Ksp problems are often more straightforward than other equilibrium problems because there is no denominator.
Use an ICE chart, but the solid's concentration is omitted.
Watch stoichiometry carefully: if a salt dissociates into multiple ions, the ICE chart must reflect the correct ratios.

Salt formula	Dissolution equation	Ksp expression
MX	MX(s) ⇄ M⁺ + X⁻	[M⁺][X⁻]
MX₂	MX₂(s) ⇄ M²⁺ + 2X⁻	[M²⁺][X⁻]²
M₃X₂	M₃X₂(s) ⇄ 3M²⁺ + 2X³⁻	[M²⁺]³[X³⁻]²

🔢 Example with multiple ions

For Ca₃(PO₄)₂:
Ca₃(PO₄)₂(s) ⇄ 3Ca²⁺(aq) + 2PO₄³⁻(aq)
ICE chart: if x is the amount that dissolves, [Ca²⁺] = 3x and [PO₄³⁻] = 2x.
Ksp = [Ca²⁺]³[PO₄³⁻]² = (3x)³(2x)² = 108x⁵
Solve for x by taking the fifth root, then calculate individual ion concentrations.

🍷 Real-world example: wine crystals

Tartaric acid in wine is very soluble, but its potassium salt (potassium hydrogen tartrate, or cream of tartar) is only slightly soluble.
Over time, especially at cool temperatures, potassium hydrogen tartrate precipitates as crystals in the bottle or on the cork.
The crystals are harmless and can be filtered out; their color comes from wine pigments.
Don't confuse: the crystals are not a sign of spoilage, just a natural precipitation of a slightly soluble salt.

🔑 Key relationships summary

🔑 Three fundamental constants

Ka: measures weak acid strength; larger Ka = stronger acid.
Kb: measures weak base strength; larger Kb = stronger base.
Kw: the product [H₃O⁺][OH⁻] in water, always 1.0 × 10⁻¹⁴ at 25°C.

🔗 How they connect

For any conjugate acid-base pair: Ka × Kb = Kw
This means if you know Ka for an acid, you can immediately find Kb for its conjugate base (and vice versa).
Example: if Ka for an acid is 1.0 × 10⁻⁵, then Kb for its conjugate base is (1.0 × 10⁻¹⁴) / (1.0 × 10⁻⁵) = 1.0 × 10⁻⁹.

🧪 Ksp is different

Ksp applies to slightly soluble salts, not acid-base equilibria.
Like Kw, Ksp expressions have no denominator because the solid's concentration is constant.
Ksp values are typically very small (e.g., 10⁻¹⁰ to 10⁻³³), reflecting very low solubility.

Oxidation-Reduction Reactions

🧭 Overview

🧠 One-sentence thesis

Oxidation-reduction (redox) reactions involve the transfer of electrons between atoms, which can be tracked using oxidation numbers to identify which atoms lose electrons (oxidation) and which gain electrons (reduction).

📌 Key points (3–5)

What redox reactions are: chemical reactions involving the transfer of electrons from one atom to another; oxidation and reduction always occur together.
How to track electrons: oxidation numbers are assigned to atoms using four rules; they are not the same as actual charges.
Oxidation vs reduction: oxidation is loss of electrons (increase in oxidation number); reduction is gain of electrons (decrease in oxidation number).
Common confusion: oxidation numbers ≠ actual charges on atoms; oxidation numbers are a bookkeeping tool to track electron assignment, not real ionic charges in many compounds.
Real-world connection: corrosion (like rusting) is a type of redox reaction; while often destructive, redox reactions can also be useful.

🔄 What are redox reactions

🔄 Electron transfer between atoms

Oxidation-reduction (or redox) reactions: chemical reactions that involve the transfer of electrons between atoms.

The excerpt uses the reaction of magnesium and chlorine as an example: Mg + Cl₂ → MgCl₂
Reactants are electrically neutral elements (same number of electrons as protons)
Product is ionic: Mg²⁺ and Cl⁻ ions
Individual Mg atoms lose two electrons to become Mg²⁺; Cl atoms gain electrons to become Cl⁻
Key insight: losing and gaining electrons happens simultaneously in the same reaction

🔗 Oxidation and reduction are inseparable

Although we can mentally separate the two processes, they always occur together
One atom cannot lose electrons unless another atom gains them
Example: In 2Na + Br₂ → 2NaBr, sodium loses electrons while bromine gains them; both processes happen at once

📊 Oxidation numbers: tracking electrons

📊 What oxidation numbers are

Oxidation numbers: values assigned to atoms based on rules to keep track of electrons in a chemical reaction.

Important distinction: Oxidation numbers are not necessarily equal to the charge on the atom
They are a bookkeeping tool, not real charges in many cases
Example: In SO₂, sulfur is assigned an oxidation number of +4, but this does not mean sulfur has a 4+ charge
We must keep the concepts of charge and oxidation numbers separate

📋 Four rules for assigning oxidation numbers

Rule	Description	Example
1	Atoms in elemental state = 0	H₂: both H atoms are 0
2	Monatomic ions = their charge	In MgCl₂: Mg is +2, Cl is −1
3	F = −1; O = −2 (usually); H = +1 (usually)	In H₂O: H is +1, O is −2
4	Sum of oxidation numbers = charge on species	In SO₂: O is −2 (×2), so S must be +4 to sum to zero

🔍 Special cases in rule 3

Oxygen exceptions:
- In peroxide compounds: O is −1 (not −2)
- In binary compounds with fluorine: O is positive
- Example: In H₂O₂ (hydrogen peroxide), each O is −1
Hydrogen exception:
- When it exists as hydride ion (H⁻): use rule 2 instead
- Example: In hydride compounds, H is −1

🧮 Using rule 4 for complex compounds

For SO₂: each O is −2; to make the sum zero, S must be +4
For Ca(NO₃)₂: separate into Ca²⁺ and NO₃⁻
- Ca²⁺ has oxidation number +2
- In NO₃⁻: three O atoms at −2 each = −6 total
- Equation: x + (−6) = −1 (the charge on NO₃⁻)
- Solving: x = +5, so N has oxidation number +5

🔬 Defining oxidation and reduction

🔬 Two equivalent definitions

In terms of electrons:

Oxidation: the loss of one or more electrons by an atom. Reduction: the gain of one or more electrons by an atom.

In terms of oxidation numbers:

Oxidation: an increase in the oxidation number of an atom. Reduction: a decrease in the oxidation number of an atom.

Both definitions describe the same process from different perspectives
The oxidation number definition is often easier to apply in practice

⚡ Identifying what is oxidized and reduced

When an atom is oxidized: its oxidation number increases (it loses electrons)
When an atom is reduced: its oxidation number decreases (it gains electrons)
Example: In 2Na + Br₂ → 2NaBr
- Na goes from 0 to +1 → oxidation number increases → Na is being oxidized
- Br goes from 0 to −1 → oxidation number decreases → Br is being reduced
Don't confuse: "being oxidized" means the atom itself loses electrons; "being reduced" means the atom itself gains electrons

🔄 Electron balance in redox reactions

The total number of electrons lost must equal the total number gained
Example: In 2Na + Br₂ → 2NaBr
- Two Na atoms each lose one electron = 2 electrons lost total
- Two Br atoms each gain one electron = 2 electrons gained total
- The electrons balance

🌍 Real-world context: corrosion

🌍 Corrosion as a redox reaction

Corrosion: the disintegration of a material due to chemical reactions with other substances in the environment.

Rusting is the informal term; corrosion is the formal term
In many cases, oxygen in the air causes the disintegration
Example of a redox reaction that occurs in everyday life

⚖️ Corrosion can be destructive or protective

Destructive: iron corrosion weakens structures (dark red-brown scale that falls off)
Protective: aluminum and copper corrosion forms a barrier on the surface, protecting from further reaction
The excerpt notes that as much as 5% of expenditures in the United States apply to fixing corrosion problems
Historical example: Silver Bridge collapse in 1967 (46 deaths) was caused by corrosion of a suspension chain

💡 Redox reactions are not inherently bad

Although we usually think of corrosion as bad, the excerpt states that redox reactions "can actually be put to good use"
The reaction type itself is neutral; the context determines whether it is helpful or harmful

🍞 Application: iron in food

🍞 Why metallic iron in fortified foods

Many foods (bread, breakfast cereals) are enriched with iron to ensure adequate dietary intake
Some use "reduced iron" (metallic iron powder) instead of Fe²⁺ compounds
Metallic iron is oxidized to Fe²⁺ in the digestive system, then absorbed

🤔 Reasons for using metallic iron over Fe²⁺ salts

Taste: fine iron filings do not affect the taste of the product
Texture: iron powder (several dozen micrometers) is not noticeable when chewing
Food properties: Fe²⁺ compounds can affect dough pliability, yeast growth, and colour during preparation and cooking
Cost: metallic iron is the least expensive of common iron substances
The excerpt notes these are suggested reasons from scientific and medical literature, not conclusive

🔄 The redox process in digestion

Metallic iron has oxidation number 0
In the digestive system, it is oxidized to Fe²⁺ (oxidation number +2)
This is a redox reaction: iron loses electrons (is oxidized) to form the biologically useful Fe²⁺ ion

Balancing Redox Reactions

🧭 Overview

🧠 One-sentence thesis

Simple redox reactions can often be balanced by inspection—adjusting coefficients back and forth between reactants and products until all atoms are balanced.

📌 Key points (3–5)

What balancing by inspection means: adjusting coefficients by looking at the equation and fixing imbalances step-by-step without formal methods.
The back-and-forth process: fix one element's imbalance, which may create a new imbalance in another element, then fix that in turn.
When inspection works: many simple redox reactions can be balanced this way; more complex reactions require other methods (like the half-reaction method mentioned but not detailed in the excerpt).
Common confusion: balancing one element may unbalance another—don't stop after the first fix; keep iterating until all atoms are balanced on both sides.

🔧 The inspection method

🔧 What "balancing by inspection" means

Balancing by inspection: adjusting coefficients in a straightforward manner by going back and forth between products and reactants until all atoms are balanced.

It is not a formal algorithm; it is a trial-and-adjustment process.
You look at the equation, spot which atoms are unbalanced, and add coefficients to fix them.
The excerpt emphasizes that this works for "simple" redox reactions.

🔄 The iterative process

Step 1: Identify which element is unbalanced.
Step 2: Add a coefficient to balance that element.
Step 3: Check if the new coefficient unbalanced another element.
Step 4: Adjust coefficients again to fix the new imbalance.
Repeat until all atoms are balanced on both sides.

Don't confuse: Balancing is not a one-step fix. Fixing one element often creates a new imbalance elsewhere, so you must iterate.

🧪 Worked examples from the excerpt

🧪 Sodium and chlorine reaction

Starting equation: Na + Cl₂ → NaCl

First observation: Chlorine atoms are not balanced (2 on the left, 1 on the right).
First fix: Put coefficient 2 in front of NaCl → Na + Cl₂ → 2NaCl
Second observation: Now sodium is unbalanced (1 on the left, 2 on the right).
Second fix: Put coefficient 2 in front of Na → 2Na + Cl₂ → 2NaCl
Result: Balanced—2 Na and 2 Cl on each side.

🧪 Sulfur dioxide and oxygen reaction

Starting equation: SO₂ + O₂ → SO₃

First observation: Sulfur is balanced (1 on each side), but oxygen is not (4 on the left, 3 on the right).
First fix: Put coefficient 2 in front of SO₃ to get more oxygen on the product side → SO₂ + O₂ → 2SO₃
Second observation: Now there are 6 oxygen atoms on the right, and sulfur is unbalanced (1 on the left, 2 on the right).
Second fix: Put coefficient 2 in front of SO₂ → 2SO₂ + O₂ → 2SO₃
Result: Balanced—2 S atoms on each side, and 6 O atoms on each side (4 from 2SO₂ plus 2 from O₂ equals 6 from 2SO₃).

Example takeaway: Balancing oxygen created a sulfur imbalance, which required another adjustment. This illustrates the back-and-forth nature of the inspection method.

🔍 Scope and limitations

🔍 When inspection is appropriate

The excerpt states that "many simple redox reactions can be balanced by inspection."
The examples given (Na + Cl₂, SO₂ + O₂) involve small molecules and straightforward stoichiometry.

🔍 When more complex methods are needed

The excerpt mentions that more complex redox reactions require the half-reaction method (not detailed in this excerpt).
The excerpt also notes that sometimes the solvent or parts of it may be used as a reactant or product in balancing (not detailed in this excerpt).
Don't confuse: Not all redox reactions can be balanced by inspection; the method works for simple cases but breaks down for more complicated reactions.

Applications of Redox Reactions: Voltaic Cells

🧭 Overview

🧠 One-sentence thesis

A voltaic cell harnesses a spontaneous redox reaction to generate electricity by physically separating the oxidation and reduction half reactions and allowing electrons to flow through an external wire, producing useful electrical work.

📌 Key points (3–5)

Physical separation enables electricity: When the two half reactions of a spontaneous redox reaction are separated into different compartments connected by a wire, electrons flow through the wire and can do useful work (light a bulb, run a motor).
Voltage from reduction potentials: The voltage of a voltaic cell is determined by combining the standard reduction potentials (E½) of the two half reactions; spontaneous reactions have positive overall voltages.
Batteries are practical voltaic cells: All batteries are based on redox reactions; different types (dry cell, alkaline, button, lead storage) use different chemistries and have different characteristics (voltage, rechargeability, size).
Common confusion—reduction potentials: All half reactions in the table are listed as reductions; to get the oxidation voltage, reverse the reaction and change the sign of E½, but do not multiply E½ even if you multiply the reaction to balance electrons.
Primary vs secondary batteries: Primary batteries (like dry cells) can only be used once; secondary batteries (like lead storage, some lithium) can be recharged and reused.

⚡ Structure and function of voltaic cells

⚡ How physical separation creates electricity

In a mixed container, the redox reaction Zn + Cu²⁺ → Zn²⁺ + Cu proceeds spontaneously but produces no usable electricity.
When the same reaction is set up with zinc/zinc ions in one compartment and copper/copper ions in another, connected by a wire, electrons transfer through the wire rather than directly.
This electron flow through the wire is electricity that can do useful work.
Example: The setup allows you to light a bulb or operate a motor as the redox reaction proceeds.

🔋 Components of a voltaic cell

Component	Definition	Role
Half cell	Individual system containing one half reaction	Houses either oxidation or reduction
Anode	Half cell where oxidation occurs	Negative electrode; electrons come from here
Cathode	Half cell where reduction occurs	Positive electrode; electrons go here
Salt bridge	Connection containing ionic solution	Maintains charge balance as electrons move
Electrodes	Anode and cathode collectively	Sites of electron transfer

Don't confuse: The anode is the negative electrode (source of electrons), while the cathode is the positive electrode (destination of electrons).

📏 Voltage and spontaneity

Voltage (E): The tendency for electrons to go from one half cell to another, expressed in volts (V).

Also called "potential."
Voltage is determined by the difference in tendencies of the individual half reactions.
Spontaneous redox reactions have positive overall voltages.
If the calculated voltage is negative, the reaction is not spontaneous as written; the reverse reaction is spontaneous instead.

📊 Standard reduction potentials

📊 The reference standard

Absolute voltages are unnecessary; only relative voltages are needed.
The hydrogen half reaction is assigned exactly 0.000 V as the reference:
- H⁺ + e⁻ → ½H₂ with E½ = 0.000 V
All other half reactions are measured relative to this standard.

Standard reduction potential (E½): The voltage of a reduction half reaction relative to the hydrogen half reaction under standard conditions (1.0 M for dissolved species, 1.0 atm for gases).

🔄 Using the table of reduction potentials

Table 14.1 lists all half reactions as reductions.
To find the voltage for an oxidation, reverse the reduction reaction and change the sign of E½.
Example: If AgCl + e⁻ → Ag + Cl⁻ has E½ = 0.222 V, then Ag + Cl⁻ → AgCl + e⁻ has E½ = −0.222 V.

➕ Calculating cell voltage

Combine the voltages of the oxidation and reduction half reactions by simple addition.
Critical rule: Do NOT multiply E½ values even if you multiply the half reaction to balance electrons.
Use the E½ values directly as listed in the table.
Example: For 2NO₃⁻ + 8H⁺ + 3Cu → 2NO + 4H₂O + 3Cu²⁺
- Reduction: NO₃⁻ + 4H⁺ + 3e⁻ → NO + 2H₂O with E½ = 0.96 V
- Oxidation: Cu → Cu²⁺ + 2e⁻ with E½ = −0.34 V
- Overall voltage: E = 0.96 + (−0.34) = 0.62 V (positive, so spontaneous)

🔋 Practical batteries

🔋 What makes a battery

Battery: A portable voltaic cell that generates electricity to power devices.

All batteries are based on redox reactions.
Only certain redox reactions are put to practical use in modern society.
Different battery types are optimized for different applications (portability, voltage, rechargeability, cost).

🪫 Primary batteries (single-use)

🪫 Dry cell (Leclanché cell)

Invented by Georges Leclanché in 1866 as a precursor to modern batteries.
Components: zinc case (anode), central carbon rod (cathode), moist paste (minimizes free liquid).
Redox reaction: Zn + 2MnO₂ + 2NH₄⁺ → Zn²⁺ + Mn₂O₃ + 2NH₃ + H₂O
Voltage: about 1.56 V
Limitations: relatively short lifetime, contains acidic components, cannot be recharged (one-use only).

🔋 Alkaline battery

Invented by Lewis Urry in the late 1950s (marketed as Energizer).
Similar to dry cells but uses a basic moist paste instead of acidic.
Redox reaction: Zn + 2MnO₂ → ZnO + Mn₂O₃
Voltage: about 1.54 V
Advantages: longer lasting, holds voltage better throughout lifetime.

🔘 Button batteries

Small batteries (can be as small as 5 mm across) for portable electronics (watches, hearing aids, gaming devices).
Common chemistries:
- Alkaline dry-cell reaction
- Silver oxide: Zn + Ag₂O → ZnO + 2Ag
- Lithium-based: Li → Li⁺ + e⁻ with E½ = 3.045 V (cathode composition varies)

🔁 Secondary batteries (rechargeable)

🔁 Lithium batteries

Some lithium-based batteries are rechargeable and can be used repeatedly.
Can be used for higher-energy applications: portable computers, electric vehicles.
Anode reaction: Li → Li⁺ + e⁻ with E½ = 3.045 V

🚗 Lead storage battery

Redox reaction: Pb + PbO₂ + 4H⁺ + SO₄²⁻ → 2PbSO₄ + 2H₂O
Voltage: about 2 V per cell (multiple cells are typically connected for higher voltage).
Unique feature: product of both half reactions is PbSO₄, which accumulates as a solid on the plates.
Characteristics: heavy (lead-based), rechargeable, should be recycled to prevent lead pollution.
Applications: starting large engines in automobiles, boats, airplanes.

⚗️ Fuel cells

⚗️ How fuel cells differ from batteries

Fuel cell: A type of battery in which reactants flow continuously into a specialized reaction chamber, products flow out continuously, and electrons are extracted from the reaction.

Unlike conventional batteries, fuel and oxidizer flow in continuously rather than being sealed inside.
All fuel cell reactions consist of a fuel and an oxidizer undergoing a redox reaction.

💧 Hydrogen-oxygen fuel cell

Most common fuel cell reaction: 2H₂ + O₂ → 2H₂O with E = 1.23 V under standard conditions
Actual operating voltage: typically 0.6–0.7 V (non-optimal conditions)
Products: only water and electricity (no pollution; water is valuable in some environments)
Historical use: provided electricity for manned space vehicles (water by-product could be used for drinking)
Other possible fuels: methane, methyl alcohol, ethyl alcohol, carbon-rich materials, magnesium metal

🚙 Fuel cells in electric vehicles

Recent resurgence of interest for use in electric cars as an alternative to heavy, expensive conventional batteries.
Example: 2008 Honda FCX (first production fuel cell vehicle)
- Capacity: 4.1 kg of highly pressurized H₂ gas
- Range: 450 km (280 mi)
- Cost: $120,000–$140,000 to build (beyond most people's ability to own)

⚠️ Current limitations

Capacity: Limited fuel storage
Cost: Very expensive to produce
Energy efficiency: Always requires more energy to produce elemental hydrogen as fuel than can be extracted from it
Energy carrier vs source: Hydrogen is an energy carrier (like electricity) rather than an energy source (like oil and gas)
Despite limitations, significant research interest continues to find ways to circumvent these barriers

Electrolysis

🧭 Overview

🧠 One-sentence thesis

Electrolysis forces nonspontaneous redox reactions to occur by introducing external electricity into a cell, enabling the isolation of elements and the electroplating of objects.

📌 Key points (3–5)

What electrolysis is: using external electricity to drive a redox reaction that would not occur spontaneously.
How it differs from voltaic cells: voltaic cells generate electricity from spontaneous reactions; electrolytic cells consume electricity to force nonspontaneous reactions.
Major applications: isolating elements (sodium, chlorine, lithium, potassium, magnesium, aluminum) from compounds and electroplating metals onto objects.
Common confusion: cathode/anode roles—in electrolytic cells, electricity is forced into the cell, reversing the spontaneous direction.
Real-world scale: aluminum electrolysis alone uses an estimated 5% of all U.S. electricity; recycling aluminum requires only 1/70th the energy of refining from ore.

⚡ What electrolysis does

⚡ Forcing the reverse reaction

Electrolytic cell: a cell in which electricity is forced through to induce a nonspontaneous redox reaction.

Electrolysis: the process that occurs in an electrolytic cell when external electricity drives a nonspontaneous redox reaction.

Normally, redox reactions that are spontaneous can generate electricity (voltaic cells).
Electrolysis reverses this: by supplying electricity from an outside source (e.g., a battery), we can make a reaction go "backward"—in the nonspontaneous direction.
Example: Sodium and chlorine spontaneously react to form NaCl. By melting NaCl and passing current through it, we force the opposite reaction: NaCl breaks down into elemental sodium and chlorine.

🔄 Contrast with voltaic cells

Cell type	Energy flow	Reaction type	Purpose
Voltaic cell	Generates electricity	Spontaneous redox	Source of electrical energy
Electrolytic cell	Consumes electricity	Nonspontaneous redox	Drive desired chemical changes

Don't confuse: both involve redox reactions, but the direction of energy flow is opposite.

🏭 Isolating elements by electrolysis

🧂 Sodium and chlorine from molten salt

When NaCl is melted at about 800°C and current is passed through:
- At the cathode: Na⁺ + e⁻ → Na (sodium metal appears)
- At the anode: 2Cl⁻ → Cl₂ + 2e⁻ (chlorine gas appears)
This forces the reverse of the spontaneous Na + Cl₂ → NaCl reaction.
Other alkali and alkaline earth metals (lithium, potassium, magnesium) are also isolated by electrolysis.

🪙 Aluminum from bauxite ore

Before 1886, aluminum was extremely rare and expensive (the Washington Monument's 2.8 kg aluminum cap was the largest piece ever isolated at the time).
The Hall-Héroult process (developed independently by Charles Hall and Paul Héroult in 1886) uses electrolysis to extract aluminum from bauxite ore (AlOₓ(OH)₃₋₂ₓ):
- Cathode: Al³⁺ + 3e⁻ → Al
- Anode: 2O²⁻ → O₂ + 4e⁻
Result: aluminum prices dropped by a factor of over 200, making aluminum common.
Energy cost: aluminum electrolysis uses an estimated 5% of all U.S. electricity annually.
Recycling saves energy: recycling aluminum requires only about 1/70th the energy of refining from ore.

🎨 Electroplating

🎨 Depositing thin metal coatings

Electroplating: the deposition of a thin layer of metal on an object for protective or decorative purposes.

How it works:
- The object to be plated is connected to the cathode of an electrolytic cell.
- The object is immersed in a solution containing cations of the plating metal.
- When current flows, metal cations are reduced to elemental metal and deposit on the object's surface.
Coating thickness: can be as thin as a few micrometers (10⁻⁶ m).

🔧 Common applications and metals

Objects electroplated: jewelry, eating utensils, electrical contacts, car parts (e.g., bumpers).
Metals commonly used: gold, silver, nickel, copper, chromium.
Purpose: protection from corrosion and/or decorative appearance.

🔋 Voltage requirements

🔋 Overcoming nonspontaneity

Because electrolytic reactions are nonspontaneous, they have negative or zero spontaneous voltage.
To drive the reaction, an external voltage must be applied that exceeds the magnitude needed to reverse the reaction.
Example from exercises:
- To electroplate copper from Cu²⁺, at least 0.34 V must be applied.
- To electroplate aluminum from Al³⁺, a higher voltage is required (aluminum is more difficult to reduce).

⚠️ Energy input is essential

Unlike voltaic cells (which produce energy), electrolytic cells consume energy.
The energy cost can be substantial, as seen with aluminum production.

Units of Radioactivity

🧭 Overview

🧠 One-sentence thesis

Radioactivity can be measured using multiple units that either count decay events per time (becquerel, curie) or quantify biological damage (rad, rem), with natural sources accounting for 82% of human radiation exposure.

📌 Key points (3–5)

Two main measurement approaches: activity units (decays per second) vs. biological-effect units (energy absorbed or tissue damage).
Activity units: becquerel (1 decay/s) and curie (3.7 × 10¹⁰ decays/s) describe how many radioactive events happen per second.
Biological units: rad measures energy absorbed by tissue; rem adjusts for emission type and tissue sensitivity.
Common confusion: rad vs. rem—rad is raw energy absorption, rem accounts for the fact that different radiation types (alpha, beta, gamma) and different tissues have different damage factors.
Most exposure is unavoidable: 82% of annual radiation comes from natural sources (radon, cosmic rays, radioactive atoms in our own bodies).

☢️ Activity units: counting decays

☢️ Becquerel (Bq)

One becquerel (Bq): one radioactive decay per second.

This is the most direct way to report radioactivity—simply count how many atoms disintegrate each second.
Even a small mass of radioactive material undergoes thousands of decays per second.
Example: if a sample has 60,000 Bq, 60,000 atoms are decaying every second.

☢️ Curie (Ci)

One curie (Ci): 3.7 × 10¹⁰ decays per second.

Originally defined as the activity of 1 gram of radium.
Named after Marie Curie (early radioactivity researcher) and Henri Becquerel (who discovered radioactivity in 1896).
Because the curie is very large, samples are often measured in microcuries (μCi) or millicuries (mCi).
Example: the americium in a smoke detector has an activity of 0.9 μCi.

🔄 Using activity over time (half-life)

Activity decreases as radioactive atoms decay.
After one half-life, activity drops to half its original value; after two half-lives, to one-quarter, and so on.
Example: radium with 16.0 mCi activity and a 1,600-year half-life will drop to 8.0 mCi after 1,600 years, 4.0 mCi after 3,200 years, 2.0 mCi after 4,800 years, and 1.0 mCi after 6,400 years (4 half-lives).
For non-integer half-lives, a more complex exponential equation is needed (referenced in the "Half-Life" section of the chapter).

🧬 Biological units: energy and damage

🧬 Rad (radiation absorbed dose)

One rad: 1 gram of tissue absorbing 0.01 joules of energy.

Measures the raw energy transferred to tissue, regardless of radiation type.
Another unit, the gray (Gy), is also used for absorption (1 Gy = 100 rad).
Example: absorbing 1 rad by 70,000 g of water (roughly a 150 lb person) raises temperature by only 0.002°C—but that energy is enough to break about 1 × 10²¹ molecular C–C bonds in the body.

🧬 Rem (röntgen equivalent man)

One rem = rad × factor, where factor ≥ 1 accounts for radiation type and tissue sensitivity.

Different emissions damage tissue differently, so rem adjusts the rad measurement.
For beta particles, factor = 1 (so rem = rad).
For alpha particles striking most tissues, factor = 10; for eye tissue, factor = 30.
A related unit, the sievert (Sv), equals 100 rem.
Example: a medical X-ray delivers about 20 millirem (mrem).

⚠️ Don't confuse rad and rem

Rad: raw energy absorbed per gram of tissue.
Rem: biologically adjusted dose that accounts for how damaging the radiation type is to specific tissues.
Alpha particles have a higher factor than beta particles because they cause more damage per unit energy.

🌍 Sources and levels of exposure

🌍 Natural vs. artificial sources

The excerpt provides a table of average annual radiation exposure:

Source	Amount (mrem)	Notes
Radon gas	200	Natural, unavoidable
Medical sources	53	Avoidable (X-rays, etc.)
Radioactive atoms in the body	39	Natural (carbon-14, potassium-40)
Terrestrial sources	28	Natural (rocks, soil)
Cosmic sources	28	Natural (from space; increases at altitude)
Consumer products	10	Avoidable
Nuclear energy	0.05	Avoidable
Total	358	82% from natural sources

82% of exposure is from natural sources we cannot avoid.
10% comes from our own bodies (radioactive isotopes like carbon-14 and potassium-40).
Flying from New York to San Francisco adds 5 mrem because planes fly above much of the atmosphere, which normally shields us from cosmic radiation.

🩺 Health effects of short-term exposure

The excerpt provides a table of effects at different exposure levels (over hours or days):

Exposure (rem)	Effect
1 (over a full year)	No detectable effect
~20	Increased risk of some cancers
~100	Damage to bone marrow, internal bleeding, decreased white blood cells
200–300	Visible skin "burns," nausea, vomiting, fatigue
>300	Loss of white blood cells, hair loss
~600	Death

Effects depend on type of radioactivity, length of exposure, and tissues exposed.
Short, intense exposure is more dangerous than the same dose spread over a long time.

🔬 Detection methods

🔬 Film badge

A piece of photographic film is worn in a badge or pen.
The film is developed regularly and compared to standard exposures to determine how much radiation the person received.
Simple and passive—no electronics needed.

🔬 Geiger counter

A gas-filled chamber (usually argon) with a thin membrane.
Radiation enters the chamber and knocks electrons off gas atoms, creating ions.
The resulting small current is detected and converted to a meter reading or audible "click."
Common portable instrument for detecting radioactivity.

🔑 Key Takeaways

Radioactivity can be expressed in activity units (becquerel, curie) that count decays per second, or biological units (rad, rem) that measure energy absorption and tissue damage.
The curie is much larger than the becquerel: 1 Ci = 3.7 × 10¹⁰ Bq.
Rem accounts for radiation type: alpha particles have a higher damage factor than beta particles.
Most human radiation exposure is natural and unavoidable: radon, cosmic rays, and radioactive atoms in our own bodies contribute 82% of the total.
Detection methods include film badges (passive exposure tracking) and Geiger counters (real-time detection via ionization).

Uses of Radioactive Isotopes

🧭 Overview

🧠 One-sentence thesis

Radioactive isotopes are useful in diverse applications—from tracing pathways and dating ancient objects to preserving food and diagnosing or treating diseases—because their radioactivity is easy to detect and their energy can be harnessed.

📌 Key points (3–5)

Two core reasons radioactive isotopes are useful: we can detect their radioactivity easily, or we can use the energy they release.
Tracers exploit detectability: radioactive atoms can be followed through structures (pipes, chemical reactions, biological processes) by tracking their radiation.
Dating relies on unchanging half-lives: radioactive decay acts like an internal clock unaffected by environmental factors, allowing age determination of rocks, artifacts, and once-living objects.
Medical applications span diagnosis and treatment: small doses image organs; large doses destroy diseased tissue.
Common confusion: irradiation of food does not make the food itself radioactive—it only kills microorganisms with radiation.

🔬 Tracers and pathway tracking

🔬 What a tracer is

Tracer: a substance that can be used to follow the pathway of that substance through some structure.

Radioactive isotopes make effective tracers because their radioactivity is easy to detect.
The key is that you can "see" where the radioactive atoms go by measuring radiation.

💧 Leak detection example

Tritium (radioactive hydrogen) can be run through underground water pipes.
A Geiger counter then locates any radioactive tritium in the ground around the pipes, revealing leaks.
Example: An organization suspects a pipe leak → runs tritium water through → detects radiation in surrounding soil → pinpoints the leak location.

🌱 Chemical reaction tracking

Radioactive atoms are incorporated into reactant molecules at the start of a reaction.
Scientists track where those atoms end up by following their radioactivity through each step.
Example: Carbon-14 was used to determine the steps of photosynthesis in plants—researchers followed the progress of carbon-14 throughout the process to map out the reaction pathway.

⏳ Radioactive dating

⏳ How radioactive dating works

The half-life of radioactive isotopes is unaffected by any environmental factors, so the isotope acts like an internal clock.
By measuring how much of the original isotope remains versus how much has decayed into a daughter isotope, scientists can calculate how many half-lives have passed.
Example: A rock contains a certain amount of uranium-235 and a certain amount of its daughter isotope. If half the uranium has decayed, the rock's age is one half-life of uranium-235, about 4.5 × 10⁹ years.

🌍 Dating the Earth and other objects

Many analyses using a wide variety of isotopes indicate the Earth itself is over 4 × 10⁹ years old.
Hydrogen-3 dating has verified the stated vintages of some old fine wines.

🦴 Carbon-14 dating of once-living artifacts

A tiny amount of carbon-14 is produced naturally in the upper atmosphere.
Living things incorporate carbon-14 into their tissues, building up to a constant (very low) level.
Once a living thing dies, it no longer acquires carbon-14; the existing carbon-14 decays over time (half-life: 5,370 years).
By comparing the remaining carbon-14 in a once-living artifact to the known constant level in living tissue, scientists can determine an approximate age.

Examples from the excerpt:

The Shroud of Turin (flax fibers, claimed by some to be 2,000 years old) was shown by carbon-14 dating to be only 600–700 years old.
A mummified body found in the ice of the Alps was dated to 5,300 years old.

Don't confuse: Carbon-14 dating only works for once-living objects; it cannot date rocks or minerals that were never alive.

🍅 Irradiation of food

🍅 How food irradiation works

Radiation emitted by some radioactive substances (e.g., cobalt-60 or cesium-137) can kill microorganisms on foodstuffs.
This extends the shelf life of products like tomatoes, mushrooms, sprouts, berries, eggs, and meat (beef, pork, poultry).
The exposure kills bacteria that cause spoilage, so produce stays fresh longer.

⚠️ Common confusion about food irradiation

Irradiation of food does NOT make the food itself radioactive.
The radiation passes through and kills microorganisms, but the food does not become a source of radiation.

🏥 Medical applications

🩺 Diagnostic uses (small doses)

Radioactive isotopes are used to diagnose illness and diseases by imaging organs.
Very little radioactive material is needed because the radiation emitted is so easy to detect.

How iodine-131 tests thyroid activity:

The thyroid gland is one of the few places in the body with significant iodine concentration.
A measured dose of iodine-131 is administered to a patient.
The next day, a scanner measures the amount of radioactivity in the thyroid gland.
The amount of radioactive iodine that collects there is directly related to thyroid activity, allowing physicians to diagnose hyperthyroidism and hypothyroidism.
Iodine-131 has a half-life of only 8 days, so potential for damage is minimal.

Other diagnostic isotopes:

Technetium-99 can test thyroid function.
Bones, heart, brain, liver, lungs, and many other organs can be imaged using appropriate radioactive isotopes.

💊 Therapeutic uses (large doses)

Therapeutic applications usually require much larger doses because their purpose is to preferentially kill diseased tissues.
Example: If a thyroid tumor is detected, a much larger infusion of iodine-131 (thousands of rem, versus a diagnostic dose of less than 40 rem) can help destroy the tumor cells.
Radioactive strontium is used to not only detect but also ease the pain of bone cancers.

☢️ Gamma ray therapy

In addition to direct application of radioactive isotopes to diseased tissue, gamma ray emissions from some isotopes can be directed toward tissue to be destroyed.
Cobalt-60 is a useful isotope for this kind of procedure.

📋 Medical isotopes summary table

Isotope	Medical Use
Phosphorus-32	Cancer detection and treatment, especially in eyes and skin
Iron-59	Anemia diagnosis
Cobalt-60	Gamma ray irradiation of tumors
Technetium-99m	Brain, thyroid, liver, bone marrow, lung, heart, and intestinal scanning; blood volume determination
Iodine-131	Diagnosis and treatment of thyroid function
Xenon-133	Lung imaging
Gold-198	Liver disease diagnosis

🍷 Wine vintage verification with cesium-137

🍷 The vintage verification problem

Wine lovers value certain vintages (years when wine grapes were grown).
Some are willing to pay much more for a bottle with a certain vintage.
But how does one verify that a bottle was in fact part of a certain vintage? Is the label fake?

☢️ How cesium-137 helps verify vintages

Cesium-137 is a radioactive isotope with a half-life of 30.1 years.
It was introduced into the atmosphere in the 1940s and 1950s by atmospheric testing of nuclear weapons.
A significant amount was released during the Chernobyl nuclear disaster in 1986.
Scientists have precise measurements of cesium-137 in the environment since 1950.
Some cesium is taken up by living plants, including grape vines.

The verification process:

Measure the current activity of cesium-137 in a wine sample (gamma rays pass through glass bottles easily—no need to open).
Compare it to the known amount of cesium-137 from the claimed vintage.
Take into account the passage of time and radioactive decay.
Collect evidence for or against the claimed vintage.

🚫 Detecting pre-1950 fakes

Before about 1950, the amount of cesium-137 in the environment was negligible.
If a wine dated before 1950 shows any measurable cesium-137 activity, it is almost surely a fake.
Example: A bottle claims to be from the 1940s but shows cesium-137 activity → it's almost definitely not over 60 years old.

Half-Life

🧭 Overview

🧠 One-sentence thesis

Half-life is the constant time it takes for half of a radioactive isotope to decay, and this property allows us to calculate how much of a substance remains after any amount of time has passed.

📌 Key points (3–5)

What half-life measures: the amount of time required for exactly one-half of a radioactive isotope to decay.
Key property: half-life is constant for each isotope—unaffected by conditions, temperature, or the initial amount present.
How decay progresses: after each half-life period, half of the remaining material decays (not half of the original amount).
Common confusion: the amount that decays in each period is half of what's currently left, not half of the starting amount—so the absolute mass decaying gets smaller each period.
Calculation methods: simple formula when time is an exact multiple of half-lives; exponential formula for any elapsed time.

⏱️ The half-life concept

⏱️ Definition and constancy

Half-life: the amount of time it takes for one-half of a radioactive isotope to decay.

This is a fixed property of each radioactive isotope.
The excerpt emphasizes that half-life is constant and independent of:
- Environmental conditions (temperature, pressure, etc.)
- The initial amount of material
Different isotopes have vastly different half-lives, ranging from microseconds to billions of years.

🔄 How decay proceeds over time

The excerpt uses tritium (hydrogen-3) as an example:

Start: 100.0 g of tritium, half-life = 12.3 years
After 12.3 y (1 half-life): 50.0 g remains
After 24.6 y (2 half-lives): 25.0 g remains
After 36.9 y (3 half-lives): 12.5 g remains

Don't confuse: Each period removes half of the current amount, not half of the original 100 g. The second half-life removes 25 g (half of 50 g), not another 50 g.

🧮 Calculating remaining amounts

🧮 When time is an exact multiple of half-lives

The excerpt provides this expression:

amount remaining = (initial amount) × (one-half) raised to the power n
Where n = the number of half-lives that have passed
This works best when n is a whole number.

Example from the excerpt: Fluorine-20 with half-life 11.0 s

Initial: 5.00 g
After 44.0 s = 4 half-lives (n = 4)
Remaining = 5.00 g × (one-half)^4 = 5.00 g × (1/16) = 0.3125 g

📐 When time is not an exact multiple

For any elapsed time, the excerpt gives a more complex formula:

amount remaining = (initial amount) × e raised to the power of [−0.693 × t / t½]
Where e = natural logarithm base (approximately 2.718)
t = elapsed time
t½ = half-life
Both t and t½ must use the same time units

Example from the excerpt: Fluorine-20 after 60.0 s

Initial: 5.00 g, half-life = 11.0 s, elapsed = 60.0 s
Result: 0.114 g remains
Note: 60.0 s is not an exact multiple of 11.0 s, so the exponential formula is needed.

📊 Half-life ranges and examples

📊 Variety across isotopes

The excerpt provides a table showing half-lives vary enormously:

Isotope	Half-Life	Notes
Seaborgium-260	4 milliseconds	Extremely short
Berkelium-248	23.7 hours	Hours scale
Iodine-131	8.04 days	Days scale
Tritium (H-3)	12.3 years	Years scale
Carbon-14	5,730 years	Thousands of years
Uranium-238	4.47 billion years	Geological timescales

🧬 Radioactivity in the human body

The excerpt notes that the human body naturally contains radioactive isotopes:

Potassium-40 and carbon-14 are the main contributors
Average human body: about 8,000 radioactive decays per second
These elements (potassium and carbon) are essential for life, so some radioactivity is unavoidable
Debate: Potassium-40 has more mass and longer half-life with higher energy per decay; carbon-14 is more likely near critical molecules like DNA
The excerpt concludes we should minimize excess exposure but cannot eliminate natural radioactivity entirely.

Radioactivity

🧭 Overview

🧠 One-sentence thesis

Radioactivity is the spontaneous emission of particles (alpha, beta) and electromagnetic radiation (gamma rays) from unstable atomic nuclei, with each type having distinct properties and penetration abilities.

📌 Key points (3–5)

Three major types of radioactive emission: alpha particles (helium nuclei), beta particles (electrons from the nucleus), and gamma rays (high-energy electromagnetic radiation).
Nuclear equations track decay: the sum of atomic numbers and mass numbers must be conserved on both sides of the equation.
Different penetration depths: alpha particles are easily stopped by matter, beta particles penetrate slightly, and gamma rays penetrate deeply.
Common confusion: beta particles are electrons, but they come from the nucleus (neutron converting to proton), not from electron shells around the nucleus.
Parent and daughter isotopes: the original radioactive atom is the parent; the resulting atom after decay is the daughter.

⚛️ Types of radioactive emissions

🔴 Alpha particles

An alpha particle is composed of two protons and two neutrons and is the same as a helium nucleus.

Symbolized by α or represented as helium-4 nucleus
Has a 2+ charge
Effect on parent nucleus: atomic number decreases by 2, mass number decreases by 4
Example: Uranium-235 decays to thorium-231 plus an alpha particle
Penetration: minimal; will not penetrate skin; easily stopped by matter

🔵 Beta particles

A beta particle is an electron ejected from the nucleus (not from the shells of electrons about the nucleus) and has a 1− charge.

Symbolized by β or represented with atomic number −1
Net effect: a neutron converts to a proton inside the nucleus
Effect on parent nucleus: mass number stays the same, atomic number increases by 1
Example: Carbon-14 decays to nitrogen-14 plus a beta particle
Don't confuse: beta particles are electrons, but they originate from nuclear transformation, not from orbital electrons
Penetration: short; will penetrate skin and some tissues slightly (a few centimeters at most)

🟢 Gamma rays

Gamma rays are very energetic electromagnetic radiation, symbolized by γ.

Not particles but electromagnetic radiation
Carry no overall electrical charge
Often emitted simultaneously with alpha or beta particles
Example: Radon-222 emits both an alpha particle and a gamma ray with energy of 8.2 × 10⁻¹⁴ J per nucleus
Ionizing radiation: can knock electrons out of atoms, making matter electrically charged
Penetration: deep; will penetrate tissues deeply

📐 Nuclear equations and conservation

⚖️ Conservation laws

Matter is conserved: the same number of protons and neutrons must appear on both sides
Atomic number sum: must be equal on both sides
Mass number sum: must be equal on both sides
Example: In alpha decay of uranium-235, the equation is balanced because 235 = 231 + 4 and 92 = 90 + 2

🏷️ Parent and daughter isotopes

Parent isotope: the original radioactive atom before decay
Daughter isotope: the product atom after radioactive decay (excluding the emitted particle)
Example: When radon-222 emits an alpha particle, radon-222 is the parent and polonium-218 is the daughter
The process of one element changing into another is called radioactive decay

💥 Spontaneous fission

💥 What fission is

Spontaneous fission (or fission): an atomic nucleus breaks apart into smaller pieces.

Found only in large nuclei; the smallest nucleus that exhibits spontaneous fission is lead-208
Different from alpha/beta decay: produces a varied mix of daughter isotopes rather than a specific isotope
Often produces excess neutrons that may be captured by other nuclei, possibly inducing additional radioactive events
Example: Uranium-235 can split into barium-141, krypton-92, and three neutrons
Used in nuclear power plants and one type of nuclear bomb

📊 Comparison of emission types

Characteristic	Alpha Particles	Beta Particles	Gamma Rays
Symbols	α, helium-4	β, electron notation	γ
Identity	Helium nucleus	Electron	Electromagnetic radiation
Charge	2+	1−	None
Mass number	4	0	0
Penetrating power	Minimal (will not penetrate skin)	Short (will penetrate skin and some tissues slightly)	Deep (will penetrate tissues deeply)

🛡️ Protection implications

Alpha particles: easily stopped by matter; minimal penetration
Beta particles: moderate penetration; can enter skin and some tissues
Gamma rays: deep penetration; can impart large amounts of energy to surrounding matter

Nuclear Energy

🧭 Overview

🧠 One-sentence thesis

Nuclear reactions release billions of kilojoules per mole by converting tiny amounts of mass into energy, far exceeding the energy output of chemical reactions like hydrocarbon combustion.

📌 Key points (3–5)

Mass-energy conversion: Nuclear reactions convert a small mass difference between reactants and products into enormous amounts of energy via Einstein's equation E = mc².
Fission vs fusion: Fission breaks large nuclei apart (e.g., uranium-235); fusion combines small nuclei (e.g., hydrogen into helium); both release energy.
Energy scale: Nuclear reactions release billions of kJ/mol, while chemical reactions (like hydrocarbon combustion) release only hundreds of kJ/mol.
Common confusion: Fission and fusion both release energy but work oppositely—fission splits large nuclei, fusion merges small ones.
Controlled vs uncontrolled: Nuclear reactors control fission for electricity; chain reactions in atomic bombs are uncontrolled exponential processes.

⚛️ Where nuclear energy comes from

🔬 Mass-energy equivalence

Energy (E) and mass (m) are related by Einstein's equation: E = mc², where c is the speed of light (3.00 × 10⁸ m/s).

In nuclear reactions, the total mass of products is slightly less than the mass of reactants.
This "missing" mass is converted into energy.
Example: When 1 mol of uranium-235 undergoes fission, the mass drops by 0.0001834 kg, releasing 16.5 billion kJ of energy.

📊 Nuclear vs chemical energy comparison

Reaction type	Energy per mole	Scale
Chemical (hydrocarbon combustion)	~650 kJ/mol per CH₂ unit	Hundreds of kJ
Nuclear (uranium-235 fission)	16.5 billion kJ/mol	Billions of kJ

Nuclear reactions are orders of magnitude more energetic than chemical reactions.
On a per-gram basis, hydrogen fusion releases 10 times more energy than uranium fission.

💥 Fission: Breaking large nuclei

⚙️ How fission works

Nuclear fission: The breaking down of large nuclei into smaller nuclei, usually with the release of excess neutrons.

Large unstable nuclei (like uranium-235 or plutonium-239) can be split by injecting a neutron.
The nucleus breaks into smaller fragments plus additional neutrons.
Example reaction: Uranium-235 + neutron → smaller nuclei + neutrons + energy.

🔗 Chain reactions

Each fission event typically produces more neutrons than it consumes (uranium fission averages two extra neutrons).
These neutrons can trigger more fission events, creating exponential growth: 1 → 2 → 4 → 8 → 16 → 32...
Don't confuse: Controlled chain reactions (nuclear reactors) vs uncontrolled chain reactions (atomic bombs).

⚡ Nuclear reactors

A nuclear reactor: An apparatus designed to carefully control the progress of a nuclear reaction and extract the resulting energy for useful purposes.

Reactors control the fission rate by carefully managing neutron injection.
Energy from fission converts water into high-pressure steam.
Steam drives turbines that generate electricity.
The overall process: controlled nuclear reaction → heat → steam → turbine → electricity.

💣 Atomic bombs

An atomic bomb uses an uncontrolled chain reaction.
Energy production grows exponentially, creating an explosion.
Requires highly enriched uranium (70%+ uranium-235) to sustain the chain reaction.
Natural uranium is only 0.7% uranium-235; nuclear reactors use uranium enriched to ~3%.

🌟 Fusion: Combining small nuclei

🔥 How fusion works

Fusion: A nuclear process in which small nuclei are combined into larger nuclei, releasing energy.

Small nuclei merge to form larger ones.
Example: Hydrogen fusion creates helium: 2 hydrogen nuclei → 1 helium nucleus + energy.
Per mole of reactant, fusion releases one-tenth the energy of uranium fission.
Per gram, fusion releases 10 times more energy than fission.

⭐ Fusion advantages and challenges

Advantages:

Product is helium gas (not a mix of radioactive isotopes like fission produces).
Higher energy output per gram of fuel.

Challenges:

Requires extremely high pressures and temperatures.
Currently only occurs naturally in stars (like the sun).
Controlled fusion for energy use remains a research goal.

💥 Fusion weapons

Hydrogen bombs use uncontrolled fusion.
An atomic bomb creates the extreme conditions needed to trigger fusion.
Researchers seek safe, controlled fusion methods for peaceful energy production.

🧮 Calculating nuclear energy

📐 The calculation process

Add masses of all reactants.
Add masses of all products.
Find the mass difference (products minus reactants).
Convert mass to kilograms.
Apply E = mc² to find energy released.

🔢 Example calculation

For plutonium-239 fission, if the mass change is negative (products lighter than reactants), energy is released.
A mass loss of even a fraction of a gram produces trillions of joules.
Example: A mass loss of 0.1002 g per mole of lead-208 releases 9.02 × 10¹² J.

Don't confuse: Mass loss means energy release; the "lost" mass becomes energy, it doesn't disappear.

Hydrocarbons

🧭 Overview

🧠 One-sentence thesis

Hydrocarbons—the simplest organic compounds made only of carbon and hydrogen—are classified into aliphatic types (alkanes, alkenes, alkynes) and aromatic compounds, with combustion being their most important reaction and primary energy source for society.

📌 Key points (3–5)

What hydrocarbons are: compounds composed of only carbon and hydrogen, divided into aliphatic (chain-based) and aromatic (ring-based) types.
Three aliphatic types: alkanes (single bonds only), alkenes (at least one C–C double bond), and alkynes (C–C triple bond).
Saturated vs unsaturated: alkanes have the maximum possible hydrogen atoms (saturated); alkenes and alkynes have fewer hydrogen atoms (unsaturated).
Common confusion: isomers—molecules like 1-butene and 2-butene have the same molecular formula but different structures and properties because the double bond is in different positions.
Why they matter: combustion of hydrocarbons is the primary energy source in modern society.

🔗 Types and structures of hydrocarbons

🔗 Two main categories

Hydrocarbons: compounds composed of only two elements—carbon and hydrogen.

The excerpt divides hydrocarbons into:

Aliphatic hydrocarbons: based on chains of carbon atoms
Aromatic hydrocarbons: flat-ring systems with continuously overlapping p orbitals (like benzene)

⛓️ Aliphatic hydrocarbons: three types

Type	Bond characteristic	Saturation status	Example
Alkanes	Only single C–C bonds	Saturated (maximum H atoms)	Methane (CH₄), ethane (C₂H₆)
Alkenes	At least one C–C double bond	Unsaturated	Ethene/ethylene (C₂H₄), propene
Alkynes	C–C triple bond	Unsaturated	Ethyne/acetylene, propyne

Don't confuse: cycloalkanes (or cycloalkenes/cycloalkynes) are aliphatic hydrocarbons arranged in rings, not chains, but they are still aliphatic, not aromatic.

🔵 Aromatic hydrocarbons

Aromatic hydrocarbons: flat-ring systems that contain continuously overlapping p orbitals, giving special energetic properties.

Benzene is the key example: six carbon atoms in a ring with alternating single and double bonds.
The term "aromatic" originally meant "fragrant," but in modern chemistry it denotes a very stable ring structure.
Aromatic compounds have markedly different physical and chemical properties from alkanes.
The special stability means benzene does not react like a typical alkene.

📛 Naming and numbering systems

📛 Alkane naming pattern

The excerpt presents the first 10 alkanes with a systematic naming pattern:

Parent chain: indicates the number of carbon atoms (meth-, eth-, prop-, but-, pent-, hex-, hept-, oct-, non-, dec-)
Suffix: -ane for alkanes
Examples: methane (1 C), ethane (2 C), propane (3 C), butane (4 C), pentane (5 C)

📛 Alkene and alkyne naming

Alkenes: same parent chain as alkanes but suffix changes to -ene
- Example: ethene (also called ethylene), propene (also called propylene)
Alkynes: same parent chain but suffix is -yne
- Example: ethyne (also called acetylene), propyne

🔢 Locants: numbering positions

Locant: a number between the parent-chain name and suffix that indicates on which carbon atom a distinguishing feature (like a double or triple bond) originates.

The lowest possible number must be used.
Example: 1-butene has the double bond between the first and second carbons; 2-butene has it between the second and third carbons.
When the feature is on the first carbon, some authors omit the locant (e.g., "butene" implies "1-butene").
Don't confuse: calling 2-butene "3-butene" would be incorrect because you must use the lowest number.

🧬 Isomers

Isomers: different molecules with the same molecular formula.

1-butene and 2-butene both have the formula C₄H₈, but the double bond is in different positions.
Isomers have different physical and chemical properties despite identical molecular formulas.
The excerpt notes that isomers are common in organic chemistry and contribute to its complexity.

🧪 Properties and reactions

🧪 Physical properties

Polarity: most hydrocarbons are nonpolar because carbon and hydrogen have close electronegativities.
Solubility: they dissolve only sparingly in water and other polar solvents.
Physical state at room temperature:
- Small hydrocarbons (methane, ethane): gases
- Larger hydrocarbons (hexane, octane): liquids
- Even larger hydrocarbons (e.g., hentriacontane, C₃₁H₆₄): solids with soft, waxy consistency

⚗️ Substitution reactions

Hydrocarbons can undergo substitution with halogen atoms:

A halogen element combines with a hydrocarbon.
Light is sometimes used to promote the reaction.
Example: methane + chlorine → a substituted product (the excerpt shows CH₄ reacting with Cl₂).

➕ Addition reactions

Addition reaction: halogen molecules react with C–C double or triple bonds and attach onto each carbon atom involved in the multiple bonds.

Halogens react with alkenes and alkynes differently than with alkanes.
Reaction conditions are usually mild; in many cases, the halogen reacts spontaneously.
Don't confuse: this is different from substitution—addition involves breaking a multiple bond and adding atoms to both carbons, not replacing hydrogen.

🔬 Hydrogenation reactions

Hydrogenation reaction: hydrogen is added across a multiple bond.

Reaction conditions may not be mild; high pressures of H₂ gas may be necessary.
A platinum or palladium catalyst is usually employed to get the reaction to proceed at a reasonable pace.
Example: an alkene reacts with H₂ to form an alkane.

🔥 Combustion reactions

Most common and important reaction:

Combination of a hydrocarbon with O₂ to make CO₂ and H₂O.
Accompanied by a release of energy.
Primary source of energy production in our society.
Example: gasoline (represented as C₈H₁₈) combusts with oxygen to produce carbon dioxide and water.

The excerpt emphasizes that combustion of hydrocarbons is a primary energy source, making this reaction particularly significant beyond just chemistry.

Branched Hydrocarbons

🧭 Overview

🧠 One-sentence thesis

Branched hydrocarbons require a systematic naming system (IUPAC nomenclature) that identifies the longest carbon chain, numbers it to give substituents the lowest positions, and combines substituent names with the parent hydrocarbon name to create unique identifiers for each molecule.

📌 Key points (3–5)

What branched hydrocarbons are: alkanes with carbon atom branches attached to a main chain; they are isomers of straight-chain alkanes with the same number of carbons but different structures and properties.
Core naming principle: identify the longest continuous carbon chain (parent chain), name branches (substituents) with -yl endings, and number positions to give substituents the lowest possible numbers.
Multiple substituents: use numerical prefixes (di-, tri-, tetra-) for identical substituents and list different substituents alphabetically with their position numbers.
Common confusion: the longest chain may not be drawn in a straight line—you must identify the actual longest continuous chain, which determines the parent name.
Bond-line structures: organic molecules are commonly drawn with hydrogens omitted and carbons represented by corners or kinks in lines for clarity.

🏗️ Structural identification and parent chains

🔗 Finding the parent chain

Parent chain: the longest continuous chain of carbon atoms in the molecule.

The parent chain determines the base name of the hydrocarbon (e.g., six carbons = hexane, seven carbons = heptane).
Critical point: the longest chain may not be drawn in a straight line—you must trace through the structure to find it.
Example: A molecule might appear to have six carbons in a row, but if you trace carefully, the longest continuous chain might actually be seven carbons.
Don't confuse: the visually obvious horizontal line with the actual longest chain—always count carefully.

🌿 Identifying substituents (branches)

Substituents (or alkyl groups): branches attached to the main chain, named by replacing the -ane ending of the parent hydrocarbon with -yl.

Number of Carbons	Substituent Formula	Substituent Name
1	CH₃	methyl-
2	CH₃CH₂	ethyl-
3	CH₃CH₂CH₂	propyl-
4	CH₃CH₂CH₂CH₂	butyl-
5	CH₃CH₂CH₂CH₂CH₂	pentyl-

Substituents are the branches that stick off the main chain.
Each substituent gets a name based on how many carbons it contains.

🔢 Numbering and naming rules

📍 Using locants (position numbers)

Locant: the numerical position of a substituent on the parent chain.

Number the parent chain to give substituents the lowest possible numbers.
The position number is followed by a hyphen, then the substituent name, then the parent name (e.g., 3-methylpentane).
Example: If a methyl group can be on position 3 (counting from the left) or position 3 (counting from the right), choose the direction that gives the lowest number overall when multiple substituents are present.

🔤 Naming with multiple substituents

When substituents are different:

Give each substituent a position number.
List substituents in alphabetical order (ignoring numerical prefixes like di-, tri-).
Separate numbers with commas; separate numbers from words with hyphens.
Example: 3-ethyl-2-methylpentane (ethyl comes before methyl alphabetically).

When substituents are identical:

Use the substituent name only once.
List all position numbers separated by commas.
Add a numerical prefix before the substituent name:

Number of Same Substituent	Prefix
2	di-
3	tri-
4	tetra-
5	penta-

Example: 2,3-dimethylbutane means two methyl groups at positions 2 and 3 on a butane chain.
Don't confuse: the number of position values must match the numerical prefix (e.g., "2,3-di" has two positions for "di-").

🎯 General naming format

The excerpt provides a systematic format:

Substituents: what is attached and where (with position numbers and prefixes).
Parent chain: how many carbons in the longest chain (determines -ane, -ene, or -yne).
Suffix: indicates the type of hydrocarbon (alkane, alkene, or alkyne).

No spaces in the final name.
Numbers are separated by commas; numbers and words by hyphens.

🖊️ Special cases and conventions

🔗 Alkenes and alkynes

The longest chain must contain the carbon-carbon double or triple bond.
When numbering, the double or triple bond gets the lowest possible number.
This takes priority over substituent positions—the chain may be numbered differently than if it were an alkane.
Example: 2,4-dimethyl-3-heptene—the "3" indicates where the double bond starts, and this takes precedence.

🖼️ Bond-line structures

Bond-line structures: simplified representations where hydrogens are omitted and carbons are shown as corners or kinks in lines.

Any unwritten covalent bonds are understood to be bonds with hydrogen atoms.
This simplifies drawing and reading organic structures.
Example: A zigzag line with a branch represents a carbon backbone; each corner is a carbon atom.

🌸 Benzene-containing molecules

Single substituent:

Name the substituent as a side chain on benzene (e.g., ethylbenzene).

Multiple substituents:

Number the benzene ring starting with the substituent that comes first alphabetically at position 1.
Number around the ring to give other substituents the lowest possible numbers.

Benzene as a substituent:

Phenyl-: the name given to a benzene ring when it acts as a substituent on a longer aliphatic chain.

If the aliphatic chain has more carbons than the benzene ring, treat benzene as a substituent.
Example: 4-phenylheptane means a benzene ring attached at position 4 of a seven-carbon chain.

✏️ Drawing structures from names

🏗️ Step-by-step construction

Draw the parent chain: create the correct number of carbon atoms for the parent name (e.g., heptane = 7 carbons).
Add double/triple bonds: if the name includes -ene or -yne, place the bond at the specified position.
Attach substituents: add branches at the numbered positions indicated in the name.
Complete with hydrogens (optional): add H atoms so each carbon has four covalent bonds total.

Start with the carbon backbone, then fill in details.
Example: From "2,3-dimethyl-4-propyl-2-heptene," draw a seven-carbon chain with a double bond starting at carbon 2, then add two methyl groups (at positions 2 and 3) and one propyl group (at position 4).

⚠️ Common pitfall

Don't confuse: the visual layout of the name with the actual structure—always count carbons carefully and place substituents at the correct numbered positions.
The name encodes the structure precisely; follow the numbers exactly.

Alkyl Halides and Alcohols

🧭 Overview

🧠 One-sentence thesis

Alkyl halides and alcohols are organic compounds defined by their functional groups—halogen atoms or OH groups—that follow systematic naming rules and undergo characteristic elimination reactions to form alkenes.

📌 Key points (3–5)

Functional groups define compound classes: a halogen atom (F, Cl, Br, I) makes an alkyl halide; a covalently bonded OH group makes an alcohol.
Two naming systems exist: a common system (e.g., "methyl chloride," "ethyl alcohol") and a systematic IUPAC system using substituent names and position numbers.
Solubility patterns differ: smaller alcohols dissolve well in water due to hydrogen bonding, but larger alcohols and most alkyl halides are insoluble.
Elimination reactions remove functional groups: alkyl halides use a strong base catalyst, alcohols use a strong acid catalyst, and both produce alkenes by removing HX or H₂O.
Common confusion: the OH group in alcohols is covalently bonded, not the hydroxide ion (OH⁻) from inorganic chemistry.

🔬 Functional groups and definitions

🧪 What is a functional group

Functional group: any collection of atoms and/or bonds with certain characteristic chemical reactions.

Not just the atoms themselves, but the specific reactivity they bring to a molecule.
Examples already covered: C–C double bonds and C–C triple bonds undergo addition reactions.
The excerpt introduces two new functional groups: halogen atoms and the OH group.

🧂 Alkyl halides

Alkyl halides: organic compounds that contain a halogen atom (F, Cl, Br, or I).

The halogen is represented generically as "X" in formulas.
These compounds form when halogens add across double or triple bonds.
Example: CH₃Cl, CH₃CH₂Br, CH₃CH₂CH₂I are all alkyl halides.

🍷 Alcohols

Alcohol functional group: a covalently bonded OH group.

Don't confuse: this is not the hydroxide ion (OH⁻); it is covalently attached to a carbon chain.
Example: CH₃OH, CH₃CH₂OH, CH₃CH₂CH₂OH are all alcohols.
The OH group is polar and can form hydrogen bonds with water.

📛 Naming alkyl halides

📛 Common naming system

Name the alkyl group (with -yl suffix) + name the halogen as if it were an anion.
Example: CH₃Cl = methyl chloride; CH₃CH₂Br = ethyl bromide; CH₃CH₂CH₂I = propyl iodide.
Limitation: this system does not work well for more complicated branched molecules.

🔢 Systematic IUPAC naming

Treat the halogen as a substituent on the main carbon chain.
Halogen substituent names: fluoro-, chloro-, bromo-, iodo-.
Use numbers to show the position of the halogen on the longest chain.
Example: 2-bromobutane has a bromine on the second carbon of a four-carbon chain.
For multiple halogens: use numerical prefixes (di-, tri-) and list positions, e.g., 2,3-dichloropentane.
When both alkyl groups and halogens are present, list substituents alphabetically (ignoring numerical prefixes like "di-" or "tri-").

🍺 Naming alcohols

🍺 Common naming system

Name the alkyl group (with -yl suffix) + the word "alcohol."
Example: CH₃OH = methyl alcohol; CH₃CH₂OH = ethyl alcohol; CH₃CH₂CH₂OH = propyl alcohol.
This system is very common in everyday usage for smaller alcohols.

🔢 Systematic IUPAC naming

Use the hydrocarbon name, drop the final -e, and add the suffix -ol.
Example: CH₃OH = methanol; CH₃CH₂OH = ethanol.
For larger molecules, use a number to indicate the OH position on the longest carbon chain.
Number the chain to give the OH group the lowest possible number.
Example: CH₃CH₂CH₂OH = 1-propanol; CH₃CHOHCH₃ = 2-propanol.

🔄 Alternative naming approach

Name the OH group as a "hydroxy" substituent with a numerical position, just like an alkyl group.
Example: 2-propanol can also be called 2-hydroxypropane.
Useful for more complicated molecules with multiple functional groups.

💧 Solubility patterns

💧 Water solubility differences

Compound type	Solubility in water	Reason
Most alkyl halides	Insoluble	Nonpolar; cannot hydrogen bond effectively
Smaller alcohols	Very soluble (all proportions for methanol)	Polar OH group can hydrogen bond with water
Larger alcohols	Low solubility (e.g., ~2.6 g pentanol per 100 g water)	Nonpolar alkyl part overwhelms the polar OH group

The excerpt emphasizes that as alcohol molecules get larger, the nonpolar carbon chain dominates and solubility drops.
Example: methanol mixes with water in any proportion, but pentanol and larger alcohols dissolve poorly.

⚗️ Elimination reactions

⚗️ What elimination removes

Elimination reaction: the removal of the functional group (either X or OH) and an H atom from an adjacent carbon.

General pattern: a functional group and a hydrogen from a neighboring carbon are removed, forming a double bond.
The result is an alkene (a molecule with a C=C double bond).
The removed atoms form either HX (for alkyl halides) or H₂O (for alcohols).

🔥 Catalyst differences

Alkyl halides: require a strong base as catalyst.
Alcohols: require a strong acid as catalyst.
Don't confuse: same reaction type, but opposite catalyst conditions.

🧪 Product mixtures

If H atoms are present on more than one adjacent carbon, a mixture of products can form.
Example: elimination from a molecule with multiple possible H atoms will produce different alkene isomers.
The excerpt shows that removing H₂O from an alcohol produces an alkene, such as propene from a three-carbon alcohol.

Other Oxygen-Containing Functional Groups

🧭 Overview

🧠 One-sentence thesis

Oxygen-containing functional groups—aldehydes, ketones, carboxylic acids, esters, and ethers—each have distinct structures and naming conventions that determine their chemical behavior and practical applications.

📌 Key points (3–5)

Carbonyl group foundation: aldehydes and ketones both contain a C=O double bond, but aldehydes have it at the end of a carbon chain (bonded to H), while ketones have it in the middle (bonded to two C atoms).
Carboxylic acids are weak acids: despite their name, all carboxylic acids are weak acids (not on the strong acid list), with dissociation percentages typically under 2% in solution.
Ester formation: esters form when a carboxylic acid and an alcohol combine, removing a water molecule and creating a new functional group with pleasant odors/flavors.
Common confusion—carbonyl position: don't confuse aldehydes (carbonyl at chain end, suffix -al) with ketones (carbonyl in middle, suffix -one); position determines classification.
Naming patterns: each functional group has specific IUPAC naming rules (aldehydes: -al, ketones: -one, carboxylic acids: -oic acid, esters: alkyl + carboxylate name).

🔬 Carbonyl-based functional groups

🧪 The carbonyl group core

Carbonyl group: an oxygen atom and a carbon atom joined by a double bond (C=O).

This C=O structure is the foundation for both aldehydes and ketones.
The R group represents any hydrocarbon chain attached to the carbonyl carbon.
What differs between aldehydes and ketones is what else bonds to the carbonyl carbon.

🔚 Aldehydes: carbonyl at the end

Aldehyde: a molecule where one bond of the carbonyl group is made to a hydrogen atom.

Key structural feature: the carbonyl group is always at the end of a carbon chain.
Naming rules:
- The main chain must include the carbonyl carbon, numbered as position 1.
- Use the parent hydrocarbon name with suffix -al.
- Example: methanal (common name: formaldehyde), ethanal, propanal.
Don't confuse: -al (aldehyde) with -ol (alcohol suffix).

⚗️ Ketones: carbonyl in the middle

Ketone: a molecule where both remaining bonds of the carbonyl group are made to carbon atoms.

Key structural feature: the carbonyl group is in the middle of a carbon chain, not at the end.
Naming rules:
- Use the parent hydrocarbon name with suffix -one.
- For larger ketones, use a locant number before the suffix to indicate carbonyl position.
- Example: propanone (common name: acetone), butan-2-one.
Alternate naming method: name the alkyl groups attached to the carbonyl + the word "ketone."
- Example: propanone = dimethyl ketone; butan-2-one = methyl ethyl ketone.
Minimum size: the smallest ketone has three carbon atoms.

🔍 Aldehyde vs ketone comparison

Feature	Aldehyde	Ketone
Carbonyl position	End of chain	Middle of chain
Bonded to carbonyl	One H atom, one C chain	Two C chains
Suffix	-al	-one
Example	Propanal	Propanone
Common confusion	Don't confuse with alcohols (-ol)	Don't confuse position with aldehydes

Despite having the same carbonyl group, aldehydes and ketones have different chemical and physical properties.
They are properly grouped as two different types of compounds.

🍋 Carboxylic acids and their behavior

🧬 The carboxyl group structure

Carboxyl group: the combination of a carbonyl functional group and a hydroxyl group.

Carboxylic acids: molecules with a carboxyl group.

Structural position: the functional group is at the end of a carbon chain (like aldehydes).
Naming rules:
- The carbon in the functional group counts as one of the carbons defining the parent name.
- Use the parent hydrocarbon name with suffix -oic acid.
- Example: methanoic acid (formic acid), ethanoic acid (acetic acid).

💧 Weak acid behavior

Key fact: all carboxylic acids are weak acids—none appear on the strong acid list.
Dissociation percentages:
- 1 M formic acid solution: only about 1.3% dissociated into H⁺ ions and formate ions.
- 1 M acetic acid solution: only about 0.4% ionized.
- Trichloroacetic acid (stronger example): about 45% dissociated.
- No carboxylic acid reaches 100% dissociation (required for strong acid classification).
Don't confuse: "carboxylic acid" name suggests strong acidity, but they are actually weak acids.

⚡ Reaction with bases

Carboxylic acids do act like acids in the presence of bases.
The H atom in the carboxyl group comes off as H⁺ ion, leaving a carboxylate ion.
Naming carboxylate ions: replace -oic acid with -oate.
- Example: ethanoic acid → ethanoate ion (commonly called acetate ion).
- Example: methanoic acid → methanoate ion (commonly called formate ion).

Example: When ethanoic acid reacts with OH⁻, the hydroxide ion removes the H atom from the carboxyl group, forming the acetate ion and water.

🌿 Real-world examples

Formic acid (methanoic acid): the compound that makes certain ant bites sting.
Acetic acid (ethanoic acid): the active substance in vinegar.

🌸 Esters: formation and applications

🔗 Ester formation reaction

Ester: a functional group formed when a carboxylic acid and an alcohol combine under proper conditions.

Reaction mechanism: a water molecule (HOH) is removed, and the remaining pieces combine.
Structure contribution:
- The acid molecule contributes one alkyl side (R).
- The alcohol contributes the other side (R′).
Naming esters: alkyl group name from the alcohol + carboxylate name from the acid.
- Example: methyl propanoate (from methanol + propanoic acid).

🌺 Fragrances and flavorings

Many esters have pleasant odors and flavors.
Many occur naturally and contribute to the fragrance of flowers and taste of fruits.
Industrially synthesized esters are added to food products as artificial flavorings.

Common esters and their scents/tastes:

Ester	Tastes/Smells Like
Allyl hexanoate	Pineapple
Benzyl acetate	Pear
Butyl butanoate	Pineapple
Ethyl butanoate	Banana
Ethyl hexanoate	Pineapple
Ethyl pentanoate	Apple
Isobutyl formate	Raspberry
Isobutyl acetate	Pear
Methyl phenylacetate	Honey
Pentyl acetate	Apple
Propyl ethanoate	Pear
Propyl isobutyrate	Rum

If a food product's ingredients include "artificial flavorings," those flavorings are likely esters.

🔗 Ethers: structure and naming

🧩 Ether functional group

Ether: a functional group consisting of an oxygen atom bonded to two organic groups.

Structure: R–O–R′ (the two R groups may be the same or different).
Naming method: similar to the alternate way of naming ketones.
- Name the R groups sequentially.
- Append the word "ether."
- Example: CH₃OCH₃ = dimethyl ether.
- Example: CH₃OCH₂CH₃ = methyl ethyl ether.

🏥 Historical and practical uses

Diethyl ether: once used as an anesthetic, but fell out of favor due to flammability and toxicity.
Smaller ether molecules (liquids at room temperature): common solvents for organic chemical reactions.

Other Functional Groups

🧭 Overview

🧠 One-sentence thesis

Functional groups containing nitrogen (amines and amides) and sulfur (thiols) are essential building blocks in organic chemistry that exhibit characteristic behaviors such as base activity, protein formation, and distinctive odors.

📌 Key points (3–5)

Nitrogen-containing groups: amines act as weak bases by accepting protons; amides form when amines combine with carboxylic acids, creating bonds crucial to protein structure.
Classification of amines: primary (one H substituted), secondary (two H substituted), and tertiary (three H substituted) based on how many hydrogen atoms from ammonia are replaced by organic groups.
Sulfur-containing groups: thiols are the sulfur analogs of alcohols; they often have strong odors and can form disulfide bonds important in protein structure.
Common confusion: don't confuse amines (nitrogen derivatives of ammonia that act as bases) with amides (combinations of amine and carbonyl groups that form structural bonds).
Biological importance: these functional groups are fundamental to amino acids and proteins, which are necessary components of all life.

🔬 Nitrogen-containing compounds

🔬 Amines: structure and classification

Amine: an organic derivative of ammonia (NH₃) where one or more hydrogen atoms are substituted with organic groups.

The excerpt distinguishes three types based on substitution:

Type	Definition	Structure pattern
Primary	One H atom substituted with R group	R–NH₂
Secondary	Two H atoms substituted with R groups	R–NH–R
Tertiary	All three H atoms substituted with R groups	R–N(R)–R

Naming: List the R groups as substituents and add the suffix "-amine," using alphabetical order.

Example: A molecule with methyl, ethyl, and propyl groups attached to nitrogen is named ethylmethylpropylamine.

🧪 Amines as bases

Amines act as Brønsted-Lowry bases because the nitrogen atom can accept a proton onto its lone electron pair, just like ammonia does.

The amine accepts a proton and becomes an ion (the organic counterpart of the ammonium NH₄⁺ ion).
All amines are weak bases with strength similar to carboxylic acids.
N-containing organic compounds are very common in nature and all act as weak bases.

Don't confuse: The base behavior is about accepting protons, not donating them.

🧬 Amides: formation and importance

Amide functional group: a combination of an amine group and a carbonyl group.

How amides form:

An amine-containing molecule combines with a carboxylic acid-containing molecule.
A water molecule (H₂O) is lost in the process, similar to ester formation.
The bond between the nitrogen of the amine group and the carbon of the carbonyl group is called an amide bond.

Biological significance:

Amide bonds are particularly important in proteins.
Proteins are composed of strings of amino acids (molecules with both an amine group and a carboxylic acid group).
The amine group on one amino acid reacts with the carboxylic acid group of another, making a chain held together by amide bonds.

Example: When ethylamine combines with butanoic acid, they lose H₂O and the nitrogen bonds to the carbonyl carbon, forming an amide.

🧪 Sulfur-containing compounds

🧪 Thiols: sulfur analogs of alcohols

Thiol: the sulfur analog of an alcohol, where a sulfur atom takes the place of an oxygen atom.

Naming:

Formal method: similar to alcohols, but use the suffix "-thiol" instead of "-ol."
Older system: uses the word "mercaptan," similar to how "alcohol" is used with small alcohols.

👃 Odor characteristics

Many thiols have strong, objectionable odors:

Skunk spray is composed of thiols and is detectable by humans at concentrations less than 10 parts per billion.
Thiols are intentionally added to natural gas (which is odorless) at very low levels so gas leaks can be detected.
Not all thiols smell bad: grapefruit mercaptan is responsible for the odor of grapefruit.

🔗 Disulfide bonds in proteins

Cysteine's role:

Cysteine is an amino acid that is a thiol.
When two cysteine amino acids in a protein chain approach each other, they can be oxidized.
An S–S bond (disulfide bond) forms between them.

Structural importance:

The disulfide bond is strong enough to fix the position of the two cysteine groups, imposing structure on the protein.
Hair is composed of about 5% cysteine.
Breaking and remaking disulfide bonds between cysteine units is the primary mechanism behind straightening and curling hair (hair "perms").

🍽️ Biological and practical applications

🍽️ Amino acids and proteins

Essential amino acids:

The human body contains 20 different amino acids.
The body can synthesize 12 amino acids on its own.
The other 8 must be obtained from the diet and are called essential amino acids.
Daily requirements range from 4 mg per kilogram of body weight (tryptophan) to 40 mg per kilogram (leucine).

Dietary considerations:

A properly balanced protein diet is necessary because of essential amino acids.
Rice and beans together provide all essential amino acids in one dish; without one component, the dish would be nutritionally incomplete.
Overreliance on corn (maize) as a primary food source deprives people of lysine and tryptophan, two essential amino acids.
People on restricted diets should vary their diet to ensure ingestion of a wide range of protein sources.

🧬 Peptides

Peptide: a short chain of amino acids connected by amide bonds.

The excerpt emphasizes counting amide bonds in peptide structures as a way to understand their composition.

Polymers

🧭 Overview

🧠 One-sentence thesis

Polymers are large molecules formed by linking many small monomer units together, and they include both synthetic materials like plastics and essential biological molecules like proteins and DNA.

📌 Key points (3–5)

What polymers are: long molecules made by joining many monomers ("one part") into a macromolecule ("many parts").
Two main types: addition polymers (monomers join directly, like polyethylene) vs. condensation polymers (monomers join while releasing a small molecule like water).
Common confusion: not all polymers are synthetic plastics—important biological materials like proteins, starch, cellulose, and DNA are also polymers.
Wide-ranging properties: polymer characteristics (solubility, melting point, hardness, transparency, etc.) vary based on monomers, structure, and additives.
Biological importance: proteins are polymers of amino acids; carbohydrates include starch and cellulose polymers; DNA and RNA are nucleotide polymers.

🔗 How polymers form

🔗 The polymerization process

Polymer: a long, virtually endless molecule formed from many parts.
Monomer: the original single part that joins to form a polymer.
Polymerization: the process of making a polymer.

The basic mechanism uses reactive sites (like double bonds) to link monomers together.
Example: Ethylene has a double bond; the pi electrons form new sigma bonds to join ethylene molecules into one continuous chain.
The result is a macromolecule—a large molecule composed of repeating units.

🏷️ Naming convention

Simple polymers are named after their monomers with the prefix "poly."
Example: ethylene → polyethylene (often written without parentheses in common use, though formally poly(ethylene)).

🧪 Types of polymers

➕ Addition polymers

Formed when monomers add directly to each other without releasing any byproduct.
The double bond in the monomer opens up and connects to other monomers.
Example: Tetrafluoroethylene polymerizes into polytetrafluoroethylene (Teflon), used for non-stick coatings.

Monomer	Polymer Name	Trade Name	Uses
Tetrafluoroethylene	Polytetrafluoroethylene	Teflon	Non-stick coatings, Gore-Tex
Vinylidene dichloride	Polyvinylidene dichloride	Saran	Food wrap
Acrylonitrile	Polyacrylonitrile	Orlon, Acrilan	Textile fibers, carpets
Methyl methacrylate	Polymethyl methacrylate	Plexiglass, Lucite	Clear plastic sheets

➖ Condensation polymers

Formed when two different monomers react and release a small molecule (like water) as a byproduct.
Example: An amine group and a carboxylic acid group react to form an amide bond, releasing H₂O.
This is the same mechanism seen in amide bond formation.

🔀 Copolymers

Polymers made from more than one type of monomer.
Example: Styrene butadiene rubber (SBR) combines styrene and butadiene monomers.
Allows mixing properties of different monomers in one material.

🧬 Biological polymers

🥩 Proteins

Proteins are condensation polymers of amino acids.
Each amino acid monomer has an amine functional group and a carboxylic acid functional group.
These two groups react to form an amide bond, releasing water.
Hundreds or thousands of amino acids link together to form proteins.
Proteins play crucial roles in living organisms.

🌾 Carbohydrates

Carbohydrate: a compound with the general formula Cₙ(H₂O)ₙ.

🍚 Starch

Formed by linking hundreds of glucose molecules together.
An important energy source in the human diet.
Glucose units are joined in a specific way that animals can digest.

🌿 Cellulose

Also made from glucose units, but joined differently than in starch.
A major component of plant cell walls.
Don't confuse with starch: Despite similar building blocks, many animals (including humans) cannot digest cellulose because they lack the proper enzymes to break apart the glucose units in this configuration.
Animals that digest cellulose rely on symbiotic bacteria in their digestive tract.
In humans, cellulose passes through as dietary fiber.

🧬 DNA and RNA

Polymers composed of long, three-part chains called nucleotides.
Each nucleotide consists of:
- A phosphate group
- A five-carbon sugar (ribose or deoxyribose)
- A nitrogen-containing base
DNA is the fundamental material in chromosomes, directly responsible for heredity.
RNA is essential for protein synthesis.

🔧 Synthetic polymer applications

🏭 Properties and versatility

Polymer properties that can be modified include:

Solubility in water and other solvents
Melting point
Flammability
Color and transparency
Hardness and flexibility
Surface friction
Moldability

🛠️ Common uses

Plastics: Nearly anything described as "plastic" is a polymer (toothbrushes, computer cases, automobile parts).
Adhesives: Many epoxy-based adhesives are condensation polymers.
Coatings: Polyurethane paints and coatings.
Fabrics: Polyester fabrics, nylon, Dacron, Mylar.
Packaging: Saran Wrap (originally polyvinylidene chloride, now polyethylene).
Construction: Poly(vinyl chloride) is the third-most produced polymer, used for tubing, toys, flooring, water pipes.

🧴 Silicones

A special class of polymers based on a backbone of silicon and oxygen atoms (not carbon).
Si atoms have organic groups attached, so they're still considered organic polymers.
Uses include:
- Oils and lubricants
- Sealants for glass (aquariums)
- Waterproofing films
- Heat-resistant cookware
- Electrical insulation

Factors that Affect the Rate of Reactions

Factors that Affect the Rate of Reactions Jessie A. Key

🧭 Overview

🧠 One-sentence thesis

Chemical reaction rates vary widely and are controlled by collision theory principles and four main factors: reactant concentration, physical state and surface area, temperature, and activation energy.

📌 Key points (3–5)

Collision theory foundation: reactions occur only when reactant molecules collide effectively—with correct orientation and sufficient kinetic energy.
Activation energy as a barrier: each reaction requires a minimum energy threshold (Ea) that molecules must possess for an effective collision to produce products.
Four controllable factors: concentration, physical state/surface area, temperature, and activation energy all influence how often and how successfully molecules collide.
Common confusion: not all collisions lead to reactions—molecules must be oriented correctly and have enough energy; simply increasing collisions is not enough without meeting both criteria.
Wide rate variation: reactions span from explosive (fireworks) to extremely slow (rusting over years), all governed by the same underlying collision principles.

🎯 Collision theory fundamentals

🎯 What makes a collision "effective"

Collision theory of reactivity: reactions occur when reactant molecules "effectively collide."

Not every molecular collision produces a reaction.
Two requirements must be met simultaneously:
- Correct spatial orientation: molecules must be positioned to allow bonds to break and form, and atoms to rearrange into products.
- Sufficient kinetic energy: molecules must possess at least the minimum energy needed (the activation energy).
Example: If two molecules collide but are oriented incorrectly, bonds cannot break and rearrange even if they have enough energy.

⚡ Activation energy as the threshold

Activation energy (Ea): the minimum amount of kinetic energy molecules must possess for an effective collision to occur.

Every reaction has its own specific activation energy value.
Higher activation energy → fewer molecules in a sample will have enough energy → slower reaction rate.
The activation energy acts as an energy barrier that must be overcome.
Don't confuse: activation energy is not the total energy of the reaction, but the minimum energy required to start the bond-breaking and bond-forming process.

🧪 Factor 1: Reactant concentration

🧪 How concentration affects collisions

Mechanism: Increasing the concentration of one or more reactants increases the rate of reaction.
Why it works: A higher concentration means more molecules of that reactant are present in the same volume.
Result: More molecules → more collisions in a specific time period → more opportunities for effective collisions → faster reaction rate.
Example: Doubling the concentration of a reactant doubles the number of molecules available to collide, increasing collision frequency.

🔲 Factor 2: Physical state and surface area

🔲 Heterogeneous mixtures and contact

The limitation: If reactant molecules exist in different phases (heterogeneous mixture), the reaction rate is limited by the surface area where phases contact each other.
Why surface area matters: Only molecules at the contact surface can collide with molecules in the other phase.

🔨 Increasing surface area

Example from the excerpt: A solid metal reactant mixed with a gas reactant.
- Only metal molecules on the surface can collide with gas molecules.
- Interior metal molecules cannot participate until surface molecules react away.
How to increase rate: Increase the surface area by:
- Pounding the metal flat
- Cutting it into many pieces
More surface area → more contact points → more simultaneous collisions → faster reaction.

🌡️ Factor 3: Temperature

🌡️ Temperature and kinetic energy

Mechanism: An increase in temperature typically increases the rate of reaction.
Why it works: Higher temperature raises the average kinetic energy of all reactant molecules.
Result: A greater proportion of molecules will have kinetic energy equal to or above the activation energy threshold.
More molecules with sufficient energy → more effective collisions per unit time → faster reaction rate.
Don't confuse: Temperature doesn't lower the activation energy; it increases the fraction of molecules that can overcome the existing energy barrier.

📊 Summary comparison

Factor	How it increases rate	Underlying mechanism
Concentration	Add more reactant molecules	More collisions per time period
Surface area	Expose more contact area (heterogeneous)	More molecules available to collide at phase boundary
Temperature	Raise average kinetic energy	Greater proportion of molecules exceed activation energy
Activation energy	(Lower Ea, if possible)	More molecules naturally have sufficient energy

⏱️ Real-world rate variation

The excerpt contrasts two extremes to illustrate the range of reaction rates:

Fast: Fireworks detonation (explosive, seconds or less)
Slow: Rusting of barbed wire (many years)

Both follow the same collision theory principles, but differ dramatically in activation energy and conditions.

Reaction Rates

Reaction Rates Jessie A. Key

🧭 Overview

🧠 One-sentence thesis

Reaction rates measure how quickly reactants turn into products over time, and they depend on effective collisions between molecules that have sufficient energy and correct orientation, as well as on concentration, surface area, temperature, and catalysts.

📌 Key points (3–5)

What reaction rate measures: the change in concentration of reactants or products over a given time period (always expressed as a positive value).
Effective collisions requirement: reactions occur only when molecules collide with correct orientation and minimum kinetic energy (activation energy).
Four main factors: reactant concentration, physical state/surface area, temperature, and presence of a catalyst all affect how fast reactions proceed.
Stoichiometry correction: when balanced equations have coefficients other than 1:1, the rate for each species must be divided by its coefficient to express the overall reaction rate consistently.
Common confusion: average rate vs instantaneous rate—reaction rates typically decrease over time as reactants are consumed, so average rates do not accurately represent the rate at any single moment.

⚛️ What makes reactions happen

⚛️ Effective collisions

For an "effective collision" to occur, the reactant molecules must be oriented in space correctly to facilitate the breaking and forming of bonds and the rearrangement of atoms that result in the formation of product molecules.

Not every collision between reactant molecules leads to a reaction.
Two requirements must be met simultaneously:
- Correct orientation: molecules must be positioned so that the right atoms can interact and bonds can break/form.
- Sufficient kinetic energy: molecules must possess at least the minimum energy needed (activation energy).
Example: if two molecules bump into each other but are facing the wrong way, no reaction occurs even if they have enough energy.

🔋 Activation energy (Ea)

Activation energy (Ea): the minimum amount of kinetic energy molecules must possess for an effective collision to occur.

This energy threshold varies for each reaction.
Higher activation energy means fewer molecules will have enough energy to react.
The rate of reaction depends on activation energy: higher Ea → slower reaction because fewer effective collisions occur.
Don't confuse: activation energy is not the total energy of the reaction; it is the energy barrier that must be overcome for reactants to become products.

📏 How to measure reaction rates

📏 Defining rate as change over time

Reaction rate measures change in concentration divided by the time period in which that change occurs.
Rate can be measured by tracking either:
- Disappearance of starting material (reactants), or
- Appearance of product.
For the hypothetical reaction A + B → C, the average rate can be expressed as:
- Rate = (change in concentration of A) / (time period), or
- Rate = (change in concentration of C) / (time period).

➖ Negative sign correction

Reaction rates are always expressed as positive values.
When measuring the disappearance of reactants, concentration decreases (a negative change).
A negative sign is included in the rate expression to correct for this decrease and keep the rate positive.
Example: if reactant A decreases, the rate is written as −(change in A)/(time) so the overall value is positive.

🔢 Stoichiometry and rate relationships

When balanced equations have coefficients other than 1:1, the rate for each species must be adjusted.
For the reaction 2A + B → 3C:
- Two molecules of A are consumed for every one molecule of B, so A is consumed twice as fast.
- To express the average rate of reaction consistently, divide each species' rate by its coefficient.
- Rate = −(1/2)(change in A)/(time) = −(change in B)/(time) = (1/3)(change in C)/(time).
This correction ensures that the rate expression reflects the overall reaction rate, not just the rate for one species.

🧪 Four factors that control reaction rate

🧪 Reactant concentration

Increasing the concentration of one or more reactants often increases the rate of reaction.
Why: higher concentration means more reactant molecules in a given volume, leading to more collisions in a specific time period.
More collisions → more opportunities for effective collisions → faster reaction.

🧊 Physical state and surface area

If reactant molecules exist in different phases (heterogeneous mixture), the rate is limited by the surface area of the phases in contact.
Example: a solid metal reacting with a gas—only molecules on the metal's surface can collide with gas molecules.
Increasing surface area (e.g., pounding the metal flat or cutting it into many pieces) increases the reaction rate.
Don't confuse: this factor applies mainly to heterogeneous reactions, not to reactions where all reactants are in the same phase.

🌡️ Temperature

An increase in temperature typically increases the rate of reaction.
Why: higher temperature raises the average kinetic energy of reactant molecules.
A greater proportion of molecules will have the minimum energy (activation energy) necessary for an effective collision.
The excerpt references a distribution of kinetic energies: at higher temperature, more molecules are above the activation energy threshold.

🧬 Presence of a catalyst

Catalyst: a substance that accelerates a reaction by participating in it without being consumed.

Catalysts provide an alternate reaction pathway to obtain products.
They lower the activation energy or change the mechanism, making effective collisions easier.
Catalysts are not used up in the reaction; they can be recovered and reused.
They are critical to many biochemical reactions and will be examined further in a later section on catalysis.

⏱️ Average vs instantaneous rates

⏱️ Why rates change over time

For most chemical reactions, the rate decreases as time passes.
As the reaction proceeds, more reactant molecules are consumed to become product.
Lower reactant concentration → fewer effective collisions → slower reaction rate.
Example: at the start of a reaction, concentration is high and collisions are frequent; later, concentration drops and collisions become less frequent.

📉 Instantaneous reaction rate

Instantaneous reaction rate: the rate of reaction at one instant in time.

Average reaction rates (measured over a time interval) do not accurately represent the actual rate at all time points.
Instantaneous rates can be determined from the slope of the tangent to a concentration-vs-time curve at a specific moment.
The excerpt mentions that instantaneous rates are more precise for understanding reaction behavior at any given time, especially when rates are changing.

Rate type	What it measures	When to use
Average rate	Change in concentration over a time interval	Quick estimate; less precise for reactions with changing rates
Instantaneous rate	Rate at one specific moment (tangent slope)	Precise snapshot; better for reactions where rate decreases over time

Rate Laws

Rate Laws Jessie A. Key

🧭 Overview

🧠 One-sentence thesis

Rate laws express the mathematical relationship between reaction rate and reactant concentrations, with exponents that must be determined experimentally and that define the reaction order.

📌 Key points (3–5)

What a rate law is: a mathematical equation linking reaction rate to reactant concentrations through a rate constant and exponents.
Reaction order: the sum of all exponents in the rate law; can also refer to the order with respect to individual reactants.
Exponents ≠ coefficients: the exponents in the rate law must be determined experimentally and do not necessarily match the balanced equation coefficients.
Common confusion: reaction order for a single reactant vs. overall reaction order—individual orders are the exponents themselves; overall order is their sum.
How to find rate laws: use the method of initial rates by varying one reactant concentration at a time and comparing how the rate changes.

🧮 What rate laws express

🧮 The mathematical relationship

Rate law: the mathematical relationship of reaction rate with reactant concentrations.

For a hypothetical reaction, the rate law takes the form: rate = k [reactant₁]^y [reactant₂]^z
The rate law may include some, all, or none of the reactant species in the actual reaction.
It shows how heavily the rate depends on each reactant's concentration.

🔑 The rate constant k

The proportionality constant k is called the rate constant.
It is specific to a particular reaction at a particular temperature.
k changes with temperature.
Its units depend on the sum of the exponents in the rate law (the overall reaction order).

📏 Understanding reaction order

📏 What reaction order means

Reaction order: the sum of the concentration term exponents in a rate law equation.

Overall reaction order: add up all the exponents in the rate law.
Order with respect to one reactant: the exponent on that specific reactant's concentration term.
Example from the excerpt: for NO₂(g) + CO(g) → NO(g) + CO₂(g), the experimentally determined rate law is rate = k[NO₂]²
- Overall reaction order: second-order (exponent sum = 2)
- Zero-order for [CO] (exponent = 0, CO doesn't appear)
- Second-order for [NO₂] (exponent = 2)

🔢 Possible values for reaction order

Most often whole numbers: 0, 1, or 2
Can also be fractions or even negative values in some instances
Don't confuse: the exponents are not the same as the coefficients in the balanced chemical equation—they must be found experimentally.

📐 Units of the rate constant

The units of k change depending on the overall reaction order:

Reaction Order	Units of rate constant
Zero-order	M s⁻¹
First-order	s⁻¹
Second-order	L mol⁻¹ s⁻¹

Why this happens: rearranging rate = k [concentration terms] to solve for k shows that the units must balance to give rate units (M s⁻¹) on the left side.

🔬 Determining rate laws experimentally

🔬 Method of initial rates

Measure the instantaneous reaction rate immediately when reactants are mixed (the initial rate).
Repeat the experiment multiple times (runs or trials).
In each run, vary the concentration of one reactant at a time while keeping others constant.
Compare the runs to see how changing each reactant's concentration affects the initial rate.

🧪 How to analyze the data

The excerpt provides a partial example with three trials:

Trial 1: [E] = 0.100, [F] = 0.100, initial rate = 2.73 × 10⁻⁵
Trial 2: [E] = 0.200, [F] = 0.100, initial rate = 5.47 × 10⁻⁵

Process:

Compare trials where only one concentration changes.
See how the rate changes in response.
Determine the exponent (order) for each reactant.
Write the complete rate law.
Solve for the rate constant k using data from any trial.

Example: Between Trial 1 and Trial 2, [E] doubles while [F] stays constant, and the rate also doubles—this suggests the reaction is first-order with respect to E.

🔗 Connection to earlier concepts

🔗 Stoichiometry and rate corrections

The excerpt mentions that in a reaction like 2A + B → 3C, two molecules of A are consumed for every one molecule of B, so A is consumed twice as fast.
To express the average rate for each species, divide each rate by its coefficient in the balanced equation.
Don't confuse: these stoichiometric coefficients correct for comparing rates of different species; they are separate from the exponents in the rate law, which describe how concentration affects rate.

⏱️ Instantaneous vs. average rates

For most reactions, the rate decreases over time as reactants are consumed.
Average rates over a time interval do not accurately represent the rate at any specific moment.
Instantaneous rate: the rate at one specific instant, found from the slope of the tangent to a concentration vs. time plot.
Initial rate: the instantaneous rate at t = 0 (the start of the reaction), which is particularly important for determining rate laws.

Concentration–Time Relationships: Integrated Rate Laws

Concentration–Time Relationships: Integrated Rate Laws Jessie A. Key

🧭 Overview

🧠 One-sentence thesis

Integrated rate laws transform differential rate equations into linear forms that allow us to determine reaction order graphically and calculate concentrations at any time, with first-order reactions uniquely exhibiting constant half-lives independent of concentration.

📌 Key points (3–5)

What integrated rate laws do: transform rate laws into equations that relate concentration directly to time, enabling graphical determination of reaction order.
How to distinguish orders graphically: each order (zero, first, second) produces a straight line when the correct function of concentration is plotted versus time.
First-order uniqueness: only first-order reactions have half-lives that remain constant regardless of concentration.
Common confusion: differential vs integrated rate laws—differential laws express rate as a function of concentration; integrated laws express concentration as a function of time.
Practical application: by plotting experimental concentration-time data in different ways, you can identify which order produces a straight line and thus determine the reaction order.

📐 From differential to integrated rate laws

📐 What integration accomplishes

Differential rate law: expresses the reaction rate as a function of reactant concentration. Integrated rate law: expresses reactant concentration as a function of time.

Integration is a mathematical procedure (from calculus) that transforms one form into the other.
The integrated form is more useful for predicting concentrations at specific times.
The excerpt notes that the integration process itself is beyond the scope but is covered in calculus courses.

🔄 Why the integrated form matters

It can be rearranged into the general form of a straight line: y = mx + b.
This allows graphical methods to determine reaction order from experimental data.
Different reaction orders produce straight lines when different functions of concentration are plotted against time.

📊 Graphical methods for each reaction order

📊 First-order reactions

The integrated rate law for a first-order reaction (A → B) is:

ln[A]_t = -kt + ln[A]_0

Where:

ln is the natural logarithm
[A]_0 is the initial concentration of A
[A]_t is the concentration of A at time t
k is the rate constant

How to identify graphically:

Plot the natural logarithm of concentration (ln[A]) versus time.
A first-order reaction yields a straight line.
The slope equals the negative rate constant (-k).
The y-intercept equals the natural logarithm of the initial concentration.

Don't confuse: Any other reaction order will not produce a straight line when ln[A] is plotted versus time.

📊 Second-order reactions

The integrated rate law for a second-order reaction (C → D) where the rate depends on a single reactant raised to the second power is:

1/[C]_t = kt + 1/[C]_0

How to identify graphically:

Plot the inverse of concentration (1/[C]) versus time.
A second-order reaction yields a straight line.
The slope equals the rate constant (k).
The y-intercept equals the inverse of the initial concentration (1/[C]_0).

📊 Zero-order reactions

The integrated rate law for a zero-order reaction (E → F) is:

[E]_t = -kt + [E]_0

How to identify graphically:

Plot concentration [E] directly versus time.
A zero-order reaction yields a straight line.
The slope equals the negative product of the rate constant and time (-kt).
The y-intercept equals the initial concentration [E]_0.

Key insight: Zero-order reactions occur when the rate of reactant disappearance is independent of reactant concentrations.

📋 Summary comparison table

Reaction Order	What to plot	Slope	y-intercept	Rate constant units
Zero	[E] vs. t	-kt	[E]_0	mol per L per s
First	ln[A] vs. t	-k	ln[A]_0	per s
Second	1/[C] vs. t	k	1/[C]_0	L per mol per s

Practical strategy: When given experimental concentration-time data, plot the data in all three ways to see which produces a straight line—that reveals the reaction order.

⏱️ Half-life in first-order reactions

⏱️ What half-life means

Half-life (t_1/2): the duration of time required for the concentration of a reactant to drop to one-half of its initial concentration.

Half-life serves as a metric to discuss the relative speeds of reactions.
A slower reaction has a longer half-life.
A faster reaction has a shorter half-life.

⏱️ First-order half-life equation

The half-life equation for a first-order reaction is derived by substituting t_1/2 for t and [A]_0/2 for [A]_t in the integrated rate law, then solving:

t_1/2 = 0.693/k

Where k is the rate constant.

⏱️ Unique property of first-order half-lives

Critical distinction: The half-life equation does not include a reactant concentration term.

This means:

Half-life is independent of concentration.
Half-life remains constant throughout the entire reaction.
Plots of first-order reaction data show a series of regularly spaced half-life intervals.

Example: If a first-order reaction has a half-life of 10 seconds, the concentration will drop from 1.0 M to 0.5 M in 10 seconds, then from 0.5 M to 0.25 M in another 10 seconds, and so on—always the same time interval regardless of starting concentration.

Don't confuse: This constant half-life property is unique to first-order reactions; second-order and zero-order reactions have half-lives that depend on concentration.

🔬 Practical applications

🔬 Determining reaction order from data

The excerpt provides a worked example showing how to determine reaction order:

Take experimental concentration-time data.
Create a table with columns for time, concentration, ln(concentration), and 1/concentration.
Plot all three characteristic graphs (concentration vs. t, ln[A] vs. t, and 1/[A] vs. t).
Whichever plot produces a straight line reveals the reaction order.

🔬 Calculating concentrations at specific times

Once you know the integrated rate law and rate constant, you can predict concentration at any time.

Example scenario from the excerpt: A pollutant decomposes in water following first-order kinetics with a known rate constant. Given an initial concentration, you can calculate the concentration after any specified time by substituting values into the first-order integrated rate law and solving.

🔬 Using half-life information

For first-order reactions, if you know the rate constant, you can:

Calculate the half-life using t_1/2 = 0.693/k.
Determine how long it takes for concentration to decrease to any fraction of the initial value.
Predict remaining concentration after multiple half-lives.

Example: To go from 1.0 M to 0.25 M requires two half-lives (1.0 → 0.5 → 0.25), so the time needed is 2 × t_1/2.

Activation Energy and the Arrhenius Equation

Activation Energy and the Arrhenius Equation Jessie A. Key

🧭 Overview

🧠 One-sentence thesis

The Arrhenius equation mathematically connects activation energy, temperature, and the rate constant, allowing scientists to calculate how energy barriers control reaction speeds.

📌 Key points (3–5)

What the Arrhenius equation does: relates the rate constant to activation energy, temperature, and collision frequency factors.
The core relationship: as activation energy increases, the rate constant decreases, slowing the reaction.
Key variables: E_a (activation energy), k (rate constant), T (temperature in Kelvin), R (gas constant), and A (frequency factor).
Practical use: the equation allows calculation of activation energy from known rate constants, or vice versa.
Common confusion: the frequency factor A accounts for both how often molecules collide and whether they are oriented correctly—not just collision frequency alone.

🔬 The Arrhenius equation and its components

🧮 What the equation relates

The Arrhenius equation: proposed in 1889 by Swedish scientist Svante Arrhenius, it relates the rate constant with activation energy, temperature, and collision factors.

The equation connects concepts discussed earlier: effective collision frequency and molecule energy levels.
It provides a mathematical framework for understanding how energy requirements affect reaction speed.
The relationship is quantitative, not just qualitative—you can calculate specific values.

🔤 The variables explained

Variable	Name	What it represents	Units
k	Rate constant	How fast the reaction proceeds	varies by order
E_a	Activation energy	Energy barrier that must be overcome	energy units
R	Gas constant	Universal constant	energy per temperature per mole
T	Temperature	Absolute temperature	Kelvin
A	Frequency factor	Collision frequency and molecular orientation	L per mol per s

⚡ The frequency factor A

A is not just about how often molecules collide.
It "takes into account the frequency of reactions and likelihood of correct molecular orientation."
Both factors matter: molecules must collide often and be aligned properly to react.
Don't confuse: A combines two separate effects (frequency + orientation) into one term.

📉 How activation energy affects reaction rate

📉 The inverse relationship

The excerpt states: "as activation energy term E_a increases, the rate constant k decreases."
Lower rate constant → slower reaction rate.
This mathematically confirms the earlier qualitative understanding.

Why this matters:

Reactions with high energy barriers are naturally slower.
Temperature and activation energy work together to determine the overall rate.
Example: A reaction with very high E_a will have a small k value, meaning it proceeds slowly even if other conditions are favorable.

🛠️ Practical applications

🛠️ Calculating activation energy or rate constants

The excerpt notes the equation "allows us to calculate activation energies if the rate constant is known, or vice versa."

Two-way calculation:

Known k → can solve for E_a
Known E_a → can solve for k
This makes the equation a practical tool, not just a theoretical relationship.

📊 Graphical determination

The excerpt mentions "We can graphically determine the" [text cuts off], indicating that activation energy can be found using graphical methods in addition to algebraic calculation.

Reaction Mechanisms

Reaction Mechanisms Jessie A. Key

🧭 Overview

🧠 One-sentence thesis

The rate of a chemical reaction is determined by its slowest elementary step, and understanding the step-by-step molecular events (the reaction mechanism) explains why overall rate laws do not always match the stoichiometry of balanced equations.

📌 Key points (3–5)

What a reaction mechanism is: the exact sequence of bond-making and bond-breaking events (elementary steps) that occur at the molecular level during a chemical reaction.
Elementary steps vs overall reactions: each elementary step has its own rate law derived directly from its molecularity (number of molecules in the collision), whereas the overall reaction rate law depends on the slowest step.
Rate-determining step: the slowest elementary step in a multi-step mechanism limits the rate of the entire reaction, just as the narrowest opening in an hourglass controls the flow of sand.
Common confusion: intermediates vs transition states—intermediates are generated in one step and consumed in another (sometimes isolable), while transition states are the highest-energy points during bond breaking/forming and cannot be isolated.
Why mechanisms matter: they reveal why the rate law of an overall reaction does not necessarily correlate to the stoichiometry of its balanced chemical equation.

🔬 Elementary steps and molecularity

🔬 What is an elementary step?

Elementary step: each individual event that occurs in a chemical reaction as a result of an effective collision.

An elementary step describes a single bond-breaking or bond-forming event at the molecular level.
We cannot directly watch these events, but we can infer them using kinetics and other chemical methods.
A complete chemical reaction may occur in one or more elementary steps.

🧮 Molecularity

Molecularity: the total number of molecules that participate in the effective collision of an elementary step.

Elementary steps are classified by molecularity:

Molecularity	Number of molecules	Example
Unimolecular	1	A → B
Bimolecular	2	2A → C
Termolecular	3	2A + D → E

Only three main categories exist because it is rare for more than three molecules to participate simultaneously in an effective collision.

📐 Rate laws for elementary steps

The rate law of a single elementary step can be derived directly from its stoichiometric equation.
This is because an elementary step is an individual effective collision describing a single event.
The rate law depends on molecularity (the number of molecules involved):

Elementary Step	Molecularity	Rate Law
A → B	Unimolecular	Rate = k[A]
2A → C	Bimolecular	Rate = k[A]²
2A + D → E	Termolecular	Rate = k[A]²[D]

Example: For the unimolecular step A → B, as the concentration of reactant A molecules increases, the number of effective collisions also increases, so Rate = k[A].

Don't confuse: The rate law of an overall reaction (potentially involving several steps) does not necessarily correlate to the stoichiometry of its balanced chemical equation, because the overall reaction may involve multiple elementary steps.

🧩 Multi-step mechanisms

🧩 What is a multi-step mechanism?

The overall reaction process often corresponds to a series of two or more elementary steps.
These elementary steps must always add up to give the overall balanced chemical equation.
Example: An elimination reaction proceeds in two elementary steps (a two-step mechanism):
1. Bromide leaves from the starting material to give the cation C₄H₉⁺.
2. C₄H₉⁺ reacts with water to generate the product C₄H₈ and H₃O⁺.

🔄 Intermediates

Intermediate: a species that does not appear in the overall balanced equation and is generated in one elementary step but used up in a subsequent step.

In the example above, the cation C₄H₉⁺ is an intermediate.
Intermediates are more stable than transition states and can sometimes be isolated and characterized by certain techniques.

⚡ Transition states (activated complexes)

Transition state (or activated complex): the highest-energy transitional point in an elementary step.

Transition states are very unstable (high energy) because bonds are in the process of breaking or forming.
Transition states cannot be isolated.
Each elementary step has its own activation energy and transition state.

Don't confuse intermediates with transition states:

Intermediates: generated in one step, consumed in another; more stable; sometimes isolable.
Transition states: highest-energy points; very unstable; cannot be isolated.

📊 Potential energy diagrams

A potential energy diagram for a multi-step reaction shows each elementary step with its own activation energy and transition state.
Intermediates appear as local minima (valleys) between the peaks (transition states).
The diagram visually represents the energy changes as the reaction progresses through each step.

⏱️ The rate-determining step

⏱️ What is the rate-determining step?

Rate-determining step: the slowest step in a multi-step mechanism, which limits the rate of the entire reaction.

For multi-step mechanisms, there is often one step that is significantly slower than the other steps.
This slowest step determines the rate law of the overall reaction.

🕰️ Hourglass analogy

An hourglass with two different-sized openings illustrates this concept.
The rate of sand falling to the bottom chamber is determined by the smaller of the two openings.
Similarly, the rate of the overall reaction is determined by its slowest step, not by the faster steps.

📏 Why it matters

The rate law of the overall reaction is determined from its rate-determining slowest step, not from the stoichiometry of the overall balanced equation.
This explains why measuring the rate of an overall reaction reveals information about the mechanism's slowest step.
Example: If the overall reaction appears to follow Rate = k[A], it suggests that the slowest step involves only A molecules in the effective collision.

Catalysis

Catalysis Jessie A. Key

🧭 Overview

🧠 One-sentence thesis

Catalysts lower activation energy by providing alternate reaction pathways and are classified into homogeneous, heterogeneous, and biological types based on their phase and mechanism of action.

📌 Key points (3–5)

What catalysts do: lower activation energy by providing alternate pathways; participate but regenerate to original state.
Three main types: homogeneous (same phase as reactants), heterogeneous (different phase, often solid surfaces), and biological (ribozymes and enzymes).
How heterogeneous catalysts work: reactants adsorb onto solid surfaces where reactions occur, then products desorb.
Common confusion: catalysts vs intermediates—catalysts regenerate and aren't consumed; intermediates form in one step and are used up in another.
Enzyme specificity: enzymes are highly specific for substrates and can increase reaction rates by factors of 10⁷ to 10¹⁴.

🔬 What catalysts are and how they work

🔬 Definition and core function

Catalysts: substances that lower the activation energy of a specific reaction by providing an alternate reaction pathway.

Catalysts participate in reactions but are not permanently changed—they regenerate to their original state.
They provide a different pathway with lower activation energy, making reactions proceed faster.
Don't confuse: catalysts are regenerated (not consumed), while intermediates are generated in one step and consumed in another.

🗂️ Three main categories

Scientists classify catalysts into three types based on their nature and how they interact with reactants:

Type	Phase relationship	Examples
Homogeneous	Same phase as reactants	Iodine catalyzing 2-butene isomerization
Heterogeneous	Different phase from reactants	Metal surfaces (palladium) for gas reactions
Biological	Within living systems	Ribozymes (RNA) and enzymes (proteins)

🧪 Homogeneous catalysts

🧪 Same-phase catalysis

Homogeneous catalyst: any catalyst that is present in the same phase as the reactant molecules.

The catalyst exists in the same physical state (gas, liquid, or solid) as the reactants.
Example from the excerpt: iodine catalyzing the isomerization of 2-butene.

🔄 The 2-butene isomerization example

2-butene exists as two isomers: cis (methyl groups on same side) and trans (methyl groups on opposite sides).
Converting between isomers requires breaking the carbon-carbon double bond and rotating—high activation energy (~264 kJ/mol).
With iodine catalyst: activation energy drops to ~118 kJ/mol via an alternate pathway.
Mechanism: iodine atom reacts with cis-2-butene → forms intermediate with broken C=C bond and new C-I bond → molecule rotates → C-I breaks to reform double bond in trans configuration.

🏭 Heterogeneous catalysts

🏭 Different-phase catalysis

Heterogeneous catalysts: those that are in a different phase from one or more of the reactants.

Commonly solid metals or metal oxides catalyzing gaseous or liquid reactants.
Solid catalysts provide a surface where reactions can occur.
Reactants adsorb (bind to the surface) to the solid catalyst.

⚗️ Hydrogenation example mechanism

The conversion of ethene (C₂H₄) to ethane (C₂H₆) using hydrogen gas and palladium metal illustrates the process:

Ethene and hydrogen adsorb onto the metal surface
H₂ breaks into two individual hydrogen atoms bonded to the metal surface
Reaction occurs between adjacent ethene and hydrogen atoms on the surface
First generates C₂H₅ intermediate, then ethane (C₂H₆)
Ethane desorbs (releases) from the surface

The metal surface facilitates bond breaking and formation by holding reactants in close proximity.

🧬 Biological catalysts

🧬 Two types of natural catalysts

Catalysts within living organisms facilitate the complex chemical reactions required for life:

Type	Nature	Discovery/Importance
Ribozymes	RNA molecules	Discovered 1982; Nobel Prize 1989 to Altman and Cech
Enzymes	Protein molecules	Highly specific; increase rates by 10⁷ to 10¹⁴

🔐 The lock-and-key model for enzymes

Enzymes: protein molecules that catalyze biochemical reactions.

Enzymes are remarkably specific for their reactants, called substrates.
The lock-and-key model describes how enzymes work:
- Enzymes provide a tight-fitting area called the active site where substrate molecules can react.
- Hydrophobicity and intermolecular forces (hydrogen bonding, London-dispersion, dipole-dipole) help substrates bind to the active site.
- This forms an enzyme-substrate complex.
- When the reaction completes at the active site, the product is released.

🧩 Key enzyme terminology

Substrates: the specific reactants an enzyme can use.
Active site: the tight-fitting area on the enzyme where substrates react.
Enzyme-substrate complex: the temporary structure formed when substrate binds to the active site.

Example: An enzyme acts like a lock that only fits specific substrate "keys," bringing them into the right orientation and environment to react efficiently, then releasing the product.

Spontaneous Change

Spontaneous Change Jessie A. Key

🧭 Overview

🧠 One-sentence thesis

Spontaneous processes are those that move a system toward equilibrium without external forces, and the term describes only the direction of change, not the speed at which it occurs.

📌 Key points (3–5)

What spontaneous means: a process that occurs without the influence of external forces and moves a system toward equilibrium.
Spontaneous vs nonspontaneous: a beaker falling and breaking is spontaneous; a broken beaker reforming and lifting itself is nonspontaneous.
Common confusion: spontaneous does NOT mean fast—it only tells you the direction of change, not the rate (which is the domain of kinetics).
Chemical context: spontaneity provides information about whether a change will proceed toward equilibrium, not how quickly.

🔄 What spontaneous means

🔄 General definition

Spontaneous process: one that occurs without the influence of external forces.

The term describes whether a process can happen on its own.
It does not require any outside intervention to proceed.
Example: A beaker falling and breaking is spontaneous—it happens naturally unless outside forces stop it.

🚫 Nonspontaneous processes

Nonspontaneous: a process that requires external intervention to occur.

The opposite of a spontaneous process.
Example: A broken beaker cannot reform itself and lift into the air on its own—it requires a skilled glassworker to fix it and someone to lift it.
These processes need external forces or work to happen.

🧪 Chemical spontaneity

🧪 Moving toward equilibrium

In chemistry, spontaneous refers to any change that moves a system toward equilibrium.
It describes the direction a system will naturally move.
The process will proceed on its own in that direction without external influence.

⚠️ What spontaneous does NOT mean

Don't confuse spontaneous with fast: The term provides no information about speed or rate.
Speed and rate are the domain of kinetics (a different area of chemistry).
A spontaneous process can be very slow or very fast—spontaneity only tells you it will happen, not when or how quickly.

Aspect	What spontaneity tells you	What it does NOT tell you
Direction	Whether the process moves toward equilibrium	—
External forces	Whether it occurs without outside intervention	—
Speed/Rate	—	How fast the process occurs
Timing	—	When the process will complete

Entropy and the Second Law of Thermodynamics

Entropy and the Second Law of Thermodynamics Jessie A. Key

🧭 Overview

🧠 One-sentence thesis

A spontaneous process increases the entropy of the universe, where entropy measures the randomness or energy dispersal of a system and can be understood through the number of possible molecular arrangements (microstates).

📌 Key points (3–5)

What entropy measures: the level of randomness (disorder) of a system, or the energy dispersal of molecules in the system.
The second law of thermodynamics: a spontaneous process will increase the entropy of the universe.
Microstates and the Boltzmann equation: entropy relates to the number of different possible arrangements of molecular position and kinetic energy (microstates).
Common confusion: "spontaneous" does not mean fast—it only indicates the direction toward equilibrium, not the speed or rate (which is kinetics).
Qualitative rule: higher temperature, more molecules, or larger volume all increase entropy.

🔄 What spontaneity means

🔄 Spontaneous vs nonspontaneous processes

A spontaneous process is one that occurs without the influence of external forces.

The excerpt uses a beaker example: dropping a beaker so it falls and breaks is spontaneous; a broken beaker reforming itself and lifting into the air is nonspontaneous.
The broken beaker cannot repair itself or defy gravity on its own—it requires a skilled glassworker and someone to lift it.

⚗️ Spontaneity in chemistry

In chemistry, "spontaneous" refers to any change that moves a system toward equilibrium.
It provides information on the direction of a reaction, not the speed or rate.
Don't confuse: spontaneity is about direction (thermodynamics), not how fast the process happens (kinetics).

🎲 Understanding entropy through microstates

🎲 The two-flask thought experiment

The excerpt describes a sealed system with two flasks connected by a stopcock:

Initially, two gas atoms (one green, one blue) are in the left flask only.
When the stopcock opens, both atoms can move freely between both flasks.
Over time, snapshots show four possible arrangements of the two atoms.
The probability that all atoms return to the original flask is only 1 in 4.
If the number of atoms increases, the probability of finding all atoms in the original flask drops dramatically, following (½) to the power of n, where n is the number of atoms.

Why this matters:

It is entropically favored for the gas to spontaneously expand and distribute between both flasks.
The increase in the number of possible arrangements is an increase in randomness/disorder.

🧮 The Boltzmann equation

The Boltzmann equation relates entropy to the number of microstates (W).

Ludwig Boltzmann (1844–1906) pioneered the idea that entropy could be calculated by examining the positions and energies of molecules.
The equation is: entropy = k × ln(W), where k is the Boltzmann constant (1.38 × 10 to the power of −23 J/K) and W is the number of microstates.

Microstates: the number of different possible arrangements of molecular position and kinetic energy at a particular thermodynamic state.

A process that increases the number of microstates increases the entropy.
Example: In the two-flask system, opening the stopcock increases W from 1 arrangement (both atoms in the left flask) to 4 possible arrangements, so entropy increases.

📈 Predicting entropy changes qualitatively

🌡️ Temperature increase

As a substance is heated, it gains kinetic energy.
This results in increased molecular motion and a broader distribution of molecular speeds.
More molecular speeds → more microstates → higher entropy.

🔢 More molecules

Increasing the number of molecules in a system increases the number of microstates.
More molecules → more possible arrangements → higher entropy.

📦 Volume increase

Increasing the volume of a substance increases the number of positions where each molecule could be.
More positions → more microstates → higher entropy.

📋 Summary rule

Change	Effect on microstates	Effect on entropy
Higher temperature	More molecular speeds and motion	Increase
More molecules	More possible arrangements	Increase
Larger volume	More possible positions	Increase

Any change that results in a higher temperature, more molecules, or a larger volume yields an increase in entropy.

🌌 The second law of thermodynamics

🌌 The universal direction of spontaneous processes

The second law of thermodynamics states that a spontaneous process will increase the entropy of the universe.

This is the key criterion for spontaneity: does the process increase the total entropy of the universe?
The excerpt emphasizes that to assess the spontaneity of a process, we must use the thermodynamic quantity known as entropy (S).
Don't confuse: entropy can decrease locally in a system (e.g., freezing water), but the entropy of the universe (system + surroundings) must increase for the process to be spontaneous.

Measuring Entropy and Entropy Changes

Measuring Entropy and Entropy Changes Jessie A. Key

🧭 Overview

🧠 One-sentence thesis

Entropy can be measured by tracking heat changes in reversible processes, and standard molar entropy values allow calculation of entropy changes in chemical reactions.

📌 Key points (3–5)

The third law provides a reference point: at absolute zero (0 K), a pure, perfect crystal has zero entropy, allowing entropy to be measured from this baseline.
How to measure entropy: measure the heat required to raise temperature in a reversible (very slow, very small) process.
Standard molar entropy trends: larger/more complex molecules have higher entropy; gases > liquids > solids; entropy increases with temperature.
Common confusion: phase changes cause large jumps in entropy due to sudden increases in molecular mobility and available volume, not gradual changes.
Calculating reaction entropy: use standard molar entropy values of products and reactants, weighted by their coefficients in the balanced equation.

🌡️ The third law and measuring entropy

🌡️ The third law of thermodynamics

At absolute zero (0 K), the entropy of a pure, perfect crystal is zero.

At absolute zero, kinetic energy is zero and only one microstate exists.
Using the Boltzmann equation with W = 1 gives S = 0.
This provides a reference point for measuring entropy of any substance.

🔬 How entropy is measured

Measure the heat required to raise the temperature by a given amount.
The process must be reversible: very slow and very small increases in heat.
The temperature must remain constant during the measurement.
Example: When 425 kJ of heat is applied to water at 50°C (323 K) reversibly, the entropy change is calculated by dividing the heat by the temperature.

📊 Standard molar entropy

📊 What standard molar entropy is

Standard molar entropy, S°: the entropy of 1 mole of a substance in its standard state, at 1 atm of pressure.

These values have been tabulated for many substances at 298 K.
Units are J/(mol·K).
Used as reference values for calculating entropy changes in reactions.

📈 Trends in standard molar entropy values

Factor	Effect on entropy	Reason
Molecular size/complexity	Larger/more complex → higher S°	More possible arrangements of atoms in space; more microstates
Phase	Gas > liquid > solid	Gases have much more molecular mobility and available volume
Temperature	Higher T → higher S°	Increased kinetic energy and molecular motion

Key examples from the tables:

Carbon: diamond (2.4) < graphite (5.7) J/(mol·K)
Water: solid < liquid (70.0) < gas (188.8) J/(mol·K)
Gases: He (126.2) < I₂ (260.7) J/(mol·K) — larger molecule has higher entropy

🌡️ Entropy vs. temperature behavior

Entropy increases gradually with temperature for a given phase.
Large jumps occur at phase changes: solid to liquid and liquid to gas.
These jumps are due to sudden increased molecular mobility and larger available volumes.
Don't confuse: the increase is not smooth—phase transitions cause discontinuous jumps, not gradual changes.

🧪 Calculating entropy change of reactions

🧪 Standard entropy change formula

The entropy change of a reaction where reactants and products are in their standard state:

ΔS° = [sum of (n × S° of products)] − [sum of (m × S° of products)]

n and m are the coefficients from the balanced chemical equation.
S° values are taken from standard molar entropy tables.
Units are typically J/K for the overall reaction.

🧪 Application example

For the synthesis of carbon dioxide: C(s) + O₂(g) → CO₂(g)

Look up S° for each substance: C(graphite), O₂(g), and CO₂(g).
Multiply each S° by its coefficient in the balanced equation.
Subtract the sum of reactant entropies from the sum of product entropies.
The result is ΔS° for the reaction.

🔗 Connection to microstates

🔗 The Boltzmann equation

The Boltzmann equation relates entropy to the number of microstates (W): S = k ln W

k is the Boltzmann constant (1.38 × 10⁻²³ J/K).
W is the number of microstates.

🔗 What microstates are

Microstates: the number of different possible arrangements of molecular position and kinetic energy at a particular thermodynamic state.

More microstates = higher entropy.
A process that increases the number of microstates increases entropy.

🔗 What increases microstates (and entropy)

Any change that results in:

Higher temperature: gains kinetic energy, increased molecular motion, broader distribution of molecular speeds.
More molecules: more possible arrangements of the molecules.
Larger volume: more positions where each molecule could be.

Example: Heating a substance increases its temperature, which increases molecular motion and the number of possible speed distributions, thus increasing microstates and entropy.

Gibbs Free Energy

Gibbs Free Energy Jessie A. Key

🧭 Overview

🧠 One-sentence thesis

Gibbs free energy provides a single state function that determines whether a reaction is spontaneous by combining enthalpy and entropy, eliminating the need to calculate the entropy of the surroundings.

📌 Key points (3–5)

What Gibbs free energy is: a state function (G = H − TS) that combines enthalpy and entropy to predict spontaneity.
Why it simplifies calculations: it avoids the need to calculate the entropy of the surroundings by consolidating system properties.
How the sign determines spontaneity: negative ΔG means spontaneous, zero means equilibrium, positive means nonspontaneous.
Common confusion: ΔG tells you the direction of spontaneity (like Q vs K from equilibrium), not just whether a reaction "can happen."
How to calculate it: either from ΔH and ΔS directly, or from standard free energies of formation.

🔬 The Gibbs free energy function

🔬 Definition and components

Gibbs free energy: G = H − TS, where H is the enthalpy of the system, S is the entropy of the system, and T is temperature.

Proposed by J. Willard Gibbs (1839–1903) as a single state function to determine spontaneity.
Combines two thermodynamic properties (enthalpy and entropy) into one term.
For an isothermal process, the change in Gibbs free energy is: ΔG = ΔH − TΔS.
At standard conditions: ΔG° = ΔH° − TΔS°.

🎯 What ΔG represents

The change in Gibbs free energy, ΔG, is the maximum amount of free energy available to do useful work.

It is not just "energy released" but specifically the useful work potential.
The excerpt emphasizes this is the maximum available—actual work may be less due to inefficiencies.

🧮 Why it simplifies spontaneity calculations

Previously, spontaneity required calculating: ΔS_universe = ΔS_system + ΔS_surroundings > 0.
The excerpt shows the derivation:
- Start with: ΔS_universe = ΔS_system + ΔS_surroundings
- Multiply both sides by −T: −TΔS_universe = −TΔS_system − TΔS_surroundings
- Since ΔS_surroundings = −ΔH_system / T, this becomes: −TΔS_universe = ΔH_system − TΔS_system
- Therefore: ΔG = −TΔS_universe
This means Gibbs free energy captures the universe's entropy change using only system properties (H and S).
Don't confuse: you still need both enthalpy and entropy—Gibbs free energy doesn't eliminate either, it just packages them together.

🧭 Interpreting the sign of ΔG

🧭 Spontaneity rules

The sign of ΔG directly indicates spontaneity:

Sign of ΔG	Meaning	Spontaneity
ΔG < 0	Negative	Spontaneous in the direction written
ΔG = 0	Zero	System is at equilibrium
ΔG > 0	Positive	Nonspontaneous in the direction written

Example: If ΔG° = −30 kJ, the reaction proceeds spontaneously under standard conditions.
Example: If ΔG° = +50 kJ, the reaction does not proceed spontaneously; the reverse reaction is spontaneous.

🔄 Relationship to equilibrium concepts

The excerpt notes that the significance of ΔG's sign parallels the relationship between the reaction quotient (Q) and the equilibrium constant (K).
This means:
- ΔG < 0 is like Q < K (reaction proceeds forward).
- ΔG = 0 is like Q = K (system at equilibrium).
- ΔG > 0 is like Q > K (reaction proceeds backward).
Don't confuse: ΔG tells you the direction of spontaneity at a given moment, not the final equilibrium position.

🧪 Calculating ΔG°

🧪 Method 1: From ΔH° and ΔS°

Use the equation: ΔG° = ΔH° − TΔS°

You need standard enthalpy change (ΔH°), standard entropy change (ΔS°), and temperature (T).
Example from the excerpt:
- Given: ΔH° = 36.2 kJ, ΔS° = 123 J/K, T = 298 K
- Convert units: ΔH° = 36,200 J (to match entropy units)
- Calculate: ΔG° = 36,200 J − (298 K)(123 J/K) = 36,200 J − 36,654 J = −454 J
- Conclusion: ΔG° is negative, so the reaction is spontaneous.
Watch units: enthalpy is often given in kJ, entropy in J/K—convert to the same energy unit.

🧪 Method 2: From standard free energies of formation

Use the equation: ΔG° = sum of (n × ΔG°_f of products) − sum of (m × ΔG°_f of reactants)

Where n and m are the stoichiometric coefficients in the balanced chemical equation.
Standard free energies of formation (ΔG°_f) are tabulated values (the excerpt references an appendix).
Example from the excerpt:
- Reaction: 5C(s) + 2SO₂(g) → CS₂(g) + 4CO(g)
- Calculate: ΔG° = [ΔG°_f(CS₂) + 4 × ΔG°_f(CO)] − [5 × ΔG°_f(C) + 2 × ΔG°_f(SO₂)]
- (The excerpt does not provide the numerical values, but states the result is positive.)
- Conclusion: ΔG° > 0, so this is not a spontaneous process.
Don't confuse: this method uses formation values, not absolute G values—elements in their standard states have ΔG°_f = 0.

🔗 Connection to entropy of surroundings

🔗 How ΔG relates to ΔS_universe

The excerpt shows the mathematical relationship:

ΔS_universe = ΔS_system + ΔS_surroundings
Under isothermal conditions: ΔS_surroundings = −ΔH_system / T
Substituting and rearranging: ΔG = −TΔS_universe

This means:

A negative ΔG corresponds to a positive ΔS_universe (spontaneous).
A positive ΔG corresponds to a negative ΔS_universe (nonspontaneous).
Gibbs free energy is essentially a repackaged form of the second law of thermodynamics.

🔗 Why this matters

You no longer need to explicitly calculate the entropy change of the surroundings.
All the information is contained in the system's enthalpy and entropy.
Example: In Example 18.3 (referenced but not fully detailed in the excerpt), the calculation shows how ΔS_surroundings and ΔS_universe can be derived from ΔH° and ΔS°_system, but Gibbs free energy makes this step unnecessary for determining spontaneity.

100

Spontaneity: Free Energy and Temperature

Spontaneity: Free Energy and Temperature Jessie A. Key

🧭 Overview

🧠 One-sentence thesis

Temperature is the key controllable factor that determines whether a reaction is spontaneous by influencing the balance between enthalpy and entropy terms in the Gibbs free energy equation.

📌 Key points (3–5)

What Gibbs free energy tells us: the sign of ΔG indicates spontaneity (negative = spontaneous, positive = nonspontaneous, zero = equilibrium).
Temperature's role: temperature is the only variable scientists can control in the Gibbs free energy equation, and it affects the magnitude of the entropy term.
When temperature decides spontaneity: when enthalpy (ΔH) and entropy (–TΔS) terms have opposite signs, temperature determines whether the reaction is spontaneous.
Common confusion: high vs low temperature effects—low temperature favors the enthalpy term; high temperature magnifies the entropy term.
Practical application: calculating the temperature at which ΔG° = 0 (equilibrium) allows scientists to adjust conditions to drive or prevent spontaneity.

🔬 Understanding Gibbs free energy

🔬 What ΔG measures

The change in Gibbs free energy (ΔG) is the maximum amount of free energy available to do useful work.

Gibbs free energy simplifies spontaneity calculations by avoiding the need to calculate the entropy of the surroundings.
It combines enthalpy and entropy into a single value.

🚦 Sign of ΔG and spontaneity

The sign of ΔG directly indicates whether a reaction will proceed:

ΔG value	Meaning	What happens
ΔG < 0	Negative	Reaction is spontaneous in the direction written
ΔG = 0	Zero	Reaction is at equilibrium
ΔG > 0	Positive	Reaction is nonspontaneous in the direction written

Example: If ΔG° is negative, the reaction proceeds spontaneously under standard conditions.
Don't confuse: ΔG tells you about spontaneity (whether it will happen), not speed (how fast it happens).

🧮 Calculating ΔG°

The standard Gibbs free energy change can be calculated from:

Method 1: ΔG° = ΔH° – TΔS° (using enthalpy and entropy values)
Method 2: Using standard free energies of formation (ΔG°f), where you sum products minus reactants, each multiplied by their coefficients

Example from the excerpt: For ΔH° = 36.2 kJ and ΔS° = 123 J/K at 298 K, the reaction is spontaneous because the calculated ΔG° is negative.

🌡️ Temperature as the control variable

🌡️ Why temperature matters

The Gibbs free energy equation can be viewed as two terms: an enthalpy term (ΔH) and an entropy term (–TΔS).
Temperature is the only part scientists can directly control in this equation.
Since all Kelvin temperatures are positive, temperature affects the magnitude of the entropy term.

⚖️ How temperature tips the balance

Temperature becomes the deciding factor when enthalpy and entropy terms have opposite signs:

Low temperature: Decreases the magnitude of the entropy term (–TΔS becomes smaller).
- Favors the enthalpy term's influence.
- If ΔH is negative and –TΔS is positive, low temperature makes the reaction spontaneous.
High temperature: Increases the magnitude of the entropy term (–TΔS becomes larger).
- Magnifies the entropy term's influence.
- If ΔH is positive and –TΔS is negative, high temperature makes the reaction spontaneous.

📊 Predicting spontaneity from signs

📊 The four scenarios

The table from the excerpt shows how the signs of ΔH and ΔS determine spontaneity:

ΔH	ΔS	–TΔS	ΔG	Spontaneity
+ (positive)	– (negative)	+ (positive)	+ (positive)	Nonspontaneous at all temperatures
– (negative)	+ (positive)	– (negative)	– (negative)	Spontaneous at all temperatures
– (negative)	– (negative)	+ (positive)	+ or –	Low temp: Spontaneous<br>High temp: Nonspontaneous
+ (positive)	+ (positive)	– (negative)	+ or –	Low temp: Nonspontaneous<br>High temp: Spontaneous

🔄 Temperature-dependent cases

Two scenarios depend on temperature:

ΔH negative, ΔS negative: Spontaneous at low temperatures only.
- The negative enthalpy dominates when temperature is low (entropy term is small).
- At high temperature, the positive entropy term grows and makes ΔG positive.
ΔH positive, ΔS positive: Spontaneous at high temperatures only.
- The negative entropy term dominates when temperature is high (entropy term is large).
- At low temperature, the positive enthalpy term dominates and makes ΔG positive.

🎯 Finding the equilibrium temperature

🎯 When ΔG° = 0

At equilibrium, ΔG° equals zero, which allows us to solve for the temperature:

Start with: ΔG° = ΔH° – TΔS° = 0
Rearrange to solve for T: T = ΔH° / ΔS°

🛠️ Practical use

Knowing the equilibrium temperature helps scientists:

Drive the process to spontaneity: adjust temperature to make ΔG negative.
Prevent spontaneous occurrence: adjust temperature to make ΔG positive.

Example: If you calculate the equilibrium temperature, you know that going above or below that value will shift the reaction toward spontaneity or nonspontaneity, depending on the signs of ΔH and ΔS.

101

Free Energy under Nonstandard Conditions

Free Energy under Nonstandard Conditions Jessie A. Key

🧭 Overview

🧠 One-sentence thesis

The Gibbs free energy of a reaction under nonstandard conditions can be calculated using the standard free energy change and the reaction quotient, which also allows us to relate the equilibrium constant directly to thermodynamic data.

📌 Key points (3–5)

What nonstandard conditions means: Many reactions occur when concentrations are not 1 M or pressures are not 1 bar, requiring adjustments to standard free energy calculations.
Two main calculation methods: Use ΔG° with the reaction quotient Q to find ΔG under any conditions, or use ΔG° to calculate the equilibrium constant K.
The relationship between ΔG, ΔG°, and Q: ΔG = ΔG° + RT ln Q, where R is the gas constant, T is temperature in Kelvin, and Q is the reaction quotient.
Common confusion—Q vs K: Q is calculated from actual concentrations at any moment; K is calculated from equilibrium concentrations. At equilibrium, Q = K and ΔG = 0.
Why it matters: These relationships let you predict spontaneity under real conditions and determine equilibrium constants from thermochemical tables.

🔄 Calculating free energy under nonstandard conditions

🔄 The nonstandard free energy equation

ΔG = ΔG° + RT ln Q

What each term means:
- ΔG: free energy change under the actual conditions
- ΔG°: standard free energy change (at 1 M or 1 bar)
- R: ideal gas constant (8.314 J/mol K)
- T: temperature in Kelvin
- Q: reaction quotient (calculated like an equilibrium constant but using actual concentrations/pressures)
How to calculate Q: For a reaction aA + bB ⇌ cC + dD, the reaction quotient is Q = [C]^c [D]^d / [A]^a [B]^b
- For gases, use partial pressures in atmospheres or bars
- For solutes, use molarity
Special case—standard conditions: When all concentrations are 1 M or all pressures are 1 bar, Q = 1, and ln(1) = 0, so ΔG = ΔG°

📊 Example calculation with nonstandard conditions

The excerpt provides an example with the reaction 4NH₃(g) + 5O₂(g) ⇌ 6H₂O(g) + 4NO(g):

First, calculate ΔG° from thermodynamic tables
Then calculate Q using the given partial pressures: 2.0 bar NH₃, 1.0 bar O₂, 1.5 bar H₂O, and 1.2 bar NO
Plug values into ΔG = ΔG° + RT ln Q to find ΔG under these specific conditions

Don't confuse: This calculation tells you about spontaneity under the given conditions, not whether the system is at equilibrium.

⚖️ The relationship between ΔG° and the equilibrium constant

⚖️ Deriving the equilibrium relationship

At equilibrium, two things are true:

ΔG = 0 (no net change)
Q = K (the reaction quotient equals the equilibrium constant)

Substituting these into ΔG = ΔG° + RT ln Q gives:

ΔG° = −RT ln K

What this means: The standard free energy change is directly related to the equilibrium constant
Rearranging: You can also write this as ln K = −ΔG° / RT

🔗 Connecting thermodynamics and equilibrium

This relationship is powerful because:

You can calculate K from thermodynamic data tables (enthalpies of formation, standard entropies)
You can determine ΔG° from measured equilibrium constants
It relates equilibrium directly to enthalpy and entropy changes

Example from the excerpt: For the precipitation reaction Cu⁺(aq) + I⁻(aq) → CuI(s), given Ksp = 1.27 × 10⁻¹², you can calculate ΔG° using ΔG° = −RT ln K. (Note: The reaction is written in reverse of the typical Ksp definition, so the sign must be adjusted.)

🎯 Practical applications

What you know	What you can calculate	How
ΔG° from tables	Equilibrium constant K	Use ΔG° = −RT ln K
Equilibrium constant K	Standard free energy ΔG°	Use ΔG° = −RT ln K
ΔG° and current conditions	Spontaneity (ΔG)	Use ΔG = ΔG° + RT ln Q

Don't confuse: ΔG° tells you about standard conditions; ΔG tells you about actual conditions. A reaction can be nonspontaneous under standard conditions (ΔG° > 0) but spontaneous under certain nonstandard conditions (ΔG < 0) if Q is small enough.

🧮 Key takeaways from the excerpt

🧮 Two main equations to remember

For nonstandard conditions: ΔG = ΔG° + RT ln Q
- Use this when you want to know if a reaction is spontaneous under specific conditions
For equilibrium: ΔG° = −RT ln K
- Use this to relate standard free energy to the equilibrium constant

🔍 When to use each equation

Use ΔG = ΔG° + RT ln Q when:
- You know the actual concentrations or pressures
- You want to determine spontaneity under those conditions
- The system is not at equilibrium
Use ΔG° = −RT ln K when:
- You want to find the equilibrium constant from thermodynamic data
- You want to find ΔG° from a known equilibrium constant
- You're relating equilibrium to enthalpy and entropy

Example scenario: If you're studying a reaction in a reactor with specific starting concentrations, first use ΔG = ΔG° + RT ln Q to see if the reaction will proceed. As the reaction progresses, Q changes until it equals K, at which point ΔG becomes zero and equilibrium is reached.