The Basics of General, Organic, and Biological Chemistry

🧭 Overview

🧠 One-sentence thesis

Chemistry is the central science that studies matter and its changes, using the scientific method to generate testable explanations about the natural universe.

📌 Key points (3–5)

• What chemistry studies: matter—what it consists of, its properties, and how it changes.
• Why chemistry is central: chemical principles are essential for understanding other sciences like biology, geology, and medicine.
• How science works: through the scientific method—proposing hypotheses, testing them through experiments, and refining them based on results.
• Common confusion: hypothesis vs. theory—a hypothesis is a testable idea, while a theory is a general statement describing a large set of observations and represents the highest level of scientific understanding.
• Chemistry's connections: chemistry overlaps with other fields (biochemistry, geochemistry) because the physical universe is interconnected.

🔬 Defining chemistry and its scope

🔬 What chemistry is

Chemistry is the study of matter—what it consists of, what its properties are, and how it changes.

• Chemistry describes real-world processes: cooking food, striking a match, shampooing hair.
• Example: describing the ingredients in a cake and how they change when baked is chemistry.
• It focuses on physical, observable phenomena, not abstract concepts.

🌍 What matter is

Matter is anything that has mass and takes up space—that is, anything that is physically real.

• Some matter is obvious (a book), some less so (air).
• Matter vs. non-matter distinction:
  • Matter: a baby, the Empire State Building, air, stars
  • Not matter: ideas, emotions, love
• Don't confuse: just because something is invisible (like air) doesn't mean it isn't matter.

🔗 Chemistry as the central science

• Chemistry lies at the center of many scientific fields because chemical principles are essential for understanding other sciences.
• The excerpt emphasizes that chemistry "pervades your life" and is fundamental to understanding the natural world.
• Chemical processes are "continuously at work all around us."

🌐 Science and its branches

🌐 What science is

Science is the process by which we learn about the natural universe by observing, testing, and then generating models that explain our observations.

• Science is a process, not just a body of knowledge.
• It focuses on the natural universe—things that are physically real and observable.
• Mathematics is described as "the language of science" used to communicate ideas.

🌳 How scientific fields relate

The excerpt describes science as divided into many branches, but with significant overlap:

Field	What it studies
Chemistry	Matter
Biology	Living things
Geology	Rocks and the earth
Biochemistry	Overlap of biology and chemistry
Geochemistry	Overlap of geology and chemistry

• Don't confuse: fields are divided for convenience, but the natural universe is interconnected, so overlap is common.
• Example: some scientists work in both biology and chemistry, creating the field of biochemistry.

🚫 What is not science

The excerpt implies that not all fields of study are science:

• Science studies "some aspect of the natural universe."
• Fields like sculpture, politics, or astrology are not branches of science because they don't study the natural universe through observation and testing.
• Example: astronomy (study of stars and planets) is science; astrology (predicting human events from star positions) is not.

🔍 The scientific method

🔍 Overview of the method

The scientific method is an organized procedure for learning answers to questions.

• It provides a systematic way to investigate questions about the natural world.
• The steps may not always be as clear-cut in real practice, but most scientific work follows this general outline.

📝 Step 1: Propose a hypothesis

A hypothesis is a testable idea to try to answer a question or explain how the natural universe works.

• A scientist generates a hypothesis to answer a specific question.
• Example question from the excerpt: "Why do birds fly toward Earth's equator during the cold months?"
• Don't confuse hypothesis with theory (see below).

🧪 Step 2: Test the hypothesis

• A scientist devises and carries out experiments to evaluate the hypothesis.
• Possible outcomes:
  • If the hypothesis passes the test → it may be a proper answer
  • If it does not pass → it may not be a good answer

🔄 Step 3: Refine the hypothesis if necessary

• Based on experimental results, a scientist may modify the hypothesis and test again.
• Sometimes results show the original hypothesis is completely wrong, requiring a new hypothesis.
• This iterative process reflects that science is self-correcting.

⚖️ Hypothesis vs. theory

Critical distinction to avoid confusion:

Term	Definition	Level of certainty
Hypothesis	A testable idea	Starting point for investigation
Theory	A general statement describing a large set of observations and data	Highest level of scientific understanding

• Don't confuse: when someone says "I have a theory that excess salt causes high blood pressure," they really have a hypothesis, not a theory.
• A theory represents extensive testing and validation across many observations.

📜 Historical context: Alchemy

📜 Alchemy as chemistry's predecessor

• Modern chemistry developed in the 1600s and 1700s based on principles considered valid today.
• Before that, the study of matter was called alchemy, practiced mainly in China, Arabia, Egypt, and Europe.

🔮 How alchemy differed from chemistry

• Alchemy was "mystical and secretive" rather than systematic and open.
• Alchemists believed all matter was composed of four basic elements: fire, water, earth, and air.
• They thought changing the proportions of these elements could transform substances.
• Major goals:
  • Transmute common metals into gold
  • Synthesize the philosopher's stone (for long life or immortality)

🔒 Secrecy vs. communication

• Alchemists used symbols to represent substances, but not to communicate ideas (as modern chemists do).
• Purpose was to "maintain the secrecy of alchemical knowledge, keeping others from sharing in it."
• Despite secrecy, alchemy was respected as a serious scholarly endeavor in its time.
• Example: Isaac Newton, the great mathematician and physicist, was also an alchemist.

🧭 Overview

🧠 One-sentence thesis

Matter can be systematically classified by its properties (physical vs. chemical), composition (element, compound, or mixture), and phase (solid, liquid, or gas), allowing chemists to describe and understand all materials in the universe.

📌 Key points (3–5)

• Two types of properties: physical properties describe matter's characteristics (size, shape, color), while chemical properties describe how matter changes chemically (e.g., flammability).
• Three composition categories: elements cannot be broken down further, compounds contain multiple elements and can be broken down, and mixtures contain multiple substances that keep their identities.
• Common confusion: homogeneous vs. heterogeneous mixtures—homogeneous mixtures (solutions) act like single substances, while heterogeneous mixtures show obvious separate components.
• Three phases: solids have definite shape and volume, liquids have definite volume but take container shape, gases expand to fill containers.
• Phase changes: substances can transition between phases (melting, boiling, freezing, etc.) when conditions like temperature change.

🔬 Properties of Matter

🔬 Physical properties

Physical properties: characteristics that describe matter, such as size, shape, color, and mass.

• These describe what matter is or looks like, not how it changes.
• They are observable features you can measure or detect without changing the substance's chemical identity.
• Example: the color of a metal, the mass of a sample, or the shape of a crystal.

⚗️ Chemical properties

Chemical properties: characteristics that describe how matter changes its chemical structure or composition.

• These describe what matter does when it undergoes chemical reactions.
• The excerpt gives flammability (ability to burn) as the key example—burning changes the chemical composition.
• Don't confuse: observing a chemical property usually requires changing the substance, while physical properties can be observed without chemical change.

🧱 Composition Categories

🧱 Elements

Element: a substance that cannot be broken down into chemically simpler components.

• The most basic chemical building blocks.
• The excerpt notes about 118 elements exist in the known universe.
• Example: aluminum (used in soda cans) and oxygen.
• The smallest part that maintains an element's identity is an atom.

🔗 Compounds

Compound: a substance that can be broken down into chemically simpler components (because it has more than one element).

• Made of two or more elements combined chemically.
• The excerpt notes tens of millions of different compounds have been identified.
• Example: water is composed of hydrogen and oxygen elements.
• The smallest part that maintains a compound's identity is a molecule (atoms attached together behaving as a unit).

🥗 Mixtures

Mixture: a material composed of two or more substances where individual substances maintain their chemical identities.

• Unlike compounds, the components don't chemically combine—they just coexist.
• Two types exist: heterogeneous and homogeneous.

🔀 Types of Mixtures

🔀 Heterogeneous mixtures

Heterogeneous mixtures: obvious combinations of two or more substances.

• You can see the different components.
• Example: a mixture of sand and water, or soil (composed of small pieces of various materials).
• The components remain visibly separate.

💧 Homogeneous mixtures (solutions)

Homogeneous mixtures (or solutions): mixtures with a consistent composition throughout that act like a single substance.

• The components are so intimately combined you cannot distinguish them.
• Example: sugar dissolved in water, saltwater, air (nitrogen and oxygen), or steel (a solid solution/metal alloy).
• Don't confuse with compounds: in solutions, substances maintain their chemical identities; in compounds, elements chemically bond to form something new.

🌡️ Phases and Phase Changes

🧊 The three phases

Phase	Shape	Volume	Behavior
Solid	Definite	Definite	Maintains fixed form
Liquid	Takes container shape	Definite	Flows but has fixed volume
Gas	Takes container shape	Expands to fill container	Neither definite shape nor volume

• Example: water exists in all three phases—ice (solid), water (liquid), and steam (gas).

🔄 Phase changes

Phase change: a physical process in which a substance goes from one phase to another.

• Typically caused by varying temperature (and less commonly, pressure).
• Common phase changes include:
  • Solid to liquid: melting or fusion
  • Liquid to gas: boiling or evaporation
  • Liquid to solid: solidification or freezing
  • Gas to liquid: condensation
  • Solid to gas: sublimation
  • Gas to solid: deposition
• Example: when liquid water boils to make gaseous water (steam), it undergoes a phase change.

🔬 Scales of Observation

🔭 Macroscopic vs. microscopic viewpoints

• Macroscopic view: working with large numbers of atoms or molecules at a time—what we observe in everyday life.
• Microscopic view: describing chemical events at the level of individual atoms or molecules.
• The excerpt notes atoms are extremely tiny—217 million iron atoms would be needed to make a line 1 inch long.
• Scientists use both viewpoints: we see bulk matter macroscopically, but understand it through microscopic particle behavior.

🧪 Substance definition

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

• By definition, any single substance is pure (the word "pure" is sometimes added but not necessary).
• There are two types: elements and compounds.
• Don't confuse substances with mixtures: substances are uniform in composition and properties; mixtures contain multiple substances.

🧭 Overview

🧠 One-sentence thesis

A proper measurement in chemistry requires both a number (how many or how much) and a unit (the scale of measurement), and without both parts the quantity cannot be communicated correctly.

📌 Key points (3–5)

• What a quantity is: an amount of something that consists of two parts—a number and a unit.
• Why both parts matter: the number tells "how many/much" and the unit tells "what scale"; missing either part makes the measurement incomplete.
• Common confusion: stating only a number (e.g., "12") without a unit leaves ambiguity—12 miles? 12 kilometers? 12 yards?
• Real-world importance: proper quantities are crucial in medicine (dosages), everyday tasks (following instructions), and all scientific measurements.

📏 What makes a proper quantity

📏 The two required components

Quantity: an amount of something that consists of a number and a unit.

• Number: tells us how many or how much of something.
• Unit: tells us the scale of measurement being used.
• Both parts must be included together to express a quantity properly.

❌ What happens without both parts

• If someone answers "12" when asked about distance, you cannot know whether they mean 12 miles, 12 kilometers, 12 furlongs, or 12 yards.
• The measurement is incomplete and cannot be properly communicated.
• Example: A classmate says the homework is "twenty"—this could mean problem #20 or 20 problems total.

🔢 Identifying numbers and units

🔢 Simple quantities

Examples from the excerpt show how to break down quantities:

Quantity	Number	Unit
one dozen eggs	one	dozen eggs
2.54 centimeters	2.54	centimeter
a box of pencils	1 (implied)	box of pencils
88 meters per second	88	meters per second

🔗 Compound units

• Some units combine two measurements together.
• Example: "88 meters per second" has a number (88) and a compound unit (meters and seconds combined).
• Other examples: miles per hour, degrees Fahrenheit.

💊 Why measurements matter in practice

💊 Medical dosages

Dosage (or dose): the specific amount of a medicine known to be therapeutic for an ailment in a patient of a certain size.

• Dosages are described by units of mass (grams or milligrams).
• The amount must be precise: too little won't work; too much can cause harmful side effects.
• Example: levothyroxine sodium tablets are available in 11 different doses ranging from 25 micrograms to 300 micrograms.

👨‍⚕️ Professional responsibility

• Doctors must prescribe the correct dosage.
• Pharmacists must provide the correct medicine at the prescribed dosage.
• Proper quantities (numbers + units) are crucial for patient health and safety.

☕ Everyday measurements

• Following instructions requires measurements: "4 cups of water and 3 scoops of coffee."
• Medical checkups involve measurements: temperature, height, weight, blood pressure.
• Chemists measure properties of matter and express them as quantities.

🧭 Overview

🧠 One-sentence thesis

Scientific notation provides a compact system for expressing extremely large or small numbers by rewriting them as a simple number multiplied by 10 raised to an appropriate power.

📌 Key points (3–5)

• Why scientific notation exists: numbers with many zeros are cumbersome to work with, so scientists use a compact system based on powers of 10.
• The convention: write a single nonzero first digit, a decimal point, the rest of the digits (excluding trailing zeros), then multiply by 10 raised to the necessary power.
• Positive vs negative powers: numbers greater than 1 use positive powers; numbers less than 1 use negative powers.
• Common confusion: the power equals the number of places the decimal moves—positive when moving left (large numbers), negative when moving right (small numbers).
• Reversibility: converting from scientific to standard notation reverses the process by moving the decimal point in the opposite direction.

🔢 What scientific notation is and why it matters

🔢 The basic idea

Scientific notation: a system for expressing very large or very small numbers in a compact manner using powers of 10.

• Instead of writing many zeros, rewrite the number as a simple figure multiplied by 10 raised to an exponent (also called a power).
• Example: 1,500,000 miles can be thought of as 1.5 times 1 million, and 1 million equals 10 × 10 × 10 × 10 × 10 × 10, or 10 to the sixth power.
• Therefore 1,500,000 = 1.5 × 10⁶.

🎯 Why it's useful

• Real-world quantities can be enormous (e.g., 5,000,000,000,000 red blood cells in a liter of blood) or tiny (e.g., iron atom diameter of 0.000000014 inches).
• Numbers with many zeros are cumbersome to write and prone to error.
• Scientific notation is more convenient than listing a large number of zeros.

📏 The convention and how to apply it

📏 Standard format rules

The convention requires:

• A single nonzero first digit
• A decimal point
• The rest of the digits (excluding any trailing zeros)
• A multiplication sign
• 10 raised to the power necessary to reproduce the original number

Example: although 1,500,000 could be written as 15. × 10⁵, the convention is to have only one digit before the decimal point, so 1.5 × 10⁶ is correct.

➡️ Converting large numbers (positive powers)

• Move the decimal point to the left until it follows the first digit.
• The power of 10 equals the number of places you moved the decimal.
• The resulting number being multiplied must be between 1 and 10.

Original number	Decimal moves	Scientific notation
67,000,000,000	10 places left	6.7 × 10¹⁰
1,689	3 places left	1.689 × 10³
12.6	1 place left	1.26 × 10¹

⬅️ Converting small numbers (negative powers)

• For numbers with magnitude less than 1, use a negative power.
• Move the decimal point to the right to follow the first nonzero digit.
• The negative power indicates the number of places moved to the right.

Example: 0.006 can be expressed as 6 divided by 1,000, which equals 6 × 10⁻³.

Original number	Decimal moves	Scientific notation
0.000006567	6 places right	6.567 × 10⁻⁶
−0.0004004	4 places right	−4.004 × 10⁻⁴
0.000000000000123	13 places right	1.23 × 10⁻¹³

Don't confuse: the negative sign on the number itself does not affect how the rules of scientific notation are applied; it's separate from the sign of the power.

🔄 Converting back to standard notation

🔄 Reversing the process

To change scientific notation back to standard notation, move the decimal point in the opposite direction.

➡️ Positive powers (move right)

• Move the decimal point to the right by the number of places indicated by the power.
• Add zeros to the end if necessary to produce a number of the proper magnitude.

Example: 5.27 × 10⁴ becomes 52,700 (decimal moved 4 places right).

⬅️ Negative powers (move left)

• Move the decimal point to the left by the number of places indicated by the power.
• Add zeros as needed.

Example: 6.22 × 10⁻² becomes 0.0622 (decimal moved 2 places left).

🧮 Key patterns to remember

🧮 The magnitude rule

Magnitude	Power sign	Example
Greater than 1	Positive power	5,230,000 = 5.23 × 10⁶
Less than 1	Negative power	0.000064 = 6.4 × 10⁻⁴

🧮 Powers of 10 reference

For large numbers:

• 10⁰ = 1
• 10¹ = 10
• 10² = 100
• 10³ = 1,000
• 10⁴ = 10,000

For small numbers:

• 10⁻¹ = 1/10
• 10⁻² = 1/100
• 10⁻³ = 1/1,000
• 10⁻⁴ = 1/10,000
• 10⁻⁵ = 1/100,000

⚠️ Calculator note

Many calculators handle scientific notation, but the method for entering it differs by model. Learning to enter scientific notation properly is essential; incorrect entry will produce wrong final answers in calculations.

🧭 Overview

🧠 One-sentence thesis

Significant figures communicate the precision of a measurement by including all known digits plus the first estimated digit, and specific rules govern how to preserve this precision when performing calculations.

📌 Key points (3–5)

• What significant figures represent: all digits known with certainty plus the first uncertain (estimated) digit in a measurement.
• Why they matter: they prevent reporting false precision beyond what the measuring instrument can actually determine.
• Rules for identifying significant figures: nonzero digits are always significant; zeros may or may not be significant depending on their position.
• Common confusion: trailing zeros—they are significant only if the number has a decimal point (1,500 has two sig figs; 1,500.00 has six).
• Calculation rules differ: addition/subtraction limits by decimal position; multiplication/division limits by count of significant figures.

🔍 What significant figures mean

🔍 Definition and purpose

Significant figures: all the digits known with certainty and the first uncertain, or estimated, digit.

• A measurement reflects the precision of the measuring instrument.
• The last digit reported is always an estimate based on the finest marking available.
• It makes no sense to report digits beyond the first uncertain one.
• Example: A meterstick marked in millimeters can measure to the nearest millimeter, with the next decimal place estimated; reporting more digits would falsely suggest greater precision.

📏 Why the last digit is estimated

• Measuring instruments have limits—marks indicate certain values, but between marks you must estimate.
• If a table measures 1,357 mm, the digits 1, 3, and 5 are certain (read directly from marks), and the 7 is estimated.
• Reporting 1,357.0 or 1,357.00 would wrongly imply the instrument could measure to tenths or hundredths of a millimeter.

🚫 Zeros as placeholders

• Zeros are used to position significant figures correctly.
• Not all zeros are significant—some only serve to place other digits in the correct decimal position.
• Example: In 0.000458, the first four zeros are not significant; they only position the digits 4, 5, and 8.

📐 Rules for identifying significant figures

✅ Rule 1: All nonzero digits are significant

• Any digit from 1 to 9 is always significant.
• Example: In 1,357, all four digits are significant.

✅ Rule 2: Captive (embedded) zeros are significant

• Zeros between nonzero digits are always significant.
• Example: In 405, all three digits are significant (the zero is between 4 and 5).

❌ Rule 3: Leading zeros are not significant

• Leading zeros appear at the beginning of a decimal number less than 1.
• They are never significant; they only position the decimal point.
• Example: In 0.000458, the first four digits (0.000) are leading zeros and not significant; this number has three significant figures (4, 5, 8).

⚠️ Rule 4: Trailing zeros depend on the decimal point

• Trailing zeros are zeros at the end of a number.
• Without a decimal point: trailing zeros are not significant.
  • Example: 1,500 has two significant figures (the two trailing zeros are not significant).
• With a decimal point: all trailing zeros are significant.
  • Example: 1,500.00 has six significant figures (all digits, including trailing zeros, are significant).
• Don't confuse: The presence or absence of a decimal point completely changes whether trailing zeros count.

Number	Decimal point?	Significant figures	Explanation
1,500	No	2	Trailing zeros not significant
1,500.00	Yes	6	All digits including trailing zeros significant
6,798,000	No	4	Three trailing zeros not significant
6,000,798.00	Yes	9	All digits significant

🧮 Calculation rules for significant figures

➕ Addition and subtraction: align by decimal position

• Rule: Stack numbers with decimal points aligned, then limit the answer to the rightmost column where all numbers have significant figures.
• The answer's precision is limited by the least precise measurement (the one with the fewest decimal places).
• Example: Adding numbers with values in the tenths, hundredths, and thousandths places—if one number only goes to the tenths place, the answer must be limited to the tenths place.
• After identifying the rightmost significant column, drop all digits to the right and round appropriately.

✖️ Multiplication and division: count significant figures

• Rule: Count the significant figures in each number, then limit the answer to the lowest count.
• The answer cannot be more precise than the least precise input.
• Example: Multiplying a number with four significant figures by a number with three significant figures—the answer must have three significant figures.
• After calculation, round the result to match the lowest count of significant figures from the inputs.

🔄 Rounding rules

• If the first dropped digit is 5 or higher: round up.
• If the first dropped digit is lower than 5: do not round up.
• Example: Dropping digits after 1,459.08—the first dropped digit (hundredths place) is 8, so round up the tenths place from 0 to 1, giving 1,459.1.
• Example: If the result is 4,094.1 and you need four significant figures, the first dropped digit is 1 (less than 5), so do not round up; the answer is 4,094.

🔬 Scientific notation removes ambiguity

• Scientific notation explicitly shows all significant figures in the leading number.
• Example: 450 with two significant figures is written as 4.5 × 10 to the power 2.
• Example: 450.0 with four significant figures is written as 4.500 × 10 to the power 2.
• All significant figures are listed explicitly, eliminating confusion about trailing zeros.

⚠️ Important reminders

🖩 Calculators do not understand significant figures

• Calculators display many digits, often far beyond the precision of the input data.
• Example: Dividing 125 by 307 gives 0.4071661238… on a calculator, but if both inputs have only three significant figures, reporting all those digits is meaningless.
• You must apply the rules: the calculator cannot determine the appropriate number of significant figures—only the user can.

🎯 Why significant figures matter

• They properly communicate the precision and reliability of measurements.
• Reporting too many digits suggests false precision; reporting too few loses information.
• Significant figures ensure that calculated results reflect the limitations of the original measurements.

🧭 Overview

🧠 One-sentence thesis

The International System of Units (SI) provides a standardized measurement framework for scientists worldwide, built from seven base units that can be combined with prefixes and mathematical operations to express any quantity needed in chemistry and other sciences.

📌 Key points (3–5)

• Why SI exists: to enable efficient communication among scientists around the world through standardized units.
• Seven base units: SI has seven fundamental units; chemistry primarily uses five (mole, kilogram, meter, second, kelvin).
• Prefix system: prefixes multiply or divide base units by powers of 10, creating convenient sizes (e.g., kilo- = 1,000×, milli- = 1/1,000×).
• Derived units: combinations of base units (multiplied or divided) create units for other quantities like volume (m³), energy (joules), and density (g/cm³).
• Common confusion: don't confuse base units with derived units—base units are fundamental, while derived units are mathematical combinations of base units.

📏 Base units and the SI foundation

📏 What are base units

Base (or basic) units are the fundamental units of SI.

• SI defines exactly seven base units by international convention.
• Each base unit measures one fundamental property (length, mass, time, etc.).
• The size of each base unit is defined by international standards—for example, the kilogram is defined by a special metal cylinder kept in France.

🧪 The five base units chemistry uses

Property	Unit	Abbreviation
Amount	mole	mol
Mass	kilogram	kg
Length	meter	m
Time	second	s
Temperature	kelvin	K

• The degree Celsius (°C) is also commonly used for temperature.
• Relationship: K = °C + 273
• Note: The kilogram itself already contains a prefix (kilo-) combined with the gram.

🌍 Why SI matters globally

• Many countries have adopted SI units for everyday use.
• The United States is one of the few countries that has not fully adopted SI for everyday measurements.
• The United States uses the English system (inches, feet, miles, gallons, pounds) for many quantities.
• Scientists worldwide use SI to communicate efficiently regardless of their country's everyday measurement system.

🔢 The prefix system

🔢 How prefixes work

• Prefixes attach to base units to create units that are larger or smaller by powers of 10.
• Some prefixes create multiples: 1 kilogram = 1,000 grams; 1 megameter = 1,000,000 meters.
• Other prefixes create fractions: 1 centimeter = 1/100 meter; 1 millimeter = 1/1,000 meter; 1 microgram = 1/1,000,000 gram.
• The combination of a prefix abbreviation with a base unit abbreviation gives the abbreviation for the modified unit (e.g., kg for kilogram).

📊 Common SI prefixes

Prefix	Abbreviation	Multiplicative Factor	Scientific Notation
giga-	G	1,000,000,000×	10⁹×
mega-	M	1,000,000×	10⁶×
kilo-	k	1,000×	10³×
deca-	D	10×	10¹×
deci-	d	1/10×	10⁻¹×
centi-	c	1/100×	10⁻²×
milli-	m	1/1,000×	10⁻³×
micro-	μ	1/1,000,000×	10⁻⁶×
nano-	n	1/1,000,000,000×	10⁻⁹×

Note: μ is the Greek lowercase letter for m, pronounced "myoo."

🎯 Why prefixes are convenient

• Base unit sizes are not always convenient for all measurements.
• Example: A meter is too large for describing human hair width.
• Instead of reporting hair diameter as 0.00012 m or 1.2 × 10⁻⁴ m, you can use a smaller unit with a prefix.
• Prefixes let you express the same quantity in a more readable form.

🧩 Derived units

🧩 What derived units are

Derived units are combinations of SI base units.

• Units can be multiplied and divided, just as numbers can.
• Derived units are built by mathematical operations on base units.
• Don't confuse: base units are fundamental and defined by convention; derived units are constructed from base units through multiplication or division.

📦 Volume

Volume is the amount of space that a given substance occupies and is defined geometrically as length × width × height.

• Each distance is expressed in meters, so volume has the derived unit m × m × m = m³ (cubic meters).
• A cubic meter is rather large, so scientists typically use 1/1,000 of a cubic meter.
• This unit has its own name: the liter (L).
• A liter is a little larger than 1 US quart.
• A liter is also 1,000 cm³.
• By definition, 1 mL = 1 cm³ (1 milliliter equals 1 cubic centimeter).

⚡ Energy

Energy is the ability to perform work, such as moving a box from one side of a room to the other.

• Energy has a derived unit of kg·m²/s² (the dot implies multiplication).
• This combination is redefined as a joule (J) because the full form is cumbersome.
• An older unit, the calorie (cal), is also widely used.
• Conversion: 4.184 J = 1 cal.
• All chemical processes occur with a simultaneous change in energy.

Food energy context:

• The food industry uses the kilocalorie and calls it the Calorie (capital C).
• 1 Calorie = 1,000 calories (lowercase c).
• Average daily energy requirement: about 2,000–2,500 Calories = 2,000,000–2,500,000 calories.
• If energy intake equals energy expenditure, body weight remains stable; excess intake leads to weight gain (stored as fat); deficit leads to weight loss.

🏋️ Density

Density is defined as the mass of an object divided by its volume; it describes the amount of matter contained in a given amount of space.

• Formula: density = mass / volume
• Units of density: units of mass divided by units of volume.
• Common density units: g/cm³ or g/mL (for solids and liquids), g/L (for gases), kg/m³.

Examples from the excerpt:

• Water: about 1.00 g/cm³
• Mercury: 13.6 g/mL (over 13 times as dense as water—contains over 13 times the amount of matter in the same space)
• Air at room temperature: about 1.3 g/L

Sample calculation:

• A 25.3 cm³ bone sample has a mass of 27.8 g.
• Density = 27.8 g / 25.3 cm³ = 1.10 g/cm³

🔄 How units follow math rules

• Units follow the same mathematical rules as numbers.
• Units can be multiplied: 2 cm × 2 cm = 4 cm² (area).
• Units can be divided: mass / volume = density.
• Example: mL × (g/mL) = g (the mL cancels out).

🌐 Approximate equivalents

🌐 SI to English conversions

SI Unit	Approximate English Equivalent
1 m	≈ 39.36 in. ≈ 3.28 ft ≈ 1.09 yd
1 cm	≈ 2.54 in.
1 km	≈ 0.62 mi
1 kg	≈ 2.20 lb
1 lb	≈ 454 g
1 L	≈ 1.06 qt
1 qt	≈ 0.946 L

• These conversions help relate SI units to the English system still used in the United States for everyday measurements.

🧭 Overview

🧠 One-sentence thesis

Unit conversion is a systematic technique using conversion factors to change measurements from one unit to another while preserving the quantity's value and correctly tracking significant figures.

📌 Key points (3–5)

• What a conversion factor is: a fraction with equivalent quantities in numerator and denominator but expressed in different units, which equals 1.
• How to set up conversions: multiply the original quantity by a conversion factor arranged so the old unit cancels and the new unit appears.
• Exact vs. measured numbers: prefix-based conversions (like kg to g) use exact numbers that don't affect significant figures, but conversions from measurements (like density) do.
• Common confusion: which conversion factor to use—always place the unit you want to cancel in the denominator so it cancels algebraically with the numerator.
• Multi-step conversions: complex conversions can be done step-by-step or combined into one calculation; both methods yield the same answer if done correctly.

🔧 What conversion factors are and why they work

🔧 Definition and structure

Conversion factor: a fraction that has equivalent quantities in the numerator and the denominator but expressed in different units.

• Because the numerator and denominator represent the same quantity (just in different units), the fraction equals 1.
• Multiplying by a conversion factor is the same as multiplying by 1, so it doesn't change the actual value—only the units.
• Example: 100 cm = 1 m, so both 100 cm / 1 m and 1 m / 100 cm are valid conversion factors that equal 1.

⚖️ Why multiplying by 1 preserves the quantity

• The excerpt emphasizes that dividing both sides of an equation by the same quantity (number and unit) maintains equality.
• When the same quantity appears in numerator and denominator, the fraction equals 1.
• This is the mathematical foundation: you're not changing the measurement, only its expression.

🎯 How to perform unit conversions

🎯 The basic procedure

The general process is:

quantity (in old units) × conversion factor = quantity (in new units)

Steps:

1. Write the quantity you are given.
2. Multiply by a conversion factor.
3. Arrange the conversion factor so the original unit cancels.
4. Perform the calculation.
5. Report the answer with correct significant figures.

🔄 Choosing the correct conversion factor orientation

• Key rule: construct the conversion factor so the original unit cancels out.
• The unit you want to eliminate must appear in the denominator of the conversion factor (so it cancels with the numerator of your starting quantity).
• The unit you want to introduce should be in the numerator of the conversion factor.

Don't confuse: If you use the conversion factor upside-down, the units won't cancel properly and you'll get a meaningless result.

Example from the excerpt: converting 3.55 m to cm

• Correct: 3.55 m × (100 cm / 1 m) = 355 cm — meters cancel
• Wrong: 3.55 m × (1 m / 100 cm) = 0.0355 m²/cm — units don't cancel correctly

📐 Canceling units algebraically

• Units follow the same mathematical rules as numbers.
• When the same unit appears in both numerator and denominator, it cancels.
• Example: (3.55 m / 1) × (100 cm / 1 m) — the "m" cancels, leaving only "cm"

🔢 Significant figures in conversions

🔢 Exact numbers vs. measured numbers

Exact numbers: defined or counted numbers, not measured numbers, and can be considered as having an infinite number of significant figures.

Type	Examples	Effect on sig figs
Exact (prefix-based)	1 kg = 1,000 g; 1 m = 100 cm	Do NOT limit significant figures
Exact (counted)	16 students in a classroom	Do NOT limit significant figures
Measured	Density values from measurement	DO limit significant figures

• Numbers in conversion factors based on prefix definitions (kilo-, milli-, etc.) are exact by definition.
• These exact numbers are not considered when determining significant figures in the final answer.
• Conversion factors from measurements or approximations have limited significant figures and must be considered.

📏 Applying sig fig rules

• For conversions using exact factors: the original measurement's significant figures determine the answer's precision.
• Example from excerpt: 4.7 L has 2 sig figs; converting to mL using the exact factor 1,000 mL/L gives 4,700 mL, reported as 4,700 mL (2 sig figs).
• Normal multiplication/division rules apply when conversion factors contain measured values.

🔗 Special conversions and multi-step problems

🔗 Using density as a conversion factor

• Density relates mass and volume, so it can convert between them.
• Example: mercury has density 13.6 g/mL, meaning 13.6 g mercury = 1 mL mercury.
• Two possible conversion factors: 13.6 g / 1 mL or 1 mL / 13.6 g
• Choose based on which unit you need to cancel.

Scenario: What is the mass of 16 mL of mercury?

• Use 13.6 g / 1 mL so mL cancels: 16 mL × (13.6 g / 1 mL) = 217.6 g
• Round to 220 g (2 sig figs, limited by the 16 mL measurement)

Scenario: What is the volume of 0.750 g of mercury?

• Use 1 mL / 13.6 g so g cancels: 0.750 g × (1 mL / 13.6 g) = 0.0551 mL

🪜 Multi-step conversions

• Sometimes you need more than one conversion to reach the desired unit.
• Two approaches: convert step-by-step, or combine all conversions in one expression.
• Both methods are acceptable and should give the same answer.

Step-by-step approach:

1. Convert to the base unit first (e.g., km → m)
2. Then convert from base unit to final unit (e.g., m → mm)

Combined approach:

• Chain multiple conversion factors together in one calculation
• Example: 54.7 km × (1,000 m / 1 km) × (1,000 mm / 1 m) = 5.47 × 10⁷ mm

Important: Apply significant figure rules only after the final step when combining conversions.

🧮 Scientific notation in conversions

• Large or small results should be expressed in scientific notation.
• Example: 54,700,000 mm is written as 5.47 × 10⁷ mm
• The excerpt shows this is standard practice for very large or very small converted values.

🏥 Practical applications

💊 Medical and health contexts

The excerpt provides several real-world scenarios:

• Nursing: A nurse with 50 mg aspirin tablets who must administer 0.2 g needs to know 0.2 g = 200 mg, so 4 tablets are needed.
• Body measurements: Bone density (0.95–1.05 g/cm³ for healthy individuals; below 0.6–0.7 g/cm³ indicates osteoporosis)
• Urine analysis: Density of urine provides health clues (normal specific gravity: 1.002 to 1.028)
• Body fat: Overall body density correlates with body fat percentage (fat is less dense than muscle)

🔬 Why the formal procedure matters

• Simple conversions might be done mentally, but the formal method works for all problems.
• The excerpt emphasizes: "In later studies, the conversion problems you will encounter will not always be so simple."
• Mastering the conversion factor technique prepares you for complex, multi-step problems.

🧭 Overview

🧠 One-sentence thesis

Elements are the fundamental chemical building blocks of matter that cannot be broken down into simpler substances, and each element is represented by a unique chemical symbol for convenient use in chemistry.

📌 Key points (3–5)

• What an element is: a substance that cannot be broken down into simpler chemical substances; about 118 elements are known today (90 naturally occurring, ~30 created by technology).
• Abundance varies widely: hydrogen dominates the universe (~90% of atoms), but Earth's crust is mostly oxygen (46.1%) and silicon (28.5%); the human body concentrates certain rare elements like carbon.
• Chemical symbols: each element has a one- or two-letter abbreviation (first letter capitalized, second lowercase) derived from its name or earlier Latin name.
• Common confusion: element abundance in the human body vs. Earth's crust—the body concentrates elements based on availability in assimilable forms (e.g., carbon from food, not air), not just crustal abundance.
• Atomic theory foundation: all elements are composed of atoms, the smallest units that maintain an element's identity; some elements exist as individual atoms, others as diatomic molecules.

🌍 Abundance of elements

🌌 Universe vs. Earth

Location	Most abundant element	Second most abundant	Key difference
Universe	Hydrogen (~90% of atoms)	Helium (most of remaining 10%)	All other elements are trace amounts
Earth's crust	Oxygen (46.1% by mass)	Silicon (28.5%)	Hydrogen is only 0.14%

• The situation on Earth is "rather different" from the universe as a whole.
• Oxygen dominates Earth's crust, mostly in combination with other elements.

🧬 Human body composition

The relative amounts of elements in the body have less to do with their abundances on Earth than with their availability in a form we can assimilate.

• Oxygen is highest in both Earth's crust and the human body.
• Carbon is the second-highest element in the body (23%) but is relatively rare on Earth (part of the 0.174% "other" in crustal composition).
• How the body concentrates rare elements: we obtain elements from accessible sources—oxygen and hydrogen from air and water, carbon and nitrogen from food (not from atmospheric CO₂ or N₂).

🔬 Phosphorus bottleneck example

• Phosphorus makes up 1.1% of the human body but only 0.105% of Earth's crust.
• It is essential for bones, teeth, and all living cells, but there is no convenient environmental source like CO₂ for carbon.
• Why it matters: phosphorus availability limits the amount of life Earth can sustain.
• Example: phosphorus-containing detergents in the 1950s increased algae growth in lakes → bacteria consumed dead algae → oxygen dropped → fish died (eutrophication). Modern detergents often omit phosphorus to prevent this.
• Don't confuse: abundance in the body with abundance in the environment; availability matters more than total crustal percentage.

🔤 Chemical symbols

🔤 What they are and why they're used

Each element name is abbreviated as a one- or two-letter chemical symbol.

• Element names can be cumbersome to write in full, especially in compound names.
• Convention: first letter is capitalized, second letter (if present) is lowercase.
• Example: Bromine → Br, Calcium → Ca, Gold → Au.

🏛️ Origin of symbols

• Usually the first letter of the element's name, plus another letter from the name.
• Some symbols derive from earlier (mostly Latin) names and may not match the English name.

Element	Symbol	Origin
Gold	Au	Latin aurum
Silver	Ag	Latin argentum
Iron	Fe	Latin ferrum
Lead	Pb	Latin plumbum
Tin	Sn	Latin stannum
Sodium	Na	Latin natrium
Potassium	K	Latin kalium
Mercury	Hg	Latin hydrargyrum
Tungsten	W	German wolfram

• Don't confuse: CO (carbon monoxide, a compound) with Co (cobalt, an element); the second letter must be lowercase for a single element symbol.

🌐 Names in other languages

• Element names in other languages are often close to their Latin names.
• Example: gold is oro in Spanish, or in French (compare Latin aurum); silver is argent in French (compare argentum).

⚛️ Atomic theory

⚛️ What the modern atomic theory states

The modern atomic theory, proposed about 1803 by the English chemist John Dalton, is a fundamental concept that states that all elements are composed of atoms.

• Atom definition: the smallest part of an element that maintains the identity of that element.
• Individual atoms are extremely small: the largest atom has a diameter of only about 5.4 × 10⁻¹⁰ meters.
• Example: it takes over 18 million of the largest atoms, lined up side by side, to equal the width of a little finger (about 1 cm).

🧪 How elements exist

• Most elements: exist as individual atoms in their pure form.
  • Example: a macroscopic chunk of iron metal is composed, microscopically, of individual atoms.
• Some elements: exist as groups of atoms called molecules.

🔗 Diatomic molecules

Several important elements exist as two-atom combinations and are called diatomic molecules.

• Represented by the element symbol with a subscript 2 (e.g., H₂, O₂).
• The seven diatomic elements: hydrogen (H₂), oxygen (O₂), nitrogen (N₂), fluorine (F₂), chlorine (Cl₂), bromine (Br₂), and iodine (I₂).

📜 Historical context

• The concept of atoms is very old: Greek philosophers Leucippus and Democritus introduced atomic concepts in the fifth century BC.
• The word atom comes from Greek atomos, meaning "indivisible" or "uncuttable."
• What made Dalton's theory "modern": he had experimental evidence (formulas of simple chemicals, behavior of gases) and used the scientific method, not just philosophical discussion.
• Don't confuse: ancient atomic philosophy (speculative) with modern atomic theory (evidence-based).

🧭 Overview

🧠 One-sentence thesis

The modern atomic theory establishes that all matter is composed of atoms—the smallest parts of an element that maintain that element's identity—and this theory is supported by experimental evidence rather than just philosophical speculation.

📌 Key points (3–5)

• What atoms are: the smallest parts of an element that maintain the identity of that element; extremely small (largest atom ≈ 5.4 × 10⁻¹⁰ m diameter).
• The fundamental concept: all elements are composed of atoms.
• How elements exist: most elements exist as individual atoms, but some exist as diatomic molecules (two-atom combinations).
• Common confusion: ancient Greek atomic concepts vs. modern atomic theory—Dalton's version is "modern" because it rests on experimental evidence (formulas, gas behavior), not just philosophical discussion.
• Key diatomic elements: hydrogen (H₂), oxygen (O₂), nitrogen (N₂), fluorine (F₂), chlorine (Cl₂), bromine (Br₂), and iodine (I₂).

🔬 What atoms are and their scale

🔬 Definition of an atom

Atom: the smallest part of an element that maintains the identity of that element.

• Atoms are the ultimate building blocks of all matter.
• They are not just "small pieces"; they are the smallest pieces that still preserve what makes an element that element.

📏 Size of atoms

• Individual atoms are extremely small.
• Even the largest atom has an approximate diameter of only 5.4 × 10⁻¹⁰ meters.
• Example: it takes over 18 million of these atoms, lined up side by side, to equal the width of your little finger (about 1 cm).
• This scale emphasizes that atoms are far beyond everyday human perception.

🧪 How elements exist in nature

🧪 Individual atoms vs. molecules

Most elements in their pure form exist as individual atoms.

• Example: a macroscopic chunk of iron metal is composed, microscopically, of individual atoms.
• However, some elements exist as groups of atoms called molecules.

🔗 Diatomic molecules

Diatomic molecule: a two-atom grouping that behaves as a single chemical entity.

• Several important elements exist as two-atom combinations.
• In representing a diatomic molecule, we use the symbol of the element and include the subscript 2 to indicate that two atoms of that element are joined together.

📋 The seven diatomic elements

The elements that exist as diatomic molecules are:

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

Don't confuse: helium exists as individual He atoms, but hydrogen exists as H₂ molecules in its elemental form. Similarly, calcium exists as individual Ca atoms, but chlorine exists as Cl₂ molecules.

🏛️ Historical context: ancient vs. modern atomic theory

🏛️ Ancient Greek origins

• The Greek philosophers Leucippus and Democritus originally introduced atomic concepts in the fifth century BC.
• The word "atom" comes from the Greek word "atomos," which means "indivisible" or "uncuttable."
• However, this was purely philosophical discussion without experimental support.

🔬 Why Dalton's theory is "modern"

Dalton's ideas are called the modern atomic theory because:

• Dalton had experimental evidence that the ancient Greek philosophers didn't have.
• His evidence included the formulas of simple chemicals and the behavior of gases.
• In the 150 years or so before Dalton, natural philosophy had been maturing into modern science, and the scientific method was being used to study nature.
• When Dalton announced his theory, he was proposing a fundamental theory to describe many previous observations of the natural world, not just participating in philosophical discussion.

👤 John Dalton

• John Dalton was an English scientist who enunciated the modern atomic theory.
• He used the scientific method and experimental evidence to support his claims.

🎯 Core takeaways

🎯 The modern atomic theory statement

The modern atomic theory states that all matter is composed of atoms.

• This is the fundamental concept that unifies chemistry.
• It means every element, every compound, every material substance is ultimately built from atoms.

🎯 Atoms as building blocks

• Atoms are the ultimate building blocks of all matter.
• They establish the concepts of how matter is composed at the most fundamental level.
• Understanding atoms is essential for understanding chemistry and the natural world.

🧭 Overview

🧠 One-sentence thesis

Atoms are composed of three subatomic particles—protons and neutrons concentrated in a central nucleus, with electrons orbiting in the surrounding space—which explains why atoms are mostly empty space despite having measurable mass.

📌 Key points (3–5)

• Three subatomic particles: protons (positive charge, large mass), neutrons (no charge, large mass), and electrons (negative charge, tiny mass).
• Arrangement: protons and neutrons are grouped in the nucleus; electrons orbit outside the nucleus.
• Mass vs. volume: most of an atom's mass is in the nucleus, but most of an atom's volume is empty space occupied by electron orbits.
• Common confusion: the planetary model (electrons in fixed circular orbits) is overly simplistic—electrons actually form fuzzy clouds around the nucleus, not discrete orbits.
• Experimental evidence: Rutherford's metal-foil experiments (1909–1911) showed that most alpha particles pass straight through atoms, proving atoms are mostly empty space with a dense central nucleus.

⚛️ The three subatomic particles

🔬 Discovery and properties

The three particles were discovered over time:

• Electron (1897): identified first.
• Proton (by 1920): experimental evidence confirmed its existence.
• Neutron (1932): evidence established the third particle.

⚡ Charge and mass characteristics

Particle	Symbol	Charge	Mass (kg)	Relative mass (proton = 1)
Proton	p⁺	+1 (positive)	1.673 × 10⁻²⁷	1
Neutron	n⁰	0 (neutral)	1.675 × 10⁻²⁷	1
Electron	e⁻	−1 (negative)	9.109 × 10⁻³¹	0.00055

Key contrasts:

• Protons and neutrons have nearly the same mass (about 2,000 times greater than an electron).
• Protons and electrons have the same amount of charge, but opposite signs.
• Neutrons have no electrical charge.

🧲 How charges interact

• Opposite charges attract each other; like charges repel.
• Protons (positive) attract electrons (negative), and vice versa.
• This attraction explains why electrons stay near the nucleus.

🎯 Rutherford's nucleus model

🧪 The Geiger-Marsden experiment (1909–1911)

Ernest Rutherford, Hans Geiger, and Ernest Marsden performed experiments to probe atomic structure:

• Setup: aimed a beam of positively charged alpha particles (combinations of two protons and two neutrons) at very thin metal foil (gold or platinum).
• Detection: used a scintillator (glows when hit) or unexposed film to track where particles ended up after hitting the foil.

🎲 Unexpected results

• Most particles traveled straight through the foil.
• Some particles were deflected to one side.
• A few particles were deflected back toward the source.

Rutherford remarked: "It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you."

🏛️ The nuclear model explanation

Nucleus: the central region of an atom that contains protons and neutrons.

Rutherford proposed:

• Protons and neutrons are concentrated in a tiny, dense nucleus.
• Electrons orbit outside the nucleus, attracted by the positive charge.
• Most of the atom's mass is in the nucleus.
• Most of the atom's size (volume) is empty space where electrons orbit.

Why the results make sense:

• Most alpha particles go straight through because atoms are mostly empty space.
• A few particles are deflected because they pass near the positive nucleus and are repelled.
• Very few ricochet back because they hit the dense nucleus head-on.

Don't confuse: The nucleus is much smaller than depicted in diagrams—it is tiny compared to the overall atom size.

🌌 From planetary model to modern understanding

🪐 The planetary model

Rutherford called his description the "planetary model":

• Electrons orbit the nucleus like planets orbit the sun.
• This replaced the earlier "plum pudding model" (electrons floating aimlessly in a "pudding" of positive charge).

☁️ Modern refinement

The planetary model is overly simplistic:

• Electrons do not occupy specific, circular orbits.
• Instead, electrons form fuzzy clouds around the nucleus.
• A better description: electrons occupy regions of space (probability clouds), not discrete paths.

Example: In a hydrogen atom, the darker the color or the more crowded the dots in a diagram, the higher the probability that an electron will be at that point. The nucleus is at the center, but the electron's exact position is not fixed.

🔄 Why the distinction matters

• The planetary model suggests fixed, predictable paths.
• The modern model reflects that we can only describe where electrons are likely to be, not where they are at any exact moment.

📦 Structure summary

🧱 How atoms are arranged

• Nucleus (center): contains protons and neutrons; accounts for most of the atom's mass.
• Electron cloud (surrounding space): electrons orbit about the nucleus; accounts for most of the atom's size.
• Overall charge: if an atom is electrically neutral, the number of protons equals the number of electrons (opposite charges cancel out).

🔍 Key takeaways from the excerpt

• Atoms can be broken down into subatomic particles (contradicting Dalton's original idea that atoms are indivisible).
• The nucleus is extremely small compared to the atom's total volume.
• Electrons are attracted to the nucleus but occupy a large region of space around it.
• The structure explains both the mass distribution (concentrated in the nucleus) and the volume (mostly empty space).

🧭 Overview

🧠 One-sentence thesis

The atomic number (number of protons) defines an element's identity, while isotopes of the same element differ only in their number of neutrons, and together protons and neutrons determine an atom's mass number.

📌 Key points (3–5)

• Atomic number defines the element: every atom of a particular element has the same number of protons; different elements have different numbers of protons.
• Neutral atoms have equal protons and electrons: the number of electrons equals the number of protons when an atom is electrically neutral, canceling out opposite charges.
• Isotopes are variants of the same element: atoms of the same element can have different numbers of neutrons, creating isotopes with different masses.
• Mass number = protons + neutrons: the mass number is the sum of protons and neutrons in the nucleus, allowing you to calculate neutrons by subtracting atomic number from mass number.
• Common confusion: atomic number vs. mass number—atomic number identifies the element (protons only), while mass number describes a specific isotope (protons + neutrons).

🔢 Atomic number and element identity

🔢 What atomic number means

Atomic number: the number of protons in the nucleus of an atom.

• Experiments with X-rays in the 1910s showed that all atoms of the same element have the same number of protons.
• Different elements have different numbers of protons.
• The atomic number is characteristic of a particular element—it defines what element an atom is.
• Example: hydrogen has atomic number 1 (1 proton); helium has atomic number 2 (2 protons). A nucleus with 2 protons cannot be hydrogen; it must be helium.

⚡ Electrons in neutral atoms

• For an electrically neutral atom, the number of electrons equals the number of protons.
• Equal numbers of opposite charges cancel out, producing a neutral atom.
• Therefore, the atomic number also tells you the number of electrons in a neutral atom.
• Don't confuse: later, elements may gain or lose electrons, making atoms no longer neutral; in those cases, electron count differs from proton count.

🧬 Isotopes and neutron variation

🧬 What isotopes are

Isotopes: atoms of the same element that have different numbers of neutrons.

• Initially scientists thought neutron number was also characteristic of an element, but this turned out to be incorrect.
• Atoms of the same element can have different numbers of neutrons.
• Example: 99% of carbon atoms on Earth have 6 neutrons and 6 protons; about 1% have 7 neutrons. Naturally occurring carbon is actually a mixture of isotopes.

🔬 Hydrogen isotopes as an example

The excerpt highlights hydrogen isotopes to illustrate variation:

Isotope	Protons	Neutrons	Notes
Most hydrogen	1	0	Single proton only
Deuterium	1	1	About 1 in 10,000 hydrogen nuclei
Tritium	1	2	Extremely rare

• All three are hydrogen (same atomic number), but they differ in neutron count and therefore mass.

📝 Minor change to Dalton's theory

• Dalton thought all atoms of the same element were exactly the same.
• The discovery of isotopes required a correction: most elements exist as mixtures of isotopes.
• Currently over 3,500 isotopes are known for all the elements.

⚖️ Mass number and isotope notation

⚖️ What mass number means

Mass number: the sum of the numbers of protons and neutrons in the nucleus of an atom.

• Mass number is not the same as atomic number.
• To find the number of neutrons: subtract the atomic number from the mass number.
• Formula in words: neutrons = mass number minus atomic number.

🏷️ How to write isotopes

Scientists use efficient notation to specify isotopes:

• Superscript-subscript notation: mass number as superscript on the left, atomic number as subscript on the left of the element symbol.
• Example: ²⁶₅₆Fe (written as 26 on bottom, 56 on top, then Fe) indicates iron with atomic number 26 and mass number 56.
• Calculating neutrons: 56 − 26 = 30 neutrons.
• Simplified notation: often only the superscript is shown (e.g., ¹³C or ²³⁵U), since each element has a unique atomic number.
• Word notation: isotopes may also be written as "carbon-13" or "uranium-235."

🧮 Working with isotope symbols

Example from the excerpt:

• ¹⁷₃₅Cl: 17 protons (atomic number), 35 − 17 = 18 neutrons.
• ⁵³₁₂₇I: 53 protons, 127 − 53 = 74 neutrons.

Don't confuse: the subscript (atomic number) is often omitted because it's redundant—the element symbol already tells you the atomic number.

📊 Summary of key relationships

Concept	What it tells you	How to use it
Atomic number	Number of protons; defines the element	Look up in periodic table; also equals electrons in neutral atom
Mass number	Protons + neutrons in a specific isotope	Subtract atomic number to find neutrons
Isotopes	Same element, different neutron counts	Same atomic number, different mass numbers
Neutral atom	Electrically balanced	Protons = electrons

🎯 Why these concepts matter

• The atomic number is fundamental: it defines what element you have.
• Isotopes explain why atoms of the same element can have different masses.
• Mass number allows you to specify exactly which isotope you're discussing.
• Understanding the relationship between protons, neutrons, and electrons is essential for describing any atom accurately.

🧭 Overview

🧠 One-sentence thesis

Atomic mass is a weighted average of all naturally occurring isotopes of an element, measured in atomic mass units (u), where 1 u equals one-twelfth the mass of a carbon-12 atom.

📌 Key points (3–5)

• What atomic mass is: a weighted average of an element's isotope masses, based on natural abundance of each isotope.
• The atomic mass unit (u): defined as 1/12th the mass of a carbon-12 atom; 1 u = 1.661 × 10⁻²⁴ grams.
• How to calculate: multiply each isotope's mass by its natural abundance (as a decimal), then sum the results.
• Common confusion: atomic mass is not the mass of a single atom—it's an average across all naturally occurring isotopes of that element.
• Why it matters: atomic mass allows conversion between atomic-scale measurements and macroscopic grams, essential for chemistry calculations.

⚖️ What atomic mass means

⚖️ Weighted average definition

Atomic mass: an average of an element's atomic masses, weighted by the natural abundance of each isotope of that element.

• It is not the mass of one specific atom; it reflects the mix of isotopes found in nature.
• Different isotopes have different masses, so the average must account for how common each isotope is.
• Example: Boron exists as 19.9% boron-10 and 80.1% boron-11 in nature, so the atomic mass reflects mostly boron-11.

🔢 The atomic mass unit (u)

1 u = 1/12 the mass of a carbon-12 atom.

• This standard reference point makes atomic masses easy to compare.
• Conversion to grams: 1 u = 1.661 × 10⁻²⁴ grams.
• Don't confuse: the atomic mass unit is a defined standard, not an arbitrary choice—it's anchored to carbon-12.

🧮 How to calculate atomic mass

🧮 The weighted average formula

The excerpt shows the calculation for boron:

• Boron-10: 10.0 u, abundance 19.9% (0.199 as a decimal)
• Boron-11: 11.0 u, abundance 80.1% (0.801 as a decimal)
• Calculation: (0.199 × 10.0 u) + (0.801 × 11.0 u) = 10.8 u

Steps:

1. Convert each isotope's natural abundance percentage to a decimal.
2. Multiply each isotope's mass by its decimal abundance.
3. Add all the products together.

🌍 Real-world example: carbon

• Carbon exists as about 99% carbon-12 and about 1% carbon-13 on Earth.
• The weighted average mass is 12.01 u (slightly above 12 u because of the small contribution from carbon-13).
• This shows why atomic masses are rarely whole numbers—they reflect the isotope mix.

🔬 Converting to grams

🔬 From atomic mass units to grams

The excerpt provides a worked example for carbon:

• Carbon's atomic mass: 12.01 u
• Conversion: 12.01 u × (1.661 × 10⁻²⁴ g / 1 u) = 1.995 × 10⁻²³ grams
• This is an extremely small mass, illustrating how tiny individual atoms are.

📏 Why this conversion matters

• Atomic mass units are convenient for comparing atoms to each other.
• Grams are needed for laboratory measurements and real-world chemistry.
• The conversion factor (1 u = 1.661 × 10⁻²⁴ g) bridges the atomic scale and the macroscopic scale.

🔑 Key takeaway from the excerpt

🔑 Mass basis

The excerpt emphasizes:

Atoms have a mass that is based largely on the number of protons and neutrons in their nucleus.

• Electrons contribute negligibly to atomic mass because they are so light.
• The atomic mass reflects the nucleus (protons + neutrons), averaged across isotopes.
• Example exercises in the excerpt ask students to find atomic masses from tables, convert to grams, and compare masses of different numbers of atoms—all reinforcing the practical use of atomic mass.

🧭 Overview

🧠 One-sentence thesis

Electrons in atoms are organized into shells and subshells with specific energy levels and capacities, and the electrons in the outermost shell (valence electrons) determine how atoms interact chemically.

📌 Key points (3–5)

• Quantum mechanics governs electron behavior: electrons can only have certain specific energies (quantized) and are organized into shells and subshells.
• Shells and subshells have fixed capacities: s subshells hold up to 2 electrons, p holds 6, d holds 10, and f holds 14.
• Electron configurations describe electron arrangement: a shorthand notation (e.g., 1s² 2s² 2p⁶) shows which shells and subshells electrons occupy.
• Common confusion—core vs. valence electrons: valence electrons are in the highest-numbered shell and determine chemical behavior; core electrons are in lower-numbered shells.
• Filling order matters: subshells fill in a specific sequence, and sometimes a higher-numbered shell begins filling before a lower-numbered shell is complete (e.g., 4s fills before 3d).

⚛️ Quantum mechanics and electron organization

⚛️ What quantum mechanics tells us about electrons

Quantum mechanics: the modern theory of electron behavior.

The theory makes four key statements about electrons in atoms:

• Electrons can only have certain specific energies—their energies are quantized (having a fixed value).
• Electrons are organized into shells (groupings of electrons within an atom), with higher-energy shells generally farther from the nucleus on average.
• Shells do not have fixed distances from the nucleus, but higher-energy electrons spend more time farther away.
• Shells are divided into subshells (groupings of electrons within a shell).

🏗️ Shell and subshell structure

Shell number	Subshells present	Maximum electrons per subshell
1	s only	s: 2
2	s, p	s: 2, p: 6
3	s, p, d	s: 2, p: 6, d: 10
4+	s, p, d, f	s: 2, p: 6, d: 10, f: 14

• The first shell has only an s subshell.
• The second shell has s and p subshells.
• The third shell has s, p, and d subshells.
• Subshells are labeled with the letters s, p, d, and f in order.

📝 Electron configurations

📝 What electron configurations show

Electron configuration: a shorthand description of the arrangement of electrons in an atom.

• Combines shell number + subshell letter + superscript for number of electrons.
• Example: 1s¹ means one electron in the s subshell of the first shell.
• Spoken as "one-ess-one."

🔢 How to write electron configurations

The excerpt provides a step-by-step filling pattern:

• Hydrogen (1 electron): 1s¹
• Helium (2 electrons): 1s² (the 1s subshell is now full)
• Lithium (3 electrons): 1s² 2s¹ (the third electron must go into the second shell because s subshells hold maximum 2 electrons)
• Beryllium (4 electrons): 1s² 2s²
• Boron through neon (5–10 electrons): electrons begin filling the 2p subshell
  • B: 1s² 2s² 2p¹
  • C: 1s² 2s² 2p²
  • N: 1s² 2s² 2p³
  • O: 1s² 2s² 2p⁴
  • F: 1s² 2s² 2p⁵
  • Ne: 1s² 2s² 2p⁶

Example from the excerpt: A neutral phosphorus atom has 15 electrons, so its electron configuration is 1s² 2s² 2p⁶ 3s² 3p³.

⚠️ Unusual filling order

• After the 3p subshell is filled, a curious thing happens: the 4s subshell begins to fill before the 3d subshell does.
• The exact ordering of subshells becomes more complicated after argon (18 electrons).
• Don't confuse: higher shell numbers don't always fill in strict numerical order.

🎯 Valence and core electrons

🎯 What valence electrons are

Valence shell electrons (or valence electrons): the electrons in the highest-numbered shell, or valence shell.

Core electrons: the electrons in lower-numbered shells.

• Chemistry results from interactions between the outermost shells of electrons on different atoms.
• It is convenient to separate electrons into these two groups.

🔍 How to identify valence vs. core electrons

Example from the excerpt: A carbon atom has electron configuration 1s² 2s² 2p².

• The highest-numbered shell is shell 2.
• Valence electrons: 2s² 2p² = 4 valence electrons.
• Core electrons: 1s² = 2 core electrons.

Example: Neutral phosphorus (1s² 2s² 2p⁶ 3s² 3p³):

• Highest-numbered shell is the third shell (3s² 3p³).
• Total valence electrons: 2 + 3 = 5.
• Core electrons: the 10 remaining electrons from the first and second shells.

💡 Why the distinction matters

• The excerpt states that chemistry results from interactions between the outermost shells of electrons on different atoms.
• Valence electrons determine chemical behavior; core electrons do not participate in typical chemical reactions.

📊 Summary of key rules

Concept	Rule
Subshell capacity	s: 2, p: 6, d: 10, f: 14
Shell structure	Shell 1: s only; Shell 2: s, p; Shell 3: s, p, d; Shell 4+: s, p, d, f
Filling order	Generally follows shell number, but exceptions exist (e.g., 4s before 3d)
Valence electrons	Electrons in the highest-numbered shell
Core electrons	All electrons in lower-numbered shells

🧭 Overview

🧠 One-sentence thesis

The periodic table organizes elements by atomic number and groups them by similar chemical properties, which arise from shared valence electron configurations and show predictable trends in atomic size and behavior.

📌 Key points (3–5)

• Historical organization: Elements were first grouped by atomic mass and similar chemical properties; Mendeleev's version predicted undiscovered elements successfully.
• Structure reflects electron filling: The table's shape mirrors the order in which electron subshells fill, and elements in the same column share the same valence shell electron configuration.
• Groups vs periods: Columns (groups/families) contain elements with similar properties; rows (periods) vary in length and represent different electron shell numbers.
• Common confusion: Atomic radius trends—radius increases going down a column (more shells) but decreases going across a period (stronger nuclear pull on the same shell).
• Classification by properties: Elements are categorized as metals, nonmetals, or semimetals based on physical and chemical characteristics.

📜 Historical development

📜 Early organization efforts

• In the 19th century, scientists noticed that certain sets of elements had similar chemical properties.
• Example: Chlorine, bromine, and iodine all react with sodium to make similar compounds; lithium, sodium, and potassium all react with oxygen similarly.

🔬 Mendeleev's breakthrough

• Julius Lothar Meyer (1864) organized elements by atomic mass and grouped them by chemical properties.
• Dmitri Mendeleev organized all known elements according to similar properties and left gaps for undiscovered elements.
• His bold predictions about the properties of missing elements were later confirmed, gaining favor for his version.
• Note: Mendeleev had to list some elements out of atomic mass order to group them with elements having similar properties.

🔄 Why "periodic"

Periodic table: a chart of elements that groups the elements by some of their properties.

• Certain properties repeat on a regular basis throughout the table—they are periodic.
• The table became known as the periodic table because of this regular repetition of properties.

🏗️ Structure and organization

🏗️ Basic arrangement

• Elements are listed in order of atomic number (not atomic mass).
• Most periodic tables provide additional data (such as atomic mass) in a box containing each element's symbol.

📊 Groups (columns)

Groups (or families): a column of elements on the periodic table.

• Elements with similar chemical properties are grouped in vertical columns.
• Groups are both numbered and named:

Group name	Location	Examples
Alkali metals	First column	Lithium, sodium, potassium, rubidium, cesium, francium
Alkaline earth metals	Second column	Magnesium, calcium, barium
Halogens	Next-to-last column	Fluorine, chlorine, bromine, iodine
Noble gases	Last column	Helium, neon, argon, radon

• Note: "Halogen" comes from Greek for "salt maker" because these elements combine with other elements to form salts.

📏 Periods (rows)

Period: a row of elements on the periodic table.

• Periods have different lengths:
  • First period: only 2 elements (hydrogen and helium)
  • Second and third periods: 8 elements each
  • Fourth and fifth periods: 18 elements each
  • Later periods: so long that segments are removed and placed beneath the main body of the table

🔬 Element classifications

🔬 Metals, nonmetals, and semimetals

Type	Properties	Location
Metal	Shiny, typically silvery, excellent conductor of electricity and heat, malleable (beaten into thin sheets), ductile (drawn into thin wires)	Left three-fourths of the periodic table
Nonmetal	Typically dull, poor conductor of electricity and heat, brittle when solid	Upper right-hand corner (except hydrogen)
Semimetal (metalloid)	Properties intermediate between metals and nonmetals	Adjacent to the bold line in the right-hand portion

🎯 Special sections

Main group elements: an element in the first two or the last six columns on the periodic table.

Transition metals: an element between the main group elements on the periodic table.

Inner transition metals: an element in the two rows beneath the main body on the periodic table (also called lanthanide and actinide elements).

• The first two columns on the left and the last six columns on the right are main group elements.
• The ten-column block between these contains the transition metals.
• The two rows beneath the main body contain the inner transition metals (lanthanide metals and actinide metals).

⚛️ Electron configuration connection

⚛️ Why similar properties occur

• The shape of the periodic table reflects the filling of subshells with electrons.
• Starting with the first period and going left to right, the table reproduces the order of filling of electron subshells in atoms.
• Crucial observation: Elements in the same column share the same valence shell electron configuration.

🔑 Valence electrons determine chemistry

• Chemistry is largely the result of interactions between the valence electrons of different atoms.
• Atoms with the same valence shell electron configuration have similar chemistry.
• Example: All elements in the first column have a single s electron in their valence shells (configuration: ns¹, where n represents the shell number).
• Example: Alkaline earth metals (second column) have valence configuration ns².
• Example: Carbon's column has valence configuration ns² np².

🧮 Using the pattern

• The variable n represents the number of the valence electron shell.
• Each group can be described by its valence shell electron configuration.
• This pattern explains why elements in the same column behave similarly chemically.

📐 Atomic radius trends

📐 What atomic radius means

Atomic radius: the approximate size of an atom.

📉 Trend going down a column (increasing)

• As you go down a column, the atomic radius increases.
• Reason: Higher shell numbers mean electrons are farther from the nucleus.
• The size of an atom is generally determined by the number of the valence electron shell.
• Example: Bismuth (Bi) atoms are larger than nitrogen (N) atoms because Bi is below N and has electrons in higher-numbered shells.

📈 Trend going across a period (decreasing)

• As you go across a period (left to right), the atomic radius decreases.
• Reason: Electrons are being added to the same valence shell, but more protons are being added to the nucleus.
• The increasing positive charge attracts electrons more strongly, pulling them closer to the nucleus.
• Example: Magnesium (Mg) atoms are larger than chlorine (Cl) atoms because both are in period 3, but Cl lies farther to the right.

🔄 Don't confuse

• Down a column = more shells = larger atoms
• Across a period = same shell but stronger nuclear pull = smaller atoms
• These two trends work in opposite directions and can be used to compare any two elements on the table.

🧭 Overview

🧠 One-sentence thesis

Atoms form chemical bonds to achieve a stable eight-electron outer shell (the octet rule), either by transferring electrons to create ionic bonds or by sharing electrons to create covalent bonds.

📌 Key points (3–5)

• The octet rule: atoms are especially stable when they have eight electrons in their outermost shell, which drives bond formation.
• Two pathways to an octet: atoms can transfer electrons (forming ionic bonds) or share electrons (forming covalent bonds).
• Ionic bonds form from charge attraction: atoms that lose electrons become positively charged ions, atoms that gain electrons become negatively charged ions, and opposite charges attract.
• Common confusion: not all atoms follow the octet rule—small atoms like hydrogen, helium, and lithium follow a "duet rule" (two electrons in the outermost shell).
• Why atoms bond: noble gases (helium, neon, argon, etc.) rarely form compounds because they already have stable electron configurations, showing that stability drives bonding.

🔬 Why atoms form bonds

🔬 The stability clue from noble gases

• Noble gas elements (helium, neon, argon, krypton, xenon, radon) occupy the rightmost column of the periodic table.
• These elements do not form compounds easily, suggesting they are especially stable as lone atoms.
• All noble gases except helium have eight valence electrons in their outermost shell.
• This observation led chemists to conclude that eight electrons in the outer shell is a particularly stable arrangement.

🎯 The octet rule

Octet rule: the concept that atoms tend to have eight electrons in their valence electron shell.

• Atoms that do not have an octet of valence electrons will seek to obtain one.
• This rule is a key to understanding why compounds form.
• The drive to achieve an octet explains why atoms make chemical bonds rather than remaining as individual atoms.

⚠️ Exception: the duet rule

• Small atoms (hydrogen, helium, lithium) have a first shell that becomes the outermost shell.
• This shell holds only two electrons, not eight.
• These atoms satisfy a "duet rule" rather than the octet rule.
• Don't confuse: the octet rule applies to most atoms, but the smallest atoms follow a different pattern.

⚡ Ionic bonding: electron transfer

⚡ How ionic bonds form

Chemical bond: a very strong attraction between two atoms, formed when electrons in different atoms interact to make an arrangement that is more stable than when the atoms are apart.

Ionic bond: an attraction between oppositely charged ions.

• One way to obtain an octet is by transferring electrons between atoms until all atoms have octets.
• Some atoms lose electrons, others gain electrons.
• There is no overall change in the number of electrons, but individual atoms acquire a nonzero electric charge.

🔋 Formation of ions

Ions: charged atoms.

• Atoms that lose electrons become positively charged.
• Atoms that gain electrons become negatively charged.
• Opposite charges attract (while like charges repel).
• These oppositely charged ions attract each other, forming ionic bonds.

🧂 Ionic compounds

Ionic compounds: compounds formed with ionic bonds.

• The compounds resulting from ionic bonding are called ionic compounds.
• Example from the excerpt: Table salt consists of sodium and chlorine, but the compound has properties completely different from either elemental sodium (a chemically reactive metal) or elemental chlorine (a poisonous, green gas).

💡 Which atoms lose vs. gain electrons

• Atoms with only a few valence electrons are more likely to lose them.
• Atoms with nearly eight valence electrons are more likely to gain the remaining electrons.

Example: Sodium atom

• A sodium atom has one valence electron.
• It is more likely to lose that single electron than to gain seven electrons.
• When it loses one electron, it becomes an ion with a net positive charge:
  • Sodium atom: 11 protons (11+), 11 electrons (11−), 0 overall charge
  • Sodium ion: 11 protons (11+), 10 electrons (10−), +1 overall charge

Example: Fluorine atom

• A fluorine atom has seven valence electrons.
• It is more likely to gain one electron than to lose seven electrons to obtain an octet.

🚫 Why ionic compounds need opposite charges

• An ionic compound is unlikely to consist of two positively charged ions because positive charges repel each other.
• Similarly, an ionic compound is unlikely to consist of two negatively charged ions because negative charges also repel each other.
• Only oppositely charged ions attract strongly enough to form stable ionic bonds.

🔗 Covalent bonding: electron sharing

🔗 The second pathway to an octet

Covalent bond: the bond made by electron sharing.

• The second way for an atom to obtain an octet is by sharing electrons with another atom.
• These shared electrons simultaneously occupy the outermost shell of more than one atom.
• Covalent bonding and covalent compounds are noted as the subject of a later chapter (not detailed in this excerpt).

📊 Comparison of bonding types

Bonding type	How octet is achieved	What forms	Key mechanism
Ionic	Transfer of electrons	Oppositely charged ions	Attraction between opposite charges
Covalent	Sharing of electrons	Shared electron pairs	Electrons occupy multiple atoms' outer shells

🧭 Overview

🧠 One-sentence thesis

Atoms form ions by losing or gaining electrons to achieve a stable octet, creating positively charged cations or negatively charged anions that combine through electrostatic attraction to form ionic compounds.

📌 Key points (3–5)

• Two types of ions: cations (positively charged, formed when atoms lose electrons) and anions (negatively charged, formed when atoms gain electrons).
• The octet rule drives ion formation: atoms lose or gain electrons to achieve eight electrons in their outermost shell.
• Periodic table patterns: elements in the same column form ions with the same charge (e.g., alkali metals form 1+ ions, halogens form 1− ions).
• Common confusion: the number of electrons lost or gained depends on which path requires fewer changes—atoms with few valence electrons lose them; atoms with nearly eight gain electrons.
• Lewis diagrams simplify visualization: dots around element symbols show valence electrons and illustrate electron transfer between atoms.

⚛️ What ions are and how they form

⚛️ Cations: positively charged ions

Cations: positively charged ions formed when atoms lose electrons.

• Most atoms do not naturally have eight electrons in their valence shell.
• Atoms with three or fewer valence electrons tend to lose those electrons.
• When electrons are lost, fewer negative charges remain to balance the positive protons in the nucleus, resulting in a net positive charge.
• Most metals become cations when forming ionic compounds.
• Example: A sodium atom loses its one valence electron to become Na⁺, the sodium ion.

⚛️ Anions: negatively charged ions

Anions: negatively charged ions formed when atoms gain electrons.

• Atoms with nearly eight valence electrons can gain additional electrons to complete an octet.
• When electrons are gained, the atom now has more electrons than protons, creating a net negative charge.
• Most nonmetals become anions when forming ionic compounds.
• Example: A chlorine atom gains one electron to become Cl⁻, the chloride ion (note the suffix changes from -ine to -ide).

⚡ Electrostatic attraction creates compounds

• Oppositely charged ions attract each other.
• This attraction holds cations and anions together to form ionic compounds.
• The compound is electrically neutral overall—the number of electrons lost equals the number gained.
• Example: In sodium chloride, one sodium atom loses one electron and one chlorine atom gains one electron, with no leftover electrons.

🔄 The electron transfer process

🔄 Achieving the octet

• The octet rule: atoms tend to gain, lose, or share electrons to have eight electrons in their outermost shell.
• Atoms choose the path requiring the fewest changes.
• Sodium (one valence electron) loses one electron rather than gaining seven.
• Chlorine (seven valence electrons) gains one electron rather than losing seven.

🔄 Electron configurations before and after

• Sodium atom electron configuration: 1s² 2s² 2p⁶ 3s¹
• After losing one electron, Na⁺ has configuration 1s² 2s² 2p⁶ (the second shell now becomes the outermost shell with eight electrons).
• Chlorine atom electron configuration: 1s² 2s² 2p⁶ 3s² 3p⁵
• After gaining one electron, Cl⁻ has a complete octet in its outermost shell.

🔄 Multiple atom transfers

• Some ionic compounds require electron transfer between more than one atom.
• The ratio of cations to anions adjusts to balance charges.
• Example: Magnesium bromide (MgBr₂) forms when one magnesium atom (loses two electrons) combines with two bromine atoms (each gains one electron).

📊 Periodic table patterns

📊 Predicting ion charges by position

Periodic table group	Typical ion charge	Examples
First column (alkali metals)	1+	Na⁺, Li⁺, K⁺
Second column (alkaline earth metals)	2+	Mg²⁺, Ca²⁺, Ba²⁺
Next-to-last column (halogens)	1−	Cl⁻, Br⁻, I⁻, F⁻
Third-to-last column	2−	S²⁻, O²⁻

• Elements in the same vertical column (group) form ions with the same charge because they have the same number of valence electrons.
• The periodic table becomes a tool for remembering ion charges.
• Convention: write the number first, then the sign (Ba²⁺, not Ba⁺²).

📊 Transition metals are different

• Transition metals can form ions with multiple different charges.
• There is no simple pattern for transition metal ion charges.
• Don't confuse: main group elements follow predictable patterns; transition metals do not.

🖊️ Lewis diagrams

🖊️ What Lewis diagrams show

Lewis diagrams (or Lewis electron dot diagrams): representations that show valence electrons as dots around the chemical symbol of an atom.

• Named after Gilbert N. Lewis, an American chemist.
• Show only valence electrons, not all electrons.
• Use up to eight dots around the element symbol (maximum two dots per side).
• Each dot represents one valence electron.

🖊️ Advantages over electron shell diagrams

1. They show only valence electrons (the ones that matter for bonding).
2. They are simpler—dots instead of circles with electrons inside.
3. They clearly illustrate electron transfer between atoms.

🖊️ Drawing electron transfer

• Start with Lewis diagrams of neutral atoms showing their valence electrons.
• Show arrows indicating electron transfer from one atom to another.
• The resulting ions are shown with their charges.
• In the final formula representation, the dots are omitted.
• Example: Lithium (one dot) transfers its electron to bromine (seven dots) to form Li⁺ and Br⁻, which combine as LiBr.

🖊️ Counting valence electrons

• For main group elements, the number of valence electrons equals the group number at the top of the periodic table.
• It does not matter which sides the dots are placed on, as long as no side has more than two dots.

🧭 Overview

🧠 One-sentence thesis

Ionic compound formulas represent the lowest whole-number ratio of ions needed to balance total positive and negative charges, following specific conventions for writing and recognizing these compounds.

📌 Key points (3–5)

• What a chemical formula shows: the elements in a compound and their ratios, not individual particles but a continuous crystal lattice.
• The balancing rule: total positive charge must always equal total negative charge; determine how many of each ion is needed to achieve this balance.
• Writing conventions: cation (usually metal) comes first, anion (usually nonmetal) second; charges are not written; use lowest whole-number ratios; subscripts indicate multiple ions.
• Common confusion: polyatomic ions vs. diatomic elements—MgCl₂ contains two separate chloride ions, not a Cl₂ molecule; when multiple polyatomic ions are needed, enclose the entire ion formula in parentheses with the subscript outside.
• How to recognize ionic compounds: look for metal + nonmetal combinations, or recognize polyatomic ion formulas within the compound.

🔬 What chemical formulas represent

🧱 Crystal structure, not individual units

Chemical formula: a concise list of the elements in a compound and the ratios of these elements.

• Ionic compounds exist as three-dimensional arrays called crystals, with alternating positive and negative ions.
• There are no individual "particles" like separate NaCl units; instead, a continuous lattice exists.
• Each ion is surrounded by ions of opposite charge, not exclusively paired with any single ion.
• Example: A sodium chloride crystal is a collection of alternating sodium and chloride ions in a regular pattern.

📐 Formula unit concept

Formula unit: a set of oppositely charged ions that compose an ionic compound.

• Although no single ion pairs exclusively with another, we use the ratio expressed in lowest whole numbers to describe the compound.
• A macroscopic sample contains myriads of these ratio units.
• Example: NaCl represents a 1:1 ratio of sodium to chloride ions, even though the crystal is a continuous array.

⚖️ The charge-balancing rule

⚖️ Total positive equals total negative

• The fundamental rule: the total positive charge must equal the total negative charge.
• This rule is based on the fact that matter is overall electrically neutral.
• Determine how many of each ion is needed to balance charges.

🔢 Working out ion ratios

Ion pair	Charges	Ratio needed	Formula	Why
Li⁺ and Br⁻	1+ and 1−	1:1	LiBr	One of each balances
Mg²⁺ and O²⁻	2+ and 2−	1:1	MgO	Equal charges balance in 1:1
Mg²⁺ and Cl⁻	2+ and 1−	1:2	MgCl₂	Two chloride ions needed to balance one magnesium
Na⁺ and S²⁻	1+ and 2−	2:1	Na₂S	Two sodium ions needed to balance one sulfur
Al³⁺ and F⁻	3+ and 1−	1:3	AlF₃	Three fluoride ions needed to balance one aluminum
Fe³⁺ and O²⁻	3+ and 2−	2:3	Fe₂O₃	Least common multiple is 6: two iron (6+) and three oxygen (6−)

• Don't confuse: Mg₂Cl₄ has balanced charges in a 1:2 ratio, but it is not the lowest whole-number ratio—MgCl₂ is correct.

📝 Writing conventions

📝 Order and notation rules

1. Cation first, anion second: because most metals form cations and most nonmetals form anions, the metal is typically listed first.
2. No charges written: even though the species are ions, not neutral atoms, charges are omitted from the formula.
3. Subscripts for multiples: when more than one ion of a type is needed, use a numerical subscript (e.g., MgCl₂).
4. No subscript "1": by convention, assume only one atom if no subscript is present; do not write "1" as a subscript.
5. Lowest whole-number ratio: always use the simplest ratio.

🔤 Reading subscripts correctly

• The subscript applies to the element immediately before it.
• Example: In MgCl₂, the "2" means two chloride ions, not a Cl₂ molecule.
• Don't confuse: Cl₂ in this context is not diatomic elemental chlorine; it represents two separate chloride ions.

🔗 Polyatomic ions

🔗 What polyatomic ions are

Polyatomic ions: ions that consist of groups of atoms bonded together with an overall electric charge.

• These ions contain more than one atom.
• They have characteristic formulas, names, and charges that must be memorized.
• Example: NO₃⁻ is the nitrate ion (one nitrogen, three oxygen atoms, overall 1− charge).

🔗 Common polyatomic ions (partial list from excerpt)

Name	Formula	Charge
Ammonium	NH₄⁺	1+
Nitrate	NO₃⁻	1−
Sulfate	SO₄²⁻	2−
Carbonate	CO₃²⁻	2−
Phosphate	PO₄³⁻	3−
Hydroxide	OH⁻	1−

📦 Parentheses rule for polyatomic ions

• If more than one polyatomic ion is needed to balance charge, enclose the entire formula for the polyatomic ion in parentheses.
• Place the numerical subscript outside the parentheses to show it applies to the entire ion.
• Example: Ba(NO₃)₂ means one barium ion and two nitrate ions.
• Example: Ca(NO₃)₂—calcium ions have 2+ charge, nitrate ions have 1− charge, so two nitrate ions are needed.

🔍 Recognizing ionic compounds

🔍 Two recognition methods

Method 1: Metal + nonmetal

• Compounds between metal and nonmetal elements are usually ionic.
• Example: CaBr₂ contains calcium (group 2A metal) and bromine (group 7A nonmetal), so it is ionic.
• Contrast: NO₂ contains two nonmetals (nitrogen from group 5A, oxygen from group 6A), so it is not ionic—it is covalent.
• Don't confuse: NO₂ with no charge specified is not the nitrite ion; it is a different type of compound.

Method 2: Recognize polyatomic ions

• If you recognize a polyatomic ion formula within a compound, the compound is ionic.
• Example: Ba(NO₃)₂—recognizing "NO₃" as the nitrate ion (NO₃⁻) is a clue that Ba is the Ba²⁺ ion.
• The 2+ charge on barium balances the overall 2− charge from two nitrate ions.
• Remember: the convention for ionic formulas is not to include the ionic charge in the written formula.

🔍 Practice examples from excerpt

Compound	Ionic or not?	Reason
Na₂O	Ionic	Sodium (metal) + oxygen (nonmetal)
PCl₃	Not ionic	Both phosphorus and chlorine are nonmetals
NH₄Cl	Ionic	Contains ammonium ion (NH₄⁺), a polyatomic ion
OF₂	Not ionic	Both oxygen and fluorine are nonmetals

📊 Additional context: Blood and seawater comparison

📊 Similar but different compositions

• Science has long recognized that blood and seawater have similar compositions—both have ionic compounds dissolved in them.
• Many scientists think the first life forms on Earth arose in the oceans, which may explain the similarity.
• However, a closer look shows they are quite different in concentration and ion types.

📊 Key differences

• Salt concentration: Blood approximates 0.9% sodium chloride; seawater is principally 3% sodium chloride (over three times the concentration).
• Hydrogen carbonate ions (HCO₃⁻): far more abundant in blood than seawater; crucial for controlling acid-base properties of blood.
• Hydrogen phosphate ions (HPO₄²⁻ and H₂PO₄⁻): very low in seawater but present in higher amounts in blood, where they also affect acid-base properties.
• Sulfate ion (SO₄²⁻): present in seawater but not in significant amounts in blood.
• Most other ions (Na⁺, Cl⁻, Mg²⁺, K⁺, Ca²⁺) are more abundant in seawater than in blood.

🧭 Overview

🧠 One-sentence thesis

Ionic compounds are named systematically by combining the names of their cation and anion, with special rules for metals that can form ions of different charges.

📌 Key points (3–5)

• Nomenclature is systematic: the formal study of naming chemical compounds follows specific rules.
• Cation naming: monatomic cations use the element name + "ion"; metals with multiple charges need either Stock system (roman numerals) or common system (-ic/-ous suffixes).
• Anion naming: monatomic anions use the element stem + "-ide ion"; polyatomic ions have their own characteristic names.
• Common confusion: distinguishing Fe²⁺ from Fe³⁺—two different charges make two different compounds with unique properties, so each needs a distinct name.
• Compound naming order: cation name first, then anion name, dropping the word "ion" from both.

🏷️ Naming individual ions

🏷️ Monatomic cations

The name of a monatomic cation is simply the name of the element followed by the word "ion."

• Na⁺ is the sodium ion, Al³⁺ is the aluminum ion, Ca²⁺ is the calcium ion.
• This straightforward rule works when the element forms only one common positive ion.
• Example: Sodium forms only a 1+ ion, so "sodium ion" is unambiguous—no need to specify the charge.

⚡ Cations with multiple charges

Some elements lose different numbers of electrons, producing ions of different charges. Iron can form Fe²⁺ or Fe³⁺; each makes a different compound with unique physical and chemical properties when combined with the same anion.

Two naming systems exist:

System	How it works	Example (Fe²⁺ / Fe³⁺)
Stock system (modern)	Roman numeral in parentheses after element name + "ion"	iron(II) ion / iron(III) ion
Common system (older, still used in health sciences)	Stem + suffix (-ous for lower charge, -ic for higher charge)	ferrous ion / ferric ion

• The Stock system is used only for elements that form more than one common positive ion.
• Don't confuse: the -ic suffix represents the greater charge, -ous represents the lower charge.
• In many cases, the stem comes from the Latin name of the element (e.g., iron → ferr-, copper → cupr-, tin → stann-, lead → plumb-, chromium → chrom-, gold → aur-).

🔻 Monatomic anions

The name of a monatomic anion consists of the stem of the element name, the suffix "-ide," and then the word "ion."

• Cl⁻ is the chloride ion, O²⁻ is the oxide ion, Se²⁻ is the selenide ion.
• Other examples: F⁻ (fluoride ion), Br⁻ (bromide ion), I⁻ (iodide ion), S²⁻ (sulfide ion), P³⁻ (phosphide ion), N³⁻ (nitride ion).

🔷 Polyatomic ions

Polyatomic ions have their own characteristic names (from earlier tables in the text).

• Examples mentioned: SO₃²⁻ (sulfite ion), NH₄⁺ (ammonium ion), SO₄²⁻ (sulfate ion), PO₄³⁻ (phosphate ion), HCO₃⁻ (hydrogen carbonate or bicarbonate ion), NO₃⁻ (nitrate ion), Cr₂O₇²⁻ (dichromate ion), CrO₄²⁻ (chromate ion), OH⁻ (hydroxide ion), CO₃²⁻ (carbonate ion).
• Note: some polyatomic ion names include prefixes like "di-" (e.g., dichromate).

🧪 Naming ionic compounds

🧪 The basic rule

Place the name of the cation first, followed by the name of the anion, and drop the word "ion" from both parts.

• Example: Ba(NO₃)₂ is named barium nitrate.
• The compound's name does not indicate the number of ions (e.g., "two nitrate ions for every barium ion").
• You must determine the relative numbers by balancing positive and negative charges.

🔍 Determining cation charge from formula

If the cation can have more than one possible charge, first determine the charge from the formula before naming.

• Example: FeCl₂ has two Cl⁻ ions (each 1− charge), so the iron ion must be Fe²⁺ → iron(II) chloride or ferrous chloride.
• Example: FeCl₃ has three Cl⁻ ions, so the iron ion must be Fe³⁺ → iron(III) chloride or ferric chloride.
• Don't confuse: these are two different compounds with different properties, so they need different names.

📋 Naming examples

• Ca₃(PO₄)₂ → calcium phosphate
• (NH₄)₂Cr₂O₇ → ammonium dichromate (the prefix "di-" is part of the anion name)
• KCl → potassium chloride
• CuCl → copper(I) chloride or cuprous chloride
• SnF₂ → tin(II) fluoride or stannous fluoride

🗺️ Step-by-step process

The excerpt provides a guide (Figure 3.7):

1. Identify the cation and anion.
2. Name the cation (use Stock or common system if the metal has multiple charges).
3. Name the anion.
4. Combine: cation name + anion name, dropping "ion" from both.
5. Do not use numerical prefixes to indicate the number of ions.

🔑 Key distinctions

🔑 When to specify charge

• Do specify: for metals that form more than one common positive ion (e.g., iron, copper, tin, lead, chromium, gold).
• Don't specify: for metals that form only one common ion (e.g., sodium, calcium, aluminum, potassium, magnesium, zinc, silver).
• Example: Na⁺ is simply "sodium ion," not "sodium(I) ion," because sodium forms only a 1+ ion.

🔑 Stock vs. common system

• Stock system: more modern, uses roman numerals—clearer and unambiguous.
• Common system: older, uses Latin stems and -ic/-ous suffixes—still prevalent in health sciences.
• Both are acceptable; the excerpt shows both in examples.
• Example: Cu⁺ is copper(I) ion (Stock) or cuprous ion (common); Cu²⁺ is copper(II) ion (Stock) or cupric ion (common).

🧭 Overview

🧠 One-sentence thesis

Formula mass enables chemists to calculate the total mass of an ionic compound by summing the atomic masses of all atoms in its chemical formula, a skill essential for quantitative chemistry work.

📌 Key points (3–5)

• What formula mass is: the sum of the atomic masses of each individual atom in the formula of an ionic compound.
• How to calculate it: add up atomic masses from the periodic table, multiplying by the number of each type of atom present.
• Key challenge with polyatomic ions: subscripts outside parentheses multiply every atom inside the polyatomic ion.
• Common confusion: forgetting to distribute subscripts through parentheses when multiple polyatomic ions are present.
• Why ions can be treated as atoms: because proper formulas are electrically neutral (no net electrons gained or lost), ions can be considered atoms for mass calculation purposes.

🧮 Basic calculation method

🔢 Simple ionic compounds

Formula mass: the sum of the masses of the elements in the formula of an ionic compound.

• Start with the chemical formula (e.g., NaCl).
• Look up each element's atomic mass on the periodic table (typically rounded to two decimal places).
• Add the atomic masses together.
• Example: For NaCl, sodium is 22.99 u and chlorine is 35.45 u, giving a total of 58.44 u.

✖️ Compounds with multiple ions

When a formula contains more than one of the same ion, multiply the atomic mass by the number present:

• For calcium fluoride (CaF₂), the subscript 2 means two fluorine atoms.
• Calculation: Ca (1 × 40.08) + F (2 × 19.00) = 40.08 + 38.00 = 78.08 u.
• The subscript tells you how many times to count that atom's mass.

🔷 Polyatomic ions

🧩 Single polyatomic ion

When the formula includes a polyatomic ion like nitrate (NO₃⁻):

• Count every atom in the polyatomic ion.
• Example: Potassium nitrate (KNO₃) contains 1 K, 1 N, and 3 O atoms.
• Calculation: K (39.10) + N (14.00) + O (3 × 16.00) = 39.10 + 14.00 + 48.00 = 101.10 u.

⚠️ Multiple polyatomic ions in parentheses

Critical rule: A subscript outside parentheses multiplies every atom inside.

• For calcium nitrate Ca(NO₃)₂, the subscript 2 refers to the entire nitrate ion.
• This means 2 nitrogen atoms (1 × 2) and 6 oxygen atoms (3 × 2).
• Calculation: Ca (1 × 40.08) + N (2 × 14.00) + O (6 × 16.00) = 40.08 + 28.00 + 96.00 = 164.08 u.
• Don't confuse: The subscript doesn't just apply to the last element—it applies to the whole group in parentheses.

📝 Step-by-step for complex formulas

For ammonium phosphate (NH₄)₃PO₄:

1. Distribute the subscript 3 through the ammonium ion: 3 nitrogen atoms, 12 hydrogen atoms.
2. Count atoms in the phosphate part: 1 phosphorus, 4 oxygen atoms.
3. Calculate: N (3 × 14.00) + H (12 × 1.00) + P (30.97) + O (4 × 16.00) = 42.00 + 12.00 + 30.97 + 64.00 = 148.97 u.

💧 Special case: Hydrates

💎 What hydrates are

Hydrates: ionic compounds with water (H₂O) incorporated within their formula unit; they are solids, not liquids or solutions, despite containing water.

• Each formula unit has a characteristic number of water molecules.
• Written with a centered dot separating the compound from the water: CuSO₄·5H₂O.
• Named with Greek prefixes: copper(II) sulfate pentahydrate (penta- = five water units).

🏥 Common hydrates and uses

Formula	Name	Use
CaSO₄·½H₂O	Calcium sulfate hemihydrate (plaster of Paris)	Casts for broken bones
MgSO₄·7H₂O	Magnesium sulfate heptahydrate (Epsom salts)	Laxative, bathing salt
AlCl₃·6H₂O	Aluminum chloride hexahydrate	Antiperspirant

🧮 Calculating formula mass with hydrates

Include the water molecules in your calculation:

• For CuSO₄·5H₂O, add the mass of CuSO₄ plus 5 times the mass of H₂O.
• Each water molecule contributes (2 × 1.00) + 16.00 = 18.00 u.

🎯 Key takeaway

The essential skill is to correctly count each atom in the formula and multiply atomic masses accordingly—especially remembering that subscripts outside parentheses distribute to all atoms within the polyatomic ion.

🧭 Overview

🧠 One-sentence thesis

Covalent bonds form when atoms share electrons to achieve stable, filled valence shells, creating molecules that differ fundamentally from ionic compounds.

📌 Key points (3–5)

• How covalent bonds form: atoms share electrons rather than transferring them, allowing both atoms to fill their valence shells.
• What defines a molecule: a discrete group of atoms connected by covalent bonds, represented by Lewis diagrams or dashes for bonding pairs.
• Bonding vs nonbonding electrons: bonding pairs join atoms together; lone pairs belong to a single atom and do not participate in bonds.
• Common confusion: covalent bonding occurs between nonmetals, while ionic bonding involves metals and nonmetals—some compounds contain both types.
• Predictable patterns: atoms typically form a characteristic number of covalent bonds based on their position in the periodic table.

🔗 How electron sharing works

🔗 The alternative to electron transfer

• Chapter 3 covered ionic bonding through electron transfer; covalent bonding offers a different path to stability.
• Instead of one atom losing and another gaining electrons, atoms can share electrons to fill their valence shells.
• Both approaches satisfy the octet rule (eight electrons in the outer shell for most atoms).

🔗 Hydrogen molecule example

• Each hydrogen atom starts with one valence electron.
• When two hydrogen atoms get close enough, they share their electrons.
• Result: both atoms now have two electrons in their valence shells (filled for hydrogen's first shell).
• This shared arrangement is more stable than two separate atoms.

Covalent bond: the sharing of electrons between atoms.

Bonding pair of electrons: the two electrons that join atoms in a covalent bond.

Molecule: a discrete group of atoms connected by covalent bonds—the smallest part of a compound that retains its chemical identity.

📐 Representing covalent bonds

📐 Lewis diagrams

• Chemists use Lewis diagrams to show valence electrons as dots around atomic symbols.
• For a hydrogen molecule, two separate atoms each show one dot; when bonded, the shared electrons appear between them.
• A dash can replace the bonding pair for simplicity: H—H represents the hydrogen molecule.

Single bond: a covalent bond formed by a single pair of electrons (represented by a dash).

📐 Bond length and forces

• The bond in a hydrogen molecule is about 74 picometers (74 × 10⁻¹² meters).
• This distance balances multiple forces:
  • Attraction between oppositely charged electrons and nuclei
  • Repulsion between two negatively charged electrons
  • Repulsion between two positively charged nuclei
• Closer nuclei → stronger repulsion; farther nuclei → weaker attraction.

📐 Nonbonding electrons

• Not all valence electrons participate in bonding.
• Example: fluorine atoms form F—F, but each fluorine has six additional electrons (three pairs) that don't bond.

Nonbonding pairs (or lone pairs): electron pairs that do not participate in covalent bonds; they belong to a single atom.

🧪 Bonding between different elements

🧪 Hydrogen fluoride example

• A hydrogen atom (one valence electron) combines with a fluorine atom (seven valence electrons).
• Each contributes one electron to form a shared pair: H—F.
• Hydrogen's valence shell is now filled (two electrons); fluorine's is filled (eight electrons).
• Fluorine retains six nonbonding electrons; hydrogen has none.

🧪 Larger molecules

• Water (H₂O): oxygen forms two covalent bonds with two hydrogen atoms.
• Methane (CH₄): carbon forms four covalent bonds with four hydrogen atoms.
• Some atoms participate in multiple covalent bonds within the same molecule.

🧪 Characteristic bonding patterns

• The excerpt notes that atoms typically form a predictable number of covalent bonds in compounds.
• Figure 4.2 in the source shows these patterns based on periodic table position.
• Example from exercises: hydrogen forms only one bond (only one valence electron to share); oxygen typically forms two bonds.

⚖️ Covalent vs ionic bonding

⚖️ When covalent bonds form

• Covalent bonds form when two or more nonmetals combine.
• Example: water (H₂O) is made from hydrogen and oxygen, both nonmetals.
• Don't confuse: ionic compounds form between metals and nonmetals.

⚖️ Compounds with both bond types

• Some compounds contain both ionic and covalent bonds.
• Example: ammonium chloride (NH₄Cl) has:
  • Ionic bonds between the ammonium ion (NH₄⁺) and chloride ion (Cl⁻)
  • Covalent bonds within the ammonium ion (between nitrogen and hydrogen atoms)
• Polyatomic ions are held together by covalent bonds but participate in ionic bonding as a unit.

Compound type	Bond participants	Example
Purely covalent	Nonmetal + nonmetal	N₂O₄ (both nitrogen and oxygen are nonmetals)
Purely ionic	Metal + nonmetal	Na₂O (sodium is a metal, oxygen is a nonmetal)
Both types	Metal + polyatomic ion (which has internal covalent bonds)	Na₃PO₄ (ionic between sodium and phosphate; covalent within phosphate)

⚖️ Molecular formulas

• The excerpt introduces the term molecular formulas for covalent compounds.
• These formulas describe molecules (discrete groups of covalently bonded atoms), not the ionic lattice structures of ionic compounds.

🧭 Overview

🧠 One-sentence thesis

Covalent compounds form when nonmetals combine, and their naming follows a systematic prefix-based system that differs from ionic compound naming by using numerical prefixes to indicate the number of atoms of each element.

📌 Key points (3–5)

• What forms covalent bonds: two or more nonmetals combining (unlike ionic bonds between metals and nonmetals).
• Molecular formulas: covalent compounds use molecular formulas because they exist as separate, discrete molecules.
• Naming system: the first element keeps its name; the second element gets the stem + "-ide" suffix; numerical prefixes specify atom counts.
• Common confusion: polyatomic ions contain covalent bonds internally but participate in ionic bonding as a whole unit—so some compounds contain both bond types.
• Key exceptions: some simple covalent compounds (water, ammonia, methane) use common names instead of systematic names.

🔗 What forms covalent bonds

🔗 Nonmetal combinations

Covalent bonds form when two or more nonmetals combine.

• This is the defining characteristic that distinguishes covalent from ionic bonding.
• Ionic bonds form between metals and nonmetals; covalent bonds form between nonmetals only.
• Example: hydrogen and oxygen are both nonmetals, so water (H₂O) forms through covalent bonding.

⚠️ Mixed bonding situations

• Some compounds contain both ionic and covalent bonds.
• Polyatomic ions have covalent bonds holding the atoms together internally, but the ion as a whole participates in ionic bonding.
• Example: ammonium chloride has ionic bonds between the ammonium ion (NH₄⁺) and chloride ions (Cl⁻), but within the ammonium ion, nitrogen and hydrogen are connected by covalent bonds.
• Don't confuse: the presence of a polyatomic ion means the compound has both bond types, not just one.

📝 Writing molecular formulas

📝 Formula structure rules

Molecular formulas: chemical formulas for covalent compounds, called this because these compounds exist as separate, discrete molecules.

• The nonmetal closest to the lower left corner of the periodic table is typically written first.
• Exception: hydrogen is almost never written first (H₂O is the prominent exception).
• Other nonmetal symbols follow in order.
• Numerical subscripts indicate more than one atom of a particular element.

🔍 Recognizing bond types from formulas

Compound type	How to identify	Example
Ionic only	Metal + nonmetal	Na₂O
Covalent only	Nonmetal + nonmetal	N₂O₄
Both ionic and covalent	Metal + polyatomic ion	Na₃PO₄

🏷️ Naming binary covalent compounds

🏷️ The systematic naming rules

The naming system follows these steps:

1. First element: use the element name as-is (no prefix if only one atom).
2. Second element: take the stem of the element name and add "-ide" suffix.
3. Numerical prefixes: specify the number of atoms in the molecule.

🔢 Numerical prefix system

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

*The "mono-" prefix is not used for the first element's name.

🎯 Applying the naming system

• No prefix on the first element's name means only one atom is present.
• Always use numerical prefixes for the second element if more than one atom.
• Special rule for oxygen: omit the trailing vowel from polysyllabic prefixes (say "monoxide" not "monooxide"; "trioxide" not "troxide") but keep it for monosyllabic prefixes.

Example: CCl₄ becomes "carbon tetrachloride"—carbon (first element, no prefix needed for one atom) + tetra (four) + chlor (stem) + ide.

📋 Working from name to formula

When converting names to formulas:

• If no prefix appears on the first element, assume one atom.
• The prefix on the second element always tells you the exact number of atoms.

Example: "dinitrogen pentoxide" → N₂O₅ (di- means two nitrogen atoms, penta- means five oxygen atoms).

🌟 Common name exceptions

🌟 Simple compounds with traditional names

Three simple covalent compounds use common names rather than systematic names:

• H₂O: water (not "dihydrogen monoxide")
• NH₃: ammonia (not "nitrogen trihydride")
• CH₄: methane (not "carbon tetrahydride")

🧪 Organic compounds

Organic compound: a compound containing carbon atoms.

• Methane is the simplest organic compound.
• Organic compounds are named by a separate nomenclature system (not covered in this excerpt).
• This is why methane uses a common name instead of following the binary covalent naming rules.

🧭 Overview

🧠 One-sentence thesis

Some molecules require multiple covalent bonds—double or triple bonds—between atoms to satisfy the octet rule when single bonds alone cannot provide each atom with eight valence electrons.

📌 Key points (3–5)

• Double bonds: two pairs of electrons shared between two atoms, represented by a double dash.
• Triple bonds: three pairs of electrons shared between two atoms (e.g., acetylene C₂H₂ and N₂).
• When multiple bonds form: if single bonds between all atoms do not give all atoms (except hydrogen) an octet, multiple covalent bonds may be present.
• Common confusion: hydrogen atoms never form double bonds—they can accept only one more electron, while multiple bonds require more than one electron pair to be shared.
• Why it matters: multiple bonds are necessary to complete the valence electron shells of many molecules.

🔗 Types of multiple bonds

🔗 Double bonds

Double bond: two pairs of electrons shared between two atoms in a molecule.

• Represented by a double dash (=) in Lewis diagrams.
• Forms when single bonds alone cannot provide eight electrons around each atom.
• Example: In formaldehyde (CH₂O), the carbon atom forms a double bond with the oxygen atom to satisfy the octet rule for both atoms.

🔗 Triple bonds

Triple bond: three pairs of electrons shared by two atoms in a molecule.

• Represented by a triple dash (≡) in Lewis diagrams.
• Example: Acetylene (C₂H₂) contains a triple bond between the two carbon atoms.
• Example: Nitrogen gas (N₂) has a triple bond between the two nitrogen atoms.

🧮 Drawing Lewis diagrams with multiple bonds

🧮 The process

• Start by attempting to draw single bonds between all atoms.
• Count the electrons around each atom (except hydrogen, which needs only two).
• If an atom does not have eight electrons (an octet), add additional bonds between atoms.
• Each additional shared pair creates a double or triple bond.

🧮 Example: Formaldehyde (CH₂O)

• The carbon atom is the central atom, surrounded by two hydrogen atoms and one oxygen atom.
• Single bonds alone do not give carbon and oxygen complete octets.
• A double bond between carbon and oxygen provides eight electrons around each atom.
• Note: Formaldehyde is also called CH₂O; aqueous solutions are called formalin and are used to preserve biological specimens.

🧮 Example: Nitrogen gas (N₂)

• Each nitrogen atom needs eight valence electrons.
• A triple bond between the two nitrogen atoms satisfies the octet rule for both.

🚫 Limitations and special cases

🚫 Why hydrogen never forms double bonds

• Hydrogen can accept only one more electron to complete its valence shell (which holds a maximum of two electrons).
• Multiple bonds require more than one electron pair to be shared.
• Therefore, hydrogen always forms single bonds only.

🚫 When not to draw multiple bonds

• Don't confuse covalent multiple bonds with ionic bonding.
• Example: It is incorrect to draw a double bond in the Lewis diagram for MgO because MgO is an ionic compound, not a covalent molecule.

🔍 Recognizing when multiple bonds are needed

🔍 The key clue

• If single bonds between all atoms do not give all atoms (except hydrogen) an octet, multiple covalent bonds may be present.
• This is the primary indicator that you need to add double or triple bonds to your Lewis diagram.
• Always check: does each atom (other than hydrogen) have eight electrons around it?

🔍 Practice molecules

Molecule	Type of multiple bond	Notes
CS₂	Double bonds	Carbon is the central atom
C₂F₄	Double bond	Between the two carbon atoms
O₂	Double bond	Between the two oxygen atoms
C₂H₄	Double bond	Between the two carbon atoms
HCN	Triple bond	Carbon is the central atom; triple bond between C and N

🧭 Overview

🧠 One-sentence thesis

Covalent bonds vary in length and polarity depending on the atoms involved, with bond length decreasing as bond multiplicity increases and polarity determined by the difference in electronegativity between bonded atoms.

📌 Key points (3–5)

• Bond length depends on identity and bond type: different atom pairs have characteristic bond lengths, and multiple bonds are shorter than single bonds between the same atoms.
• Electronegativity determines polarity: the difference in electronegativity between two atoms determines whether a bond is nonpolar, polar covalent, or ionic.
• Common confusion—equal vs unequal sharing: nonpolar bonds share electrons equally (same element or very small electronegativity difference), while polar bonds share unequally (moderate difference), and ionic bonds transfer electrons (large difference).
• Thresholds for bond types: electronegativity differences less than ~0.4 are nonpolar, greater than ~0.4 are polar, and greater than ~1.8 are ionic.
• Molecular polarity vs bond polarity: even if individual bonds are polar, the molecule's overall polarity depends on how those bonds are oriented in space.

📏 Bond length patterns

📏 What determines bond length

Bond length: the distance between two atoms in a covalent bond.

• Bond lengths are characteristic for specific atom pairs and depend on:
  • The identities of the atoms in the bond
  • Whether the bond is single, double, or triple
• The excerpt provides tables of approximate bond lengths that are close to actual values but may vary slightly depending on the molecule.

🔗 Single bond lengths

The excerpt provides a table of approximate single bond lengths (in units of 10⁻¹² m):

Bond	Length
H–H	74
H–C	110
H–O	97
C–C	154
C–O	143
N–N	145

• These are reference values for comparing different bonds.
• Example: a C–C bond (154) is longer than a C–O bond (143).

⚡ Multiple bonds are shorter

Key pattern: as the number of covalent bonds between two atoms increases, the bond length decreases—without exception.

Bond type	C–C	C=C	C≡C
Length	154	134	120

Bond type	C–O	C=O	C≡O
Length	143	120	113

• Why this happens: with more electrons between the two nuclei, the nuclei can get closer together before internuclear repulsion balances the attraction.
• Example: a triple bond (C≡C at 120) is significantly shorter than a single bond (C–C at 154) between the same atoms.

⚖️ Electronegativity and bond polarity

⚖️ What electronegativity measures

Electronegativity: a relative measure of how strongly an atom attracts electrons when it forms a covalent bond.

• It is not about how many electrons an atom has, but how strongly it pulls on shared electrons in a bond.
• The excerpt references the Pauling scale, where fluorine has the highest value (4.0).
• Different elements have different electronegativities; this difference determines bond polarity.

🔄 Equal vs unequal electron sharing

Covalent bonds fall into two categories based on electron distribution:

Nonpolar covalent bond: a covalent bond with a balanced (equal) electron distribution across the bond.

Polar covalent bond: a covalent bond with an unbalanced (unequal) electron distribution across the bond.

Key distinction:

• Nonpolar: electrons are equally shared by both atoms (e.g., H–H, where both atoms are identical).
• Polar: one atom attracts electrons more strongly, creating partial charges (δ− on one side, δ+ on the other).
• Example: in H–F, fluorine attracts electrons more than hydrogen, leading to an imbalance—this is polar.

📊 Using electronegativity differences to predict bond type

Electronegativity difference	Bond type	Electron behavior
Zero	Nonpolar covalent	Equal sharing
Less than ~0.4	Nonpolar covalent	Nearly equal sharing
Greater than ~0.4	Polar covalent	Unequal sharing
Greater than ~1.8	Ionic	Transfer (not sharing)

• General rule: the greater the difference in electronegativities, the greater the imbalance of electron sharing.
• Don't confuse: all bonds between different elements are technically polar, but only those with differences greater than ~0.4 are considered meaningfully polar.
• Ionic bonds can be thought of as the extreme case of polarity—electrons are transferred rather than shared.

🧪 Examples of electronegativity differences

The excerpt provides worked examples:

C and H:

• Carbon: 2.5, Hydrogen: 2.1
• Difference: 0.4 (rather small)
• Result: nonpolar C–H bond

Na and Cl:

• Sodium: 0.9, Chlorine: 3.0
• Difference: 2.1 (rather high)
• Result: ionic compound (not covalent)

O and H:

• Oxygen: 3.5, Hydrogen: 2.1
• Difference: 1.4
• Result: very polar bond, but not ionic

H and H:

• Both: 2.1
• Difference: 0
• Result: nonpolar bond

🌐 Molecular polarity vs bond polarity

🌐 How bond orientation affects molecular polarity

Even when individual bonds are polar, the molecule's overall polarity depends on geometry:

Water (H₂O):

• Two O–H bonds are polar (oxygen attracts electrons more strongly).
• The bonds are oriented in a bent shape.
• Result: one end of the molecule has partial positive charge, the other has partial negative charge—the molecule itself is polar.
• Impact: water's polarity causes strong intermolecular attraction, leading to a high boiling point (100°C).

Carbon dioxide (CO₂):

• Two C=O bonds are polar.
• The bonds lie directly opposite each other (linear geometry).
• Result: the polar effects cancel each other out—the molecule is nonpolar overall.
• Impact: carbon dioxide becomes a gas at −77°C, almost 200° lower than water's boiling point.

🔍 Don't confuse bond polarity with molecular polarity

• A molecule can have polar bonds but be nonpolar overall if the bond dipoles cancel due to symmetry.
• Example: CO₂ has polar bonds but is a nonpolar molecule; H₂O has polar bonds and is a polar molecule.

🧭 Overview

🧠 One-sentence thesis

Covalent molecules are discrete units with a calculable mass and a three-dimensional shape determined by electron-pair repulsion, unlike ionic compounds that form extended crystal lattices.

📌 Key points (3–5)

• Molecular mass: the sum of the masses of all atoms in a molecule, calculated by tracking each element's count in the molecular formula.
• Discrete units vs lattices: covalent molecules exist as separate units with characteristic mass and shape, unlike ionic compounds arranged in crystal lattices.
• VSEPR theory: molecular shape is determined by electron pairs (bonded and lone) repelling each other to maximize distance.
• Common confusion: molecular shape is described by atom positions only, not by lone electron pairs—e.g., NH₃ is pyramidal (not tetrahedral) even though four electron pairs arrange tetrahedrally.
• Multiple bonds: treated as one group when determining shape, simplifying the geometry prediction.

🧮 Molecular mass calculation

🧮 What molecular mass means

Molecular mass: the mass of a molecule, which is the sum of the masses of its atoms.

• Also called molecular weight.
• Unlike formula mass for ionic compounds, molecular mass applies to discrete covalent molecules.
• Each molecule has a characteristic, fixed mass.

📝 How to calculate molecular mass

• Step 1: Identify the molecular formula and count each type of atom.
• Step 2: Look up atomic masses from the periodic table.
• Step 3: Multiply each atom's mass by its count in the formula.
• Step 4: Sum all the results.

Example: For H₂O, two hydrogen atoms (2 × 1.01 = 2.02 u) plus one oxygen atom (16.00 u) gives a total molecular mass of 18.02 u.

⚠️ Tracking atom counts

• The most important step is keeping track of the number of atoms of each element.
• Different compounds with the same elements can have very different molecular masses.
• Example: NO₂ has a molecular mass of 46.01 u, while N₂O₅ has 108.02 u—both contain nitrogen and oxygen but in different proportions.

🔷 Molecular shape fundamentals

🔷 Why shape matters

• Covalent molecules have specific three-dimensional shapes, unlike the extended lattices of ionic crystals.
• Shape is determined by the arrangement of atoms in space.
• The shape affects molecular properties and behavior.

🔋 VSEPR theory basics

Valence shell electron pair repulsion (VSEPR) theory: the general concept that estimates the shape of a simple molecule based on electron-pair repulsion.

• Core principle: covalent bonds are composed of negatively charged electrons that repel one another.
• Electron pairs (both bonded pairs and lone pairs) arrange themselves to be as far apart as possible.
• This repulsion determines the three-dimensional geometry of the molecule.

📐 Common molecular geometries

📐 Linear shape

• Occurs when two electron groups repel each other.
• The groups end up 180° apart.
• Example: BeCl₂ has two covalent bonds that stay as far from each other as possible, resulting in a linear molecule.
• Example: CO₂ is linear because the two double bonds (treated as one group each) repel to 180° apart.

🔺 Trigonal planar shape

• Occurs when three electron groups repel each other.
• The groups form 120° angles in a plane.
• Example: BF₃ has three covalent bonds that repel to form a flat, triangular arrangement.
• Molecules with double bonds can also adopt this shape when they have three groups around the central atom.

🔶 Tetrahedral arrangement

• Occurs when four electron groups repel each other.
• The groups point toward the corners of a tetrahedron, making bond angles of 109.5°.
• Example: CCl₄ has four covalent bonds arranged three-dimensionally in a tetrahedral shape.

🔻 Pyramidal shape

• Based on a tetrahedral electron arrangement but with one lone pair.
• Key distinction: the shape is described by atom positions only, not electron pairs.
• Example: NH₃ has four electron pairs (three bonded, one lone) arranged tetrahedrally, but the molecular shape is pyramidal because only the three atoms are counted.
• Don't confuse: the electron arrangement is tetrahedral, but the molecular shape is pyramidal.

🌊 Bent shape

• Occurs when the central atom has lone pairs in addition to bonded pairs.
• Example: H₂O has four electron pairs (two bonded, two lone) in a tetrahedral arrangement, but the molecular shape is bent because only the two hydrogen atoms define the shape.
• The lone pairs influence the geometry but are not included in the shape description.

🔍 Determining molecular shape

🔍 Step-by-step process

1. Draw the Lewis diagram for the molecule to identify all electron pairs.
2. Count electron groups around the central atom (bonded pairs + lone pairs).
3. Determine electron arrangement based on repulsion (linear, trigonal planar, tetrahedral, etc.).
4. Describe the molecular shape using only the positions of atoms, ignoring lone pairs.

🔗 Multiple bonds simplification

• Multiple bonds (double or triple) are treated as one group for shape determination.
• This simplifies the geometry prediction.
• Example: CH₂O has a double bond to oxygen, but this is treated as one group, giving the molecule a shape similar to BF₃ (trigonal planar around the carbon).

🎯 Shape vs electron arrangement

Electron pairs	Electron arrangement	Example molecule	Molecular shape
2 bonded, 0 lone	Linear	CO₂	Linear
3 bonded, 0 lone	Trigonal planar	BF₃	Trigonal planar
4 bonded, 0 lone	Tetrahedral	CCl₄	Tetrahedral
3 bonded, 1 lone	Tetrahedral	NH₃	Pyramidal
2 bonded, 2 lone	Tetrahedral	H₂O	Bent

🧭 Overview

🧠 One-sentence thesis

Organic chemistry focuses on carbon compounds because carbon's unique ability to form strong bonds with itself and other elements creates an unmatched chemical diversity that underlies all living things.

📌 Key points (3–5)

• Why carbon is special: Carbon bonds strongly with other carbon atoms, bonds strongly with other elements, and makes four covalent bonds—giving it unrivaled chemical diversity.
• Hydrocarbons as building blocks: The simplest organic compounds contain only carbon and hydrogen, classified by bond types (single, double, or triple).
• Functional groups define reactivity: Specific structural arrangements of atoms or bonds (functional groups) give molecules characteristic chemical behaviors.
• Common confusion: Carbon-containing compounds like carbonates, bicarbonates, CO₂, and CO are excluded from organic chemistry by convention, even though they contain carbon.
• Health connection: Simple structural differences (e.g., single vs. double bonds in fats) can significantly impact human health.

🔬 What makes carbon unique

🔬 Carbon's bonding characteristics

Organic chemistry: the study of the chemistry of carbon compounds.

Carbon is singled out for three key reasons:

• Carbon atoms bond reasonably strongly with other carbon atoms.
• Carbon atoms bond reasonably strongly with atoms of other elements.
• Carbon atoms make a large number of covalent bonds (four).

These properties allow carbon to form chains, branches, and complex structures that no other element can match.

🌍 Carbon's role despite scarcity

• Elemental carbon is not particularly abundant in Earth's crust.
• Nevertheless, all living things consist of organic compounds.
• Most organic chemicals are covalent compounds.

⚠️ Convention exceptions

Don't confuse: Compounds containing carbonate ions, bicarbonate ions, carbon dioxide, and carbon monoxide are not considered part of organic chemistry, even though they contain carbon.

🔗 Hydrocarbon families

⛓️ Alkanes (saturated hydrocarbons)

Hydrocarbons: the simplest organic compounds, composed of carbon and hydrogen atoms only.

Alkanes (saturated hydrocarbons): hydrocarbons with only single covalent bonds, existing as a chain of carbon atoms also bonded to hydrogen atoms.

• Alkanes have only single bonds and appear as chains (straight or branched).
• Named with a stem indicating carbon count plus the ending -ane.
• Examples: meth- = one carbon (methane), eth- = two carbons (ethane), prop- = three carbons (propane).

🔀 Alkenes

Alkenes: hydrocarbons with one or more carbon–carbon double bonds.

• Contain one or more carbon–carbon double bonds (C=C).
• Named with the same stem as alkanes but with the ending -ene.
• Examples: ethene (two carbons, one double bond), propene (three carbons, one double bond).
• Common names: ethene is commonly called ethylene; propene is commonly called propylene.

≡ Alkynes

Alkynes: hydrocarbons with a carbon–carbon triple bond.

• Contain a carbon–carbon triple bond (C≡C).
• Named with the same stem as alkanes but with the ending -yne.
• Examples: ethyne (commonly called acetylene), propyne.

Hydrocarbon type	Bond type	Ending	Example
Alkane	Single bonds only	-ane	Methane (CH₄)
Alkene	One or more double bonds	-ene	Ethene (C₂H₄)
Alkyne	Triple bond	-yne	Ethyne (C₂H₂)

🧪 Functional groups

🧪 What functional groups are

Functional group: a specific structural arrangement of atoms or bonds that imparts a characteristic chemical reactivity to a molecule.

• Alkanes have no functional group.
• Carbon–carbon double and triple bonds are functional groups because they react in specific ways that differ from alkanes.
• Example: Under certain circumstances, alkenes react with water; alkanes do not.

🍷 Alcohol functional group

Alcohol: an organic compound with an OH functional group.

• An OH group (hydroxyl group) substituted for a hydrogen atom in a hydrocarbon.
• Named using the parent hydrocarbon name with the final -e dropped and the suffix -ol attached.
• Examples: methanol (one carbon), ethanol (two carbons).
• Note: Ethanol is the alcohol in alcoholic beverages; methanol and isopropyl alcohol are toxic and should not be ingested.

🧂 Carboxyl functional group

Carboxyl group: a functional group that contains a carbon–oxygen double bond and an OH group also attached to the same carbon atom.

Carboxylic acids: organic compounds that have a carboxyl functional group.

• A carbon atom is double-bonded to an oxygen atom and to an OH group.
• Named with the ending -oic acid.
• Sometimes written as COOH in molecular formulas.
• Examples: formic acid (found in ant stingers), acetic acid (found in vinegar).

🏥 Health implications

🥑 Saturated vs. unsaturated fats

Fats are combinations of long-chain organic compounds (fatty acids) and glycerol. The carbon chains can have:

• All single bonds → classified as saturated fats (typically solids at room temperature, e.g., beef fat).
• One or more double bonds → classified as monounsaturated or polyunsaturated fats (typically liquids/oils at room temperature, e.g., olive oil, fish oils).

📊 Health correlations

Fat type	Physical state	Health correlation
Saturated	Solid at room temp	Linked to higher likelihood of heart disease, high cholesterol
Unsaturated (mono- or poly-)	Liquid at room temp	Linked to lower incidence of certain diseases
Trans fats	Varies	Implicated in heart disease; now required on US food labels

Don't confuse: The difference is as simple as a single vs. double carbon–carbon bond, yet it can have significant health impacts.

🍽️ Dietary recommendations

• Government bodies and health associations recommend decreasing saturated fat and increasing unsaturated fat proportions.
• Most organizations also recommend decreasing total fat intake.
• US law now requires food labels to list trans fat content per serving.

🔍 Complexity in organic molecules

🔍 Multiple functional groups

• Many organic compounds contain more than one functional group.
• Example: Cholesterol (mentioned in the chapter-opening essay) has an alcohol functional group.
• Formal names can be quite complex for molecules with multiple functional groups.

🧬 Beyond simple examples

The excerpt notes that many organic compounds are considerably more complex than the simple examples described, and further chapters will examine additional important organic compounds and functional groups in detail.

🧭 Overview

🧠 One-sentence thesis

The law of conservation of matter establishes that the amount of matter in a closed system remains constant, meaning chemical reactions must have the same number and type of atoms before and after the change.

📌 Key points (3–5)

• What the law states: in any closed system, the amount of matter stays constant and is conserved.
• Status as scientific law: laws are the highest form of scientific knowledge, verified many times under many conditions and considered inviolable.
• Application to chemistry: chemical changes must preserve the same number and type of atoms because matter is neither created nor destroyed.
• Common confusion: you cannot change chemical formulas to balance equations—only coefficients (the number of molecules) can be adjusted.
• Why it matters: this law is the foundation for understanding chemical reactions and requires that chemical equations be balanced.

🔬 What scientific laws are

🔬 Definition and status

A law: a general statement that explains a large number of observations.

• Before acceptance, a law must be verified many times under many conditions.
• Laws are considered the highest form of scientific knowledge.
• They are generally thought to be inviolable (cannot be violated).
• Scientific laws form the core of scientific knowledge.

⚖️ The conservation principle

⚖️ The law of conservation of matter

The law of conservation of matter: In any given system that is closed to the transfer of matter (in and out), the amount of matter in the system stays constant.

• A concise way to express this: the amount of matter in a system is conserved.
• "Closed to the transfer of matter" means no matter enters or leaves the system.
• The law applies to any given system, not just chemical reactions.

🔄 What "conserved" means

• Matter is neither created nor destroyed.
• The total amount stays the same throughout any process.
• Example: If a closed container starts with 100 grams of matter, it will still contain 100 grams after any changes inside.

🧪 How the law applies to chemistry

🧪 Chemical changes and atoms

• In any chemical change, one or more initial substances change into different substances.
• Both initial and final substances are composed of atoms (all matter is composed of atoms).
• According to the law: we must have the same number and type of atoms after the chemical change as were present before.

⚛️ Counting atoms matters

• The law requires tracking every atom through a reaction.
• You cannot lose atoms or gain new ones during a chemical reaction.
• Example: If you start with 2 hydrogen atoms and 2 oxygen atoms, you must end with exactly 2 hydrogen atoms and 2 oxygen atoms, even if they are rearranged into different molecules.

📝 Chemical equations must reflect conservation

• Chemical equations are abbreviated ways of using symbols to represent chemical changes.
• An equation that does not have the same number of atoms of each element on both sides does not satisfy the law of conservation of matter.
• Such equations are called "not balanced."

⚠️ Common mistakes and clarifications

⚠️ What you cannot do

• You cannot change chemical formulas to balance equations.
• Every substance has a characteristic chemical formula that cannot be altered.
• Example: You cannot change elemental oxygen from O₂ to O just to make the numbers work.

✅ What you can do

• You can adjust coefficients—the numbers in front of formulas.
• Coefficients indicate how many molecules of each substance are involved.
• Example: Writing 2H₂O means two water molecules are formed, giving you 4 hydrogen atoms and 2 oxygen atoms total.

🔍 Don't confuse: formula vs. coefficient

Aspect	Chemical formula	Coefficient
What it is	The symbols showing which atoms make up a substance (e.g., H₂O)	The number in front of a formula (e.g., the "2" in 2H₂O)
Can you change it?	No—it defines the substance's identity	Yes—to balance the equation
What it tells you	Which elements and how many of each in one molecule	How many molecules participate in the reaction

📊 Practical implications

📊 Mass conservation in reactions

• The law of conservation of matter says that in chemical reactions, the total mass of the products must equal the total mass of the reactants.
• This is a practical consequence: if you weigh everything before and after a reaction in a closed system, the mass will be the same.

📊 Foundation for chemistry

• The law provides the foundation for understanding in chemistry.
• It is the reason chemists must balance chemical equations.
• Without this law, we could not predict or understand chemical behavior reliably.

🧭 Overview

🧠 One-sentence thesis

Chemical equations use symbols and coefficients to represent reactions in a way that satisfies the law of conservation of matter by ensuring equal numbers of each element's atoms on both sides.

📌 Key points (3–5)

• What a chemical equation is: an abbreviated symbolic representation of a chemical reaction, showing reactants (left of arrow) and products (right of arrow).
• Why balancing matters: equations must be balanced to satisfy the law of conservation of matter—the same number of atoms of each element must appear on both sides.
• How to balance: adjust coefficients (numbers in front of formulas) to get equal atom counts; you cannot change the chemical formulas themselves.
• Common confusion: coefficients vs. formulas—you must use the proper chemical formula and only change the coefficients, not the subscripts in the formula.
• What stoichiometry means: the study of numerical relationships between reactants and products based on the coefficients in a balanced equation.

🧪 What chemical equations represent

🧪 From words to symbols

• A chemical reaction can be described in words: "hydrogen and oxygen react to make water."
• Chemical equations replace names with formulas and use symbols:
  • Plus sign (+) connects multiple reactants or products.
  • Arrow (→) represents the chemical change.
• Example: H₂ + O₂ → H₂O

🏷️ Parts of a chemical equation

Chemical equation: an abbreviated way of using symbols to represent a chemical change.

Reactants: substances on the left side of the arrow in a chemical equation.

Products: substances on the right side of the arrow in a chemical equation.

• Phase labels are often included: (s) solid, (ℓ) liquid, (g) gas, (aq) aqueous solution.
• Example with phases: H₂(g) + O₂(g) → H₂O(ℓ)

⚖️ Balancing chemical equations

⚖️ Why equations must be balanced

• An equation must satisfy the law of conservation of matter.
• This means: the same number of atoms of each element must appear on both sides.
• Example problem: H₂(g) + O₂(g) → H₂O(ℓ) has two oxygen atoms on the left but only one on the right—not balanced.

🔢 What coefficients do

Coefficient: a number that gives the number of molecules of a substance in a balanced chemical equation.

• Coefficients are placed in front of chemical formulas.
• They multiply the entire formula.
• Example: 2H₂O means two water molecules (four hydrogen atoms, two oxygen atoms total).

Critical rule: You cannot change the chemical formula itself to balance an equation; you must use coefficients only.

🔧 How to balance an equation

The excerpt describes a back-and-forth approach:

1. Count atoms of one element on both sides.
2. Adjust a coefficient if needed to make the counts equal.
3. Move to another element and repeat.
4. Continue until all elements have equal atom counts on both sides.

Example walkthrough (from the excerpt):

• Start: H₂(g) + O₂(g) → H₂O(ℓ)
• Add coefficient 2 to water: H₂(g) + O₂(g) → 2H₂O(ℓ) (now oxygen is balanced but hydrogen is not)
• Add coefficient 2 to hydrogen: 2H₂(g) + O₂(g) → 2H₂O(ℓ) (now both are balanced)

Balanced: a property of a chemical equation when there are the same number of atoms of each element in the reactants and products.

✅ Checking if an equation is balanced

Count atoms of each element on each side:

Equation	Balanced?	Reason
2Na(s) + O₂(g) → 2Na₂O(s)	No	Two Na and two O on left; four Na and two O on right
CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(ℓ)	Yes	One C, four H, four O on each side

Don't confuse: different numbers of molecules (coefficients) vs. different numbers of atoms—balancing requires equal atom counts, not equal molecule counts.

📐 Stoichiometry and quantitative relationships

📐 What stoichiometry studies

Stoichiometry: the study of the numerical relationships between the reactants and the products in a balanced chemical equation.

• The coefficients in a balanced equation determine the molecular ratio in which substances react and form.
• These ratios allow quantitative predictions.

🔗 Ratios from balanced equations

From the balanced equation 2C₂H₂ + 5O₂ → 4CO₂ + 2H₂O, we can construct ratios:

Statement	Ratio	Inverse ratio
Two C₂H₂ molecules react with five O₂ molecules	2C₂H₂ / 5O₂	5O₂ / 2C₂H₂
Two C₂H₂ molecules make four CO₂ molecules	2C₂H₂ / 4CO₂	4CO₂ / 2C₂H₂
Five O₂ molecules make two H₂O molecules	5O₂ / 2H₂O	2H₂O / 5O₂

These ratios work like conversion factors for predicting amounts.

🍪 Everyday analogy: cooking recipes

The excerpt uses a biscuit recipe analogy:

• A recipe (like a chemical equation) shows ratios: 2 cups flour + 1 egg + other ingredients → 12 biscuits.
• If you have 4 cups of flour, you can predict: (4 cups flour) × (12 biscuits / 2 cups flour) = 24 biscuits.
• Doubling or halving a recipe is a type of stoichiometry.
• Example: the ratio "12 biscuits / 2 cups flour" acts as a conversion factor, just like molecular ratios in chemistry.

🧭 Overview

🧠 One-sentence thesis

Stoichiometry uses the coefficients in a balanced chemical equation to predict how much of one substance will react with or be produced from a given amount of another substance.

📌 Key points (3–5)

• What stoichiometry is: the study of numerical relationships between reactants and products in a balanced chemical equation.
• Where the ratios come from: the coefficients in the balanced equation determine the molecular ratios in which substances react and form.
• How to use stoichiometric ratios: construct conversion factors from the coefficients, then multiply the given amount by the appropriate ratio to find the unknown amount.
• Common confusion: stoichiometry only works with a balanced equation—without balancing first, predictions will be incorrect.
• Why it matters: stoichiometry allows powerful predictive calculations about how much product forms or how much reactant is needed.

🔢 What stoichiometry measures

🔢 Definition and origin

Stoichiometry: the study of the numerical relationships between the reactants and the products in a balanced chemical equation.

• The word is pronounced "stow-eh-key-OM-et-tree."
• It comes from mixed Greek and English origins, meaning roughly "measure of an element."
• It is not about the chemical properties themselves, but about the quantities involved.

🧮 The role of coefficients

• A balanced chemical equation shows what reacts with what to make what products.
• The coefficients (the numbers in front of each formula) determine the molecular ratio in which reactants react and products are made.
• These coefficients are the foundation of all stoichiometric calculations.
• Example: In the equation 2 C₂H₂ + 5 O₂ → 4 CO₂ + 2 H₂O, the coefficient 2 in front of C₂H₂ means 2 molecules of C₂H₂ react with 5 molecules of O₂.

🍪 Building stoichiometric ratios

🍪 The cooking analogy

• The excerpt uses a biscuit recipe to illustrate stoichiometry:
  • 2 cups flour + 1 egg + 4 tablespoons shortening + 1 teaspoon salt + 1 teaspoon baking soda + 1 cup milk → 12 biscuits.
• This "equation" gives ratios: 2 cups of flour (with the right amounts of other ingredients) yields 12 biscuits.
• You can construct conversion factors: 12 biscuits per 2 cups flour.
• Example: If you have 4 cups of flour, you can make 4 cups flour × (12 biscuits / 2 cups flour) = 24 biscuits.
• Key insight: Doubling or halving a recipe is a type of stoichiometry.

⚖️ Constructing ratios from chemical equations

• From a balanced equation, you can make statements and ratios.
• Example: For 2 C₂H₂ + 5 O₂ → 4 CO₂ + 2 H₂O, you can say:
  • "Two C₂H₂ molecules react with five O₂ molecules" → ratio: 2 C₂H₂ / 5 O₂ (or its inverse 5 O₂ / 2 C₂H₂).
  • "Two C₂H₂ molecules react to make four CO₂ molecules" → ratio: 2 C₂H₂ / 4 CO₂ (or its inverse).
  • "Five O₂ molecules react to make two H₂O molecules" → ratio: 5 O₂ / 2 H₂O (or its inverse).
  • "Four CO₂ molecules are made at the same time as two H₂O molecules" → ratio: 4 CO₂ / 2 H₂O (or its inverse).
• The excerpt notes that 12 different conversion factors can be constructed from this one equation.
• In each ratio, the unit is assumed to be molecules (because that is how we interpret the chemical equation).

Statement from the equation	Ratio	Inverse ratio
Two C₂H₂ react with five O₂	2 C₂H₂ / 5 O₂	5 O₂ / 2 C₂H₂
Two C₂H₂ make four CO₂	2 C₂H₂ / 4 CO₂	4 CO₂ / 2 C₂H₂
Five O₂ make two H₂O	5 O₂ / 2 H₂O	2 H₂O / 5 O₂
Four CO₂ made with two H₂O	4 CO₂ / 2 H₂O	2 H₂O / 4 CO₂

🧪 Using stoichiometric ratios in calculations

🧪 The conversion-factor method

• Any stoichiometric ratio can be used as a conversion factor to relate an amount of one substance to an amount of another.
• General approach:
  1. Start with the amount you are given.
  2. Multiply by a conversion factor that cancels out the original unit and introduces the unit you want.
  3. The conversion factor comes directly from the coefficients in the balanced equation.

🔬 Worked example from the excerpt

• Question: How many CO₂ molecules are formed when 26 molecules of C₂H₂ are reacted?
• Equation: 2 C₂H₂ + 5 O₂ → 4 CO₂ + 2 H₂O
• From the equation, the ratio is 4 CO₂ / 2 C₂H₂.
• Calculation:
  • 26 C₂H₂ × (4 CO₂ / 2 C₂H₂) = 52 CO₂
• The C₂H₂ units cancel, leaving CO₂.
• Result: 52 molecules of CO₂ are formed.

⚠️ Why balancing is essential

• The excerpt emphasizes: "This application of stoichiometry is extremely powerful in its predictive ability, as long as we begin with a balanced chemical equation."
• Without a balanced equation, the predictions made by stoichiometric calculations will be incorrect.
• Don't confuse: you cannot use stoichiometry on an unbalanced equation—the coefficients must reflect the true molecular ratios.

📝 Verifying and applying stoichiometry

📝 Example with a complex equation

• Equation: KMnO₄ + 8 HCl + 5 FeCl₂ → 5 FeCl₃ + MnCl₂ + 4 H₂O + KCl
• The excerpt walks through verifying balance:
  • Each side has 1 K atom and 1 Mn atom.
  • H atoms: 8 from HCl on the left, 8 from 4 H₂O on the right → balanced.
  • Fe atoms: 5 from 5 FeCl₂ on the left, 5 from 5 FeCl₃ on the right → balanced.
  • Cl atoms: 8 from HCl + 10 from 5 FeCl₂ = 18 on the left; 15 from 5 FeCl₃ + 2 from MnCl₂ + 1 from KCl = 18 on the right → balanced.
• Two ratios relating HCl and FeCl₃:
  • 8 HCl / 5 FeCl₃
  • 5 FeCl₃ / 8 HCl
• The excerpt notes that a total of 42 possible ratios can be constructed from this equation.

📝 Another example

• Equation: 2 KMnO₄ + 3 CH₂=CH₂ + 4 H₂O → 2 MnO₂ + 3 HOCH₂CH₂OH + 2 KOH
• The excerpt asks the reader to verify balance and construct ratios between KMnO₄ and CH₂=CH₂.
• A total of 30 relationships can be constructed from this equation.

🎯 Key takeaway and concept review

🎯 The main lesson

A balanced chemical equation gives the ratios in which molecules of substances react and are produced in a chemical reaction.

• Stoichiometric ratios are made using the coefficients of the substances in the balanced chemical equation.
• A balanced chemical equation is necessary so one can construct the proper stoichiometric ratios.
• Without balancing, the ratios are meaningless and predictions will be wrong.

🎯 How to construct stoichiometric ratios

1. Start with a balanced chemical equation.
2. Identify the coefficients in front of each substance.
3. Write ratios using those coefficients (e.g., coefficient of A / coefficient of B).
4. Use these ratios as conversion factors in calculations.

🧭 Overview

🧠 One-sentence thesis

Most chemical reactions can be classified into a small number of general types—combination, decomposition, and combustion—which helps us recognize patterns and predict products.

📌 Key points (3–5)

• Why classify reactions: to recognize similarities and to predict products of reactions.
• Combination reactions: two or more reactants make a single substance.
• Decomposition reactions: a single substance breaks down into two or more products (the reverse of combination).
• Combustion reactions: a substance combines with molecular oxygen to make oxygen-containing compounds, usually with heat/light.
• Common confusion: a reaction can fall into more than one category; for example, some reactions can be both combination and combustion.

🔗 Combination reactions

🔗 What combination means

Combination (composition) reaction: a chemical reaction that makes a single substance from two or more reactants.

• There may be more than one molecule of product in the balanced equation, but only one substance is produced.
• The key is "multiple reactants → one product substance."

🧪 Examples of combination

• Elements combining: 4Fe + 3O₂ → 2Fe₂O₃ (iron and oxygen make iron oxide).
• Compounds combining: Fe₂O₃ + 3SO₃ → Fe₂(SO₄)₃ (iron oxide combines with sulfur trioxide).
• Combination reactions do not have to combine elements; compounds can also combine.

✅ How to identify

• Look for multiple reactants on the left side.
• Look for a single product substance on the right side.
• Example: Co(s) + Cl₂(g) → CoCl₂(s) is a combination reaction (two reactants, one product).
• Example: N₂H₄(ℓ) + O₂(g) → N₂(g) + 2H₂O(ℓ) is not a combination reaction (multiple products).

💥 Decomposition reactions

💥 What decomposition means

Decomposition reaction: a chemical reaction in which a single substance is converted into two or more products.

• This is the reverse of a combination reaction.
• There may be more than one molecule of the reactant, but there is only one substance initially.

🧪 Examples of decomposition

• Baking soda decomposition: 2NaHCO₃(s) → Na₂CO₃(s) + CO₂(g) + H₂O(ℓ) (occurs when heated).
• Potassium chlorate decomposition: 2KClO₃(s) → 2KCl(s) + 3O₂(g) (once commonly used to generate oxygen in labs).

✅ How to identify

• Look for a single reactant substance on the left side.
• Look for multiple products on the right side.
• Example: (NH₄)₂Cr₂O₇(s) → N₂(g) + Cr₂O₃(s) + 4H₂O(ℓ) is a decomposition reaction (one reactant, several products).

🔥 Real-world application

• The decomposition of NaHCO₃ (baking soda) is used when baking soda is poured on a small kitchen fire.
• The H₂O and CO₂ produced by the decomposition smother the flames.

🔥 Combustion reactions

🔥 What combustion means

Combustion reaction: a chemical reaction that occurs when a substance combines with molecular oxygen to make oxygen-containing compounds of other elements in the reaction.

• Oxygen (in its elemental form) is a crucial reactant.
• Oxygen is also present in the products.
• Typically a vigorous reaction accompanied by light and/or heat.

🧪 Examples of combustion

• Acetylene burning: 2C₂H₂ + 5O₂ → 4CO₂ + 2H₂O (used in torches).
• Methane burning: CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(ℓ).

✅ How to identify

• Look for molecular oxygen (O₂) as a reactant.
• Look for oxygen-containing compounds (like CO₂ and H₂O) as products.
• Energy in the form of heat is usually given off as a product.
• Example: C₂H₅OH + 3O₂ → 2CO₂ + 3H₂O is a combustion reaction (oxygen reacts with a compound to make carbon dioxide and water).

⚠️ Don't confuse with combination

• A combustion reaction is usually a vigorous reaction with oxygen, accompanied by light and/or heat.
• A combination reaction simply produces a certain substance from multiple reactants.
• Some reactions can be both: for example, 2Ca(s) + O₂(g) → 2CaO(s) is both a combination (two reactants → one product) and a combustion (reaction with oxygen).

🔄 Multiple classifications

🔄 Reactions can fit more than one type

• The excerpt states: "A particular reaction may fall into more than one of the categories."
• Example: Hg(ℓ) + ½O₂(g) → HgO(s) can be classified as both combustion (reaction with oxygen) and combination (two reactants → one product).

📋 Summary table

Reaction type	Key feature	Example
Combination	Multiple reactants → one product substance	2K(s) + S(s) + 2O₂(g) → K₂SO₄(s)
Decomposition	One reactant substance → multiple products	2NaHCO₃(s) → Na₂CO₃(s) + CO₂(g) + H₂O(ℓ)
Combustion	Reaction with O₂ → oxygen-containing products, usually with heat/light	CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(ℓ)

🎯 Why classification matters

• Helps recognize similarities among millions of possible reactions.
• Enables prediction of products for certain reactions.
• Makes learning and understanding chemistry more systematic.

🧭 Overview

🧠 One-sentence thesis

Redox reactions involve the transfer of electrons between substances, and they are central to energy production in combustion, batteries, and biological metabolism.

📌 Key points (3–5)

• What redox reactions are: chemical reactions in which electrons are transferred from one atom to another; oxidation and reduction always occur together.
• Oxidation vs reduction: oxidation is the loss of electrons (or gain of oxygen/loss of hydrogen); reduction is the gain of electrons (or loss of oxygen/gain of hydrogen).
• How to track electron transfer: half reactions separate the oxidation and reduction parts, showing electrons as products (oxidation) or reactants (reduction); electrons must cancel when half reactions are combined.
• Common confusion: oxidation can be defined three ways—loss of electrons, addition of oxygen, or removal of hydrogen—but all describe the same process from different perspectives.
• Why redox matters: all batteries, combustion reactions, respiration, and many organic chemistry transformations depend on redox reactions.

⚡ What happens in a redox reaction

⚡ Electron transfer between atoms

Oxidation-reduction reactions (redox reactions): chemical reactions in which electrons are transferred from one atom to another.

• The excerpt illustrates this with zinc metal reacting with hydrochloric acid: electrons are transferred from zinc atoms to hydrogen ions.
• The zinc atoms lose electrons (changing from Zn to Zn²⁺), and the hydrogen ions gain electrons (changing from H⁺ to H₂ gas).
• Because one substance must lose electrons for another to gain them, oxidation and reduction always occur together—they are two sides of the same reaction.

🔄 Oxidation and reduction defined

Oxidation: the loss of electrons by an atom.

Reduction: the gain of electrons by an atom.

• The atom that loses electrons is oxidized; the atom that gains electrons is reduced.
• Oxidizing agent: the species being reduced (it causes oxidation in the other substance).
• Reducing agent: the species being oxidized (it causes reduction in the other substance).
• Example: In the zinc–hydrogen reaction, zinc is the reducing agent (it is oxidized), and hydrogen ions are the oxidizing agent (they are reduced).

🧮 Balancing redox reactions with half reactions

🧮 What half reactions show

Half reactions: chemical reactions that show only oxidation or reduction.

• Each half reaction includes:
  • The reactant being oxidized or reduced
  • The corresponding product
  • Any other species needed to balance the equation
  • The electrons being transferred
• Electrons lost are written as products; electrons gained are written as reactants.
• Example: For zinc oxidation, the half reaction is Zn → Zn²⁺ + 2e⁻ (two electrons appear as products).

⚖️ Balancing charge and electrons

• Each half reaction must be balanced for both atoms and overall charge.
• Example: The reduction half reaction for hydrogen is 2H⁺ + 2e⁻ → H₂. The two electrons (reactants) neutralize the 2+ charge on the hydrogen ions, so both sides have zero net charge.
• When combining half reactions, the electrons must cancel exactly—this is the key criterion for a balanced redox reaction.
• Sometimes you must multiply one half reaction by an integer so that the number of electrons matches.

🔢 Example: silver and aluminum

The excerpt walks through balancing the reaction of silver ions with aluminum metal:

• Silver is reduced: Ag⁺ + e⁻ → Ag
• Aluminum is oxidized: Al → Al³⁺ + 3e⁻
• To cancel all electrons, multiply the silver half reaction by 3:
  • 3Ag⁺ + 3e⁻ → 3Ag
  • Al → Al³⁺ + 3e⁻
• Combined: 3Ag⁺ + Al → 3Ag + Al³⁺ (the three electrons on each side cancel).
• The overall charge is balanced: +3 on the left (from 3Ag⁺) and +3 on the right (from Al³⁺).

🧪 Alternative definitions: oxygen and hydrogen

🧪 Oxidation and reduction in terms of composition

The excerpt notes that oxidation and reduction can also be defined by changes in oxygen or hydrogen content:

Definition	Oxidation	Reduction
Electron transfer	Loss of electrons	Gain of electrons
Oxygen	Addition of oxygen	Loss of oxygen
Hydrogen	Loss of hydrogen	Addition of hydrogen

• These definitions describe the same underlying process from different perspectives.
• Example (oxygen): Acetaldehyde (CH₃CHO) takes on an oxygen atom to become acetic acid (CH₃COOH), so acetaldehyde is being oxidized.
• Example (hydrogen): Acetaldehyde (CH₃CHO) adds hydrogen atoms to become ethanol (CH₃CH₂OH), so acetaldehyde is being reduced.

🔍 Recognizing oxidation or reduction

• If a molecule adds oxygen atoms, it is being oxidized.
• If a molecule loses oxygen atoms, it is being reduced.
• If a molecule adds hydrogen atoms, it is being reduced.
• If a molecule loses hydrogen atoms, it is being oxidized.
• Don't confuse: the same molecule can be oxidized in one reaction and reduced in another, depending on what is added or removed.

🔋 Applications of redox reactions

🔋 Batteries and pacemakers

• All batteries are based on redox reactions because batteries supply electricity (a stream of electrons).
• Example: Pacemakers used to use NiCad batteries, in which cadmium is oxidized and nickel is reduced: Cd(s) + 2NiOOH(s) + 2H₂O(ℓ) → Cd(OH)₂(s) + 2Ni(OH)₂(s).
• Modern pacemakers use lithium/iodine batteries: 2Li(s) + I₂(s) → 2LiI(s). Lithium is oxidized, and iodine is reduced.
• Although lithium/iodine batteries cannot be recharged, they last up to 10 years.

🔥 Combustion reactions

• All combustion reactions are redox reactions.
• Example: Burning methane (natural gas): CH₄ + 2O₂ → CO₂ + 2H₂O. Methane is oxidized (gains oxygen), and oxygen is reduced.
• Similar redox reactions occur when burning gasoline and coal.

🫁 Respiration and metabolism

Respiration: the biochemical process by which the oxygen we inhale oxidizes foodstuffs to carbon dioxide and water.

• Redox reactions in respiration provide energy to living cells.
• Example: Oxidation of glucose (C₆H₁₂O₆): C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O. Glucose is oxidized, and oxygen is reduced.
• The metabolism of foods that keeps us alive involves redox reactions.

🧬 Organic chemistry transformations

• Organic chemists use redox reactions to transform molecules.
• Example: Potassium dichromate (K₂Cr₂O₇) oxidizes alcohols (ROH).
  • If the OH group is on a terminal carbon and the product is distilled off, the product is an aldehyde (RCHO).
  • Example: Ethyl alcohol (C₂H₅OH) is oxidized to acetaldehyde (CH₃CHO) in the Breathalyzer test: 3C₂H₅OH + Cr₂O₇²⁻ + 8H⁺ → 3CH₃CHO + 2Cr³⁺ + 7H₂O.
  • If acetaldehyde is not removed, it is further oxidized to acetic acid (CH₃COOH).
  • If the OH group is on an interior carbon, oxidation produces a ketone (RCOR). Example: 2-propanol (CH₃CHOHCH₃) is oxidized to acetone [(CH₃)₂CO].
• In these reactions, the chromium atom is reduced (from Cr₂O₇²⁻ to Cr³⁺), and the alcohol is oxidized.

🧭 Overview

🧠 One-sentence thesis

Redox reactions are central to both organic chemistry and biochemistry, powering combustion, respiration, metabolism, and photosynthesis—the fundamental processes that sustain civilization and life on Earth.

📌 Key points

• Combustion and respiration are redox reactions: burning fuels and metabolizing food both involve oxidation-reduction processes that release energy.
• Organic redox reactions transform functional groups: alcohols can be oxidized to aldehydes, ketones, or carboxylic acids; aldehydes and ketones can be reduced back to alcohols.
• Antioxidants are reducing agents: substances like vitamin C and vitamin E protect living cells by undergoing reduction reactions that prevent harmful oxidation.
• Photosynthesis is the ultimate redox reaction: plants reduce carbon dioxide to glucose and oxidize water to oxygen, making almost all life on Earth possible.
• Common confusion—direction of electron transfer: oxidation means losing electrons (or gaining oxygen, or losing hydrogen); reduction means gaining electrons (or losing oxygen, or gaining hydrogen).

🔥 Combustion and respiration as redox reactions

🔥 Combustion of fuels

Combustion reactions: reactions that combine molecular oxygen with the atoms of another reactant; all combustion reactions are also redox reactions.

• Burning fuels provides the energy that maintains civilization.
• Example: methane (natural gas) combustion:
  • CH₄ + 2O₂ → CO₂ + 2H₂O
  • Methane is oxidized; oxygen is reduced.
• Similar reactions occur with gasoline and coal.

🫁 Respiration in living cells

Respiration: the biochemical process by which the oxygen we inhale in air oxidizes foodstuffs to carbon dioxide and water.

• Respiration provides energy to living cells through redox reactions.
• Example: oxidation of glucose (C₆H₁₂O₆):
  • C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O
  • Glucose is oxidized; oxygen is reduced.
  • This is the same simple sugar that makes up the diet of yeast.
• Don't confuse: combustion and respiration both oxidize organic molecules with oxygen, but respiration occurs in controlled biochemical steps inside cells, while combustion is rapid burning.

🧪 Redox reactions in organic chemistry

🍷 Oxidation of alcohols

• Organic chemists use redox reactions to transform functional groups.
• Potassium dichromate (K₂Cr₂O₇) is a common oxidizing agent for alcohols (ROH).
• The product depends on:
  • Location of the OH group in the molecule.
  • Relative proportions of alcohol and dichromate.
  • Reaction conditions (e.g., temperature).

🧴 Terminal alcohols → aldehydes or carboxylic acids

• When the OH group is attached to a terminal carbon atom:
  • If the product is distilled off as it forms → aldehyde (RCHO) with a terminal carbonyl group (C=O).
  • Example: ethyl alcohol (C₂H₅OH) oxidized to acetaldehyde (CH₃CHO):
    • 3C₂H₅OH + Cr₂O₇²⁻ + 8H⁺ → 3CH₃CHO + 2Cr³⁺ + 7H₂O
    • This reaction is used by the Breathalyzer to detect alcohol in breath.
  • If acetaldehyde is not removed, it is further oxidized to acetic acid (CH₃COOH):
    • 3C₂H₅OH + 2Cr₂O₇²⁻ + 16H⁺ → 3CH₃COOH + 4Cr³⁺ + 11H₂O
• In both reactions, chromium is reduced from Cr₂O₇²⁻ to Cr³⁺.

🧪 Interior alcohols → ketones

• When the OH group is bonded to an interior carbon atom → ketone (RCOR, with C=O double bond).
• Example: 2-propanol (CH₃CHOHCH₃) oxidized to acetone [(CH₃)₂CO]:
  • 3CH₃CHOHCH₃ + Cr₂O₇²⁻ + 8H⁺ → 3(CH₃)₂CO + 2Cr³⁺ + 7H₂O
  • Acetone is a common solvent used in varnishes, lacquers, rubber cement, and nail polish remover.

🔄 Reduction of aldehydes and ketones

• Aldehydes and ketones can be reduced back to alcohols.
• Reduction of the carbonyl group is important in living organisms.

🧬 Redox reactions in biochemistry

🏃 Anaerobic metabolism

Anaerobic metabolism: a biochemical process that takes place in the absence of oxygen.

• Example: pyruvic acid (CH₃COCOOH) is reduced to lactic acid (CH₃CHOHCOOH) in muscles:
  • CH₃COCOOH → CH₃CHOHCOOH
  • Pyruvic acid is both a carboxylic acid and a ketone; only the ketone group is reduced.
• The buildup of lactic acid during vigorous exercise is responsible in large part for the fatigue we experience.

🛡️ Antioxidants as reducing agents

Antioxidants: substances in foods that act as reducing agents.

• Antioxidants are reducing agents that protect living cells by undergoing reduction reactions.
• Ascorbic acid (vitamin C, C₆H₈O₆):
  • Thought to retard potentially damaging oxidation of living cells.
  • In the process, it is oxidized to dehydroascorbic acid (C₆H₆O₆).
  • In the stomach, ascorbic acid reduces nitrite ion (NO₂⁻) to nitric oxide (NO):
    • C₆H₈O₆ + 2H⁺ + 2NO₂⁻ → C₆H₆O₆ + 2H₂O + 2NO
  • Why this matters: if this reaction did not occur, nitrite ions from foods would oxidize the iron in hemoglobin, destroying its ability to carry oxygen.
• Tocopherol (vitamin E):
  • Also an antioxidant.
  • In the body, thought to act by scavenging harmful by-products of metabolism, such as highly reactive molecular fragments called free radicals.
  • In foods, vitamin E prevents fats from being oxidized and becoming rancid.
• Citrus fruits (oranges, lemons, limes) are good sources of vitamin C.

🌱 Photosynthesis: the ultimate redox reaction

🌿 How photosynthesis works

Photosynthesis: the process by which plants use solar energy to convert carbon dioxide and water to glucose and oxygen.

• Green plants carry out the redox reaction that makes possible almost all life on Earth.
• The overall change:
  • 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
  • Carbon dioxide is reduced to glucose.
  • Water is oxidized to oxygen gas.
• The synthesis of glucose requires:
  • A variety of proteins called enzymes.
  • A green pigment called chlorophyll that converts sunlight into chemical energy.

🌍 Why photosynthesis matters

• Other reactions convert the glucose to more complex carbohydrates, plant proteins, and oils.
• Photosynthesis is the fundamental process that sustains almost all life on Earth.
• It is the ultimate source of all food on Earth.
• Don't confuse: photosynthesis is the reverse of respiration in terms of overall reactants and products, but the mechanisms and purposes are completely different—photosynthesis stores energy, respiration releases it.

🔍 Summary of key redox concepts

Process	What is oxidized	What is reduced	Role in life
Combustion	Fuel (e.g., methane)	Oxygen	Provides energy for civilization
Respiration	Glucose	Oxygen	Provides energy to living cells
Anaerobic metabolism	(varies)	Pyruvic acid → lactic acid	Energy production without oxygen
Antioxidants	Vitamin C, vitamin E	Harmful oxidizing agents	Protects cells from damage
Photosynthesis	Water	Carbon dioxide	Produces glucose and oxygen; basis of food chain

🧠 How to identify oxidation vs. reduction

• Oxidation: loses electrons, gains oxygen atoms, or loses hydrogen atoms.
• Reduction: gains electrons, loses oxygen atoms, or gains hydrogen atoms.
• Oxidizing agent: the species being reduced (it causes oxidation in another species).
• Reducing agent: the species being oxidized (it causes reduction in another species).

🧭 Overview

🧠 One-sentence thesis

The mole is a unit that represents 6.022 × 10²³ items (Avogadro's number) and allows chemists to relate macroscopic masses of substances to the number of atoms or molecules they contain.

📌 Key points (3–5)

• What a mole is: A counting unit equal to 6.022 × 10²³ things (atoms, molecules, or formula units).
• Why we need it: Individual atoms are too small to count one-by-one, so the mole lets us work with billions of billions of particles using measurable masses.
• Key relationship: 1 mole of any substance has a mass in grams numerically equal to one atom/molecule's mass in atomic mass units (u).
• Common confusion: The mole is a number (like "dozen"), not a type of particle—you must specify moles of what (atoms, molecules, or formula units).
• Practical use: Molar mass allows conversion between the number of moles and the mass in grams of a substance.

🔢 What the mole unit means

🔢 Definition and scale

Mole (mol): A number of things equal to 6.022 × 10²³ items.

Avogadro's number: The value 6.022 × 10²³.

• Just as "dozen" means 12, "mole" means 6.022 × 10²³.
• This is an enormous number: if 1 mol of quarters were stacked, the column could stretch between Earth and the sun 6.8 billion times.
• Example: 1 mol of O atoms = 6.022 × 10²³ O atoms; 2 mol of Na atoms = 2 × (6.022 × 10²³) = 1.2044 × 10²⁴ Na atoms.

🧪 What you can count in moles

• The mole can apply to different chemical entities:
  • Atoms (e.g., 1 mol of H atoms)
  • Molecules (e.g., 0.5 mol of C₆H₆ molecules)
  • Formula units of ionic compounds (e.g., 2.34 mol of NaCl)
• Don't confuse: "Mole" by itself doesn't specify what is being counted—you must state moles of atoms, molecules, or formula units.

🔗 Relating moles to atoms in compounds

🔗 Molecular relationships

• Chemical formulas show how many atoms of each element are in one molecule or formula unit.
• This ratio scales up to moles.

Example with ethanol (C₂H₆O):

1 molecule of C₂H₆O contains	1 mol of C₂H₆O contains
2 C atoms	2 mol of C atoms
6 H atoms	6 mol of H atoms
1 O atom	1 mol of O atoms

• If you have 2.5 mol of C₂H₆O molecules, you have:
  • 2.5 mol × (2 mol C / 1 mol C₂H₆O) = 5.0 mol of C atoms
  • 2.5 mol × (6 mol H / 1 mol C₂H₆O) = 15 mol of H atoms
  • 2.5 mol × (1 mol O / 1 mol C₂H₆O) = 2.5 mol of O atoms

🔄 Converting moles to number of particles

• Use Avogadro's number as a conversion factor.
• Example: How many formula units in 2.34 mol of NaCl?
  • 2.34 mol NaCl × (6.022 × 10²³ units / 1 mol) = 1.41 × 10²⁴ NaCl units
  • Since each NaCl has 2 ions, total ions = 1.41 × 10²⁴ × 2 = 2.82 × 10²⁴ ions

⚖️ Molar mass: connecting moles to grams

⚖️ The key principle

One mole of a substance has the same mass in grams that one atom or molecule has in atomic mass units.

• 1 hydrogen atom ≈ 1 u → 1 mol of H atoms ≈ 1 g
• 1 sodium atom ≈ 23 u → 1 mol of Na atoms ≈ 23 g
• The periodic table atomic masses tell you both the mass of one atom (in u) and the mass of 1 mol of atoms (in g).

⚖️ Calculating molar mass for compounds

Molar mass: The mass of 1 mol of a substance (element, ionic compound, or covalent compound).

How to calculate:

• Sum the molar masses of all atoms in the chemical formula.
• Multiply each element's molar mass by the number of atoms of that element in the formula.

Example: NaCl

• 1 Na: 23.00 g
• 1 Cl: 35.45 g
• Total molar mass = 58.45 g/mol

Example: C₃₃H₃₆N₄O₆ (bilirubin)

• 33 C: 33 × 12.01 = 396.33 g
• 36 H: 36 × 1.01 = 36.36 g
• 4 N: 4 × 14.00 = 56.00 g
• 6 O: 6 × 16.00 = 96.00 g
• Total molar mass = 584.69 g/mol

⚖️ Why mass ratios stay constant

• The ratio of masses of equal numbers of different atoms is always the same.
• Example: oxygen atom to hydrogen atom mass ratio ≈ 16:1
  • 2 O atoms : 2 H atoms ≈ 32:2 = 16:1
  • 100 O atoms : 100 H atoms ≈ 1600:100 = 16:1
• This consistency allows us to use mass measurements instead of counting individual atoms.

🎯 Why the mole matters

🎯 Practical necessity

• Atoms and molecules are far too small and numerous to count individually.
• Even tiny samples contain billions of billions of particles.
• The mole bridges the gap between the atomic scale (measured in u) and the laboratory scale (measured in grams).

🎯 Real-world context

• The excerpt opens with a historical example: Lavoisier used mass measurements to demonstrate the law of conservation of matter (total mass before = total mass after).
• Modern applications mentioned:
  • Medical dosing (the chapter-opening essay references a dosing error)
  • Food science (test kitchens tracking ingredient amounts)
  • Quality control (measuring substances in products)
  • Commerce (weighing meat and produce)
• Stoichiometry (the study of numerical relationships between reactants and products in chemical reactions) depends on the mole concept.

🧭 Overview

🧠 One-sentence thesis

The mole connects atomic-scale masses (in atomic mass units) to laboratory-scale masses (in grams) because one mole of any substance has the same numerical mass in grams that one atom or molecule has in atomic mass units.

📌 Key points (3–5)

• The core relationship: 1 mole of a substance has the same mass in grams that one atom or molecule has in atomic mass units (u).
• Why Avogadro's number matters: the number 6.022 × 10²³ is chosen specifically to make this gram-to-u correspondence work.
• Molar mass definition: the mass of 1 mol of atoms or molecules, expressed in grams per mole (g/mol).
• How to calculate molar mass for compounds: sum the molar masses of all individual atoms in the formula, counting carefully when polyatomic ions have subscripts.
• Common confusion: the periodic table atomic mass tells you both the mass of one atom in u and the mass of 1 mol of atoms in grams—same number, different units.

🔗 The mole-to-mass connection

🔗 Why the mole uses that specific number

• The excerpt asks: why is a mole 6.022 × 10²³ and not some other number?
• Answer: Avogadro's number is related to the relative sizes of the atomic mass unit and the gram.
• This relationship creates a direct numerical correspondence between atomic-scale and lab-scale masses.

⚖️ The fundamental correspondence rule

One mole of a substance has the same mass in grams that one atom or molecule has in atomic mass units.

• Example: one hydrogen atom has a mass of approximately 1 u → 1 mol of H atoms has a mass of approximately 1 gram.
• Example: one sodium atom has an approximate mass of 23 u → 1 mol of Na atoms has an approximate mass of 23 grams.
• This is not a coincidence; it is the defining feature of the mole.

📖 Reading the periodic table for molar mass

• The atomic masses listed in the periodic table serve a dual purpose:
  • They tell the mass of one atom in atomic mass units (u).
  • They tell the mass of 1 mol of atoms in grams (g).
• Example: aluminum's atomic mass is 26.98, so 1 mol of Al atoms has a mass of 26.98 g.
• Example: uranium's atomic mass is 238.03, so 1 mol of U atoms has a mass of 238.03 g, and 2 mol has a mass of 476.06 g.

🧮 Calculating molar mass for compounds

🧮 Extending the concept to molecules and formula units

• The same principle applies to molecules and ionic compounds.
• A single molecule of O₂ has a mass of 32.00 u → 1 mol of O₂ molecules has a mass of 32.00 g.
• To find the molar mass of any substance, sum the masses of all individual atoms in its formula.

🧪 Step-by-step calculation for simple compounds

Example: NaCl

• 1 Na atom: molar mass 23.00 g
• 1 Cl atom: molar mass 35.45 g
• Total molar mass of NaCl: 58.45 g/mol

Example: bilirubin (C₃₃H₃₆N₄O₆)

• 33 C atoms: 33 × 12.01 g = 396.33 g
• 36 H atoms: 36 × 1.01 g = 36.36 g
• 4 N atoms: 4 × 14.00 g = 56.00 g
• 6 O atoms: 6 × 16.00 g = 96.00 g
• Total molar mass: 584.69 g/mol

⚠️ Counting atoms in formulas with parentheses

• Be careful with polyatomic ions in parentheses: the subscript outside applies to every atom inside.
• Example: Ba(OH)₂
  • 1 Ba atom: 1 × 137.33 g = 137.33 g
  • 2 O atoms (from the subscript 2 outside parentheses): 2 × 16.00 g = 32.00 g
  • 2 H atoms (from the subscript 2 outside parentheses): 2 × 1.01 g = 2.02 g
  • Total: 171.35 g/mol
• Don't confuse: the subscript outside parentheses multiplies all atoms inside, not just the last one.

📏 Expressing and using molar mass

📏 Units: grams per mole

• Molar mass is defined as the mass for 1 mol of a substance.
• It is expressed in grams per mole (g/mol).
• The division sign "/" means "per," and "1" is implied in the denominator.
• Example: bilirubin's molar mass is 584.05 g/mol, read as "five hundred eighty-four point zero five grams per mole."

🔄 Molar mass as a conversion factor

• Molar mass connects mole units and mass units.
• For aluminum: 1 mol Al = 26.98 g Al
• This equality gives two conversion factors:
  • (1 mol Al) / (26.98 g Al) — to convert from mass to moles
  • (26.98 g Al) / (1 mol Al) — to convert from moles to mass

Example: What is the mass of 3.987 mol of Al?

• Use the conversion factor (26.98 g Al) / (1 mol Al) to cancel mole units.
• Calculation: 3.987 mol Al × (26.98 g Al / 1 mol Al) = 107.6 g Al
• The mol units cancel algebraically, leaving grams.

🧩 Summary table

Concept	What it means	How to use it
Atomic mass (from periodic table)	Mass of one atom in u	Also the molar mass in g/mol
Molar mass	Mass of 1 mol in grams	Sum atomic masses for all atoms in formula
Conversion factor	Relates moles and grams	Multiply by (g/mol) or (mol/g) to switch units

🧭 Overview

🧠 One-sentence thesis

Mole-mass conversions use molar mass as a conversion factor to translate between the number of moles of a substance and its mass in grams, enabling quantitative predictions in chemical reactions.

📌 Key points (3–5)

• What molar mass enables: it acts as a bridge between the mole unit (counting particles) and mass in grams.
• The conversion factor relationship: 1 mol of any substance equals its molar mass in grams, which can be flipped depending on the direction of conversion.
• Two-step mole-mass problems: convert moles of substance A to moles of substance B using the balanced equation, then convert moles of B to grams using molar mass.
• Three-step mass-mass problems: convert grams of A to moles of A, then moles of A to moles of B, then moles of B to grams of B.
• Common confusion: remembering which conversion factor to use—check whether you need to cancel moles or grams in the starting quantity.

🔄 The basic mole-mass conversion

🔄 How molar mass works as a conversion factor

Molar mass: the mass in grams of one mole of a substance, numerically equal to the atomic or formula mass in amu.

• The excerpt establishes that 1 mol Al = 26.98 g Al.
• This equality can be written as two conversion factors:
  • 1 mol Al / 26.98 g Al (converts mass to moles)
  • 26.98 g Al / 1 mol Al (converts moles to mass)
• Which factor you use depends on what unit you want to cancel.

🧮 Choosing the correct conversion factor

• Start with the given quantity and identify its unit.
• If you start with moles and want grams, use the factor with grams in the numerator.
• If you start with grams and want moles, use the factor with moles in the numerator.
• Example: To find the mass of 3.987 mol of Al, multiply by (26.98 g Al / 1 mol Al) so the mol unit cancels, yielding 107.6 g Al.

⚠️ Don't confuse the direction

• The excerpt emphasizes that the algebra is the same as unit conversions from earlier chapters.
• Always write out units and cancel them explicitly to avoid errors.

🧪 Mole-mass calculations in reactions

🧪 Combining stoichiometry with molar mass

• A mole-mass calculation links moles of one substance in a reaction to the mass of another substance.
• The sequence is:
  1. Start with moles of substance A.
  2. Use the balanced equation coefficients to find moles of substance B.
  3. Use the molar mass of B to convert moles of B to grams of B.

📐 Example walkthrough

• The excerpt gives the reaction: Fe₂O₃ + 3 SO₃ → Fe₂(SO₄)₃
• Question: If you have 3.59 mol of Fe₂O₃, how many grams of SO₃ react?
• Step 1: Use the molar ratio (3 mol SO₃ / 1 mol Fe₂O₃) to find moles of SO₃: 3.59 mol Fe₂O₃ × (3 mol SO₃ / 1 mol Fe₂O₃) = 10.77 mol SO₃.
• Step 2: Convert moles of SO₃ to grams using molar mass (80.06 g/mol): 10.77 mol SO₃ × (80.06 g SO₃ / 1 mol SO₃) = 862 g SO₃.
• The excerpt notes you can do both steps in one line or separately; the answer is the same.

🔗 Why this matters

• Real lab work measures masses, not moles directly.
• Mole-mass conversions let you predict how much of a reactant you need or how much product you will get.

⚖️ Mass-mass calculations

⚖️ The three-step sequence

Mass-mass calculation: a stoichiometry problem that starts with the mass of one substance and finds the mass of another substance in the same reaction.

• The full sequence is:
  1. Convert grams of substance A to moles of A (using molar mass of A).
  2. Convert moles of A to moles of B (using the balanced equation).
  3. Convert moles of B to grams of B (using molar mass of B).

📝 Example walkthrough

• Reaction: CH₄ + 4 Cl₂ → CCl₄ + 4 HCl
• Question: How many grams of HCl are produced from 100.0 g of CH₄?
• Step 1: 100.0 g CH₄ × (1 mol CH₄ / 16.05 g CH₄) = 6.231 mol CH₄.
• Step 2: 6.231 mol CH₄ × (4 mol HCl / 1 mol CH₄) = 24.92 mol HCl.
• Step 3: 24.92 mol HCl × (36.46 g HCl / 1 mol HCl) = 908.5 g HCl.
• The excerpt shows you can also write all three conversions in one line.

🎯 Stepwise vs. single-line calculation

• Doing the calculation in separate steps lets you round at each stage (may introduce small rounding differences).
• Doing it in one line keeps all intermediate precision until the final answer.
• The excerpt notes both methods give essentially the same result.

🧬 Real-world application: complex molecules

🧬 Calculating with large formulas

• The excerpt includes an example with bilirubin (C₃₃H₃₆N₄O₆), molar mass 584.69 g.
• To find the mass of 0.00655 mol of bilirubin: 0.00655 mol × (584.69 g / 1 mol) = 3.83 g.
• The same logic applies no matter how complicated the molecule.

💊 Health context: Taxol synthesis

• The excerpt describes Taxol (C₄₇H₅₁NO₁₄), a cancer drug originally from Pacific yew trees.
• Laboratory synthesis requires over 30 reactions with less than 0.05% efficiency.
• To get a single 300 mg dose, you must start with 600 g of material—illustrating why improving synthesis efficiency matters.
• This shows how mole-mass conversions underpin practical pharmaceutical production.

🌱 Dietary minerals

• The excerpt includes a table of recommended daily intakes (RDIs) for minerals, given in both mass (mg or μg) and moles.
• Example: an adult male needs 1,000 mg (0.025 mol) of calcium per day.
• Iron needs differ by sex: women need 18 mg (3.2 × 10⁻⁴ mol) vs. 8 mg (1.4 × 10⁻⁴ mol) for men.
• This illustrates that mole amounts vary widely across different minerals, and molar thinking helps compare nutritional needs on a particle basis.

📊 Summary of conversion pathways

Starting quantity	Target quantity	Conversion pathway
Moles of A	Grams of A	Multiply by molar mass of A
Grams of A	Moles of A	Divide by molar mass of A (or multiply by 1/molar mass)
Moles of A	Moles of B (in reaction)	Use coefficient ratio from balanced equation
Moles of A	Grams of B (in reaction)	Moles A → moles B → grams B (two steps)
Grams of A	Grams of B (in reaction)	Grams A → moles A → moles B → grams B (three steps)

🧭 Overview

🧠 One-sentence thesis

Balanced chemical equations can be interpreted in terms of moles, allowing us to use molar ratios to predict how much of one substance will react with or produce a given amount of another substance.

📌 Key points (3–5)

• Coefficients represent moles: The numbers in front of chemical formulas represent not just molecules but also molar amounts.
• Molar ratios from balanced equations: Any ratio of coefficients (e.g., 2:1:2) can be used to construct conversion factors between substances.
• Stoichiometry definition: The study of numerical relationships between reactants and products in balanced chemical reactions.
• Common confusion: Coefficients can be written in different multiples (4:2:4 or 22:11:22) as long as they reduce to the same ratio—the equation remains balanced.
• Practical use: These molar ratios allow us to calculate how many moles of one substance are needed or produced when given moles of another substance.

🔢 Understanding coefficients as moles

🔢 From molecules to moles

• Chemical equations are traditionally written with the lowest whole-number coefficients (e.g., 2H₂ + O₂ → 2H₂O).
• The equation remains balanced as long as the coefficient ratio stays the same.
• Example: 4H₂ + 2O₂ → 4H₂O has a 4:2:4 ratio, which reduces to 2:1:2—still balanced.

🧪 The mole interpretation

Balanced chemical equations are balanced not only at the molecular level but also in terms of molar amounts of reactants and products.

• Since 6.022 × 10²³ molecules = 1 mol, we can scale up coefficients to molar quantities.
• The equation 2H₂ + O₂ → 2H₂O means "two moles of hydrogen react with one mole of oxygen to produce two moles of water."
• This interpretation is just as valid as counting individual molecules.

⚖️ Multiple valid forms

• An equation like 12.044 × 10²³ H₂ + 6.022 × 10²³ O₂ → 12.044 × 10²³ H₂O is balanced because the ratio is still 2:1:2.
• This simplifies to 2 mol H₂ + 1 mol O₂ → 2 mol H₂O.
• Don't confuse: different coefficient sets are valid as long as they maintain the same ratio.

🧮 Constructing and using molar ratios

🧮 Building conversion factors

For the reaction 2H₂ + O₂ → 2H₂O, we can construct several molar ratios:

• 2 mol H₂ : 1 mol O₂
• 2 mol H₂O : 1 mol O₂
• 2 mol H₂ : 2 mol H₂O

Each ratio can be written as a fraction in two ways (numerator/denominator can be flipped depending on what you need to cancel).

🔄 Applying ratios in calculations

• These ratios work as conversion factors to determine amounts of substances.
• Example from the excerpt: To find how many moles of O₂ react to produce 27.6 mol of H₂O:
  • Use the ratio with H₂O in the denominator (to cancel) and O₂ in the numerator (to introduce).
  • Calculation: 27.6 mol H₂O × (1 mol O₂ / 2 mol H₂O) = 13.8 mol O₂
• The key is choosing the correct ratio orientation so units cancel properly.

📚 Stoichiometry fundamentals

📚 What stoichiometry means

Stoichiometry: The study of the numerical relationships between the reactants and the products in balanced chemical reactions.

• It is the quantitative aspect of chemistry—how much reacts and how much is produced.
• All stoichiometric calculations rely on the balanced equation as the foundation.

🎯 Key takeaway from the excerpt

• The balanced chemical reaction can be used to determine molar relationships between substances.
• This extends the usefulness of balanced equations beyond just showing what reacts to showing how much reacts.

🔍 How to relate molar amounts

• Amounts of substances in chemical reactions are related by their coefficients in the balanced chemical equation.
• The coefficients provide the fixed ratios that govern all quantitative predictions about the reaction.
• Don't confuse: the coefficients tell you the ratio, not the absolute amounts—you can scale up or down as needed for a particular problem.

🧭 Overview

🧠 One-sentence thesis

Balanced chemical equations allow us to convert between masses and moles of different substances in a reaction by using molar ratios and molar masses as conversion factors in a systematic sequence.

📌 Key points (3–5)

• Mole-mass calculations: convert from moles of one substance to mass of another using a two-step sequence (moles → moles → mass).
• Mass-mass calculations: convert from mass of one substance to mass of another using a three-step sequence (mass → moles → moles → mass).
• The conversion sequence: always use the balanced equation to find molar ratios between substances, then apply molar mass as the final conversion factor.
• Common confusion: you must convert mass to moles first before using the molar ratio from the balanced equation; you cannot directly convert mass to mass without going through moles.
• Why it matters: these calculations let you determine how much of a reactant is needed or how much product will form in real-world chemical reactions.

🔄 The mole-mass calculation sequence

🔄 What mole-mass calculations do

Mole-mass calculations: a stoichiometry calculation converting between masses and moles of different substances in a chemical reaction.

• You start with a known number of moles of one substance.
• You end with the mass of a different substance.
• The process uses two conversion steps.

📐 The two-step sequence

The excerpt describes the following order:

1. Moles of first substance → moles of second substance: use the molar ratio from the balanced equation.
2. Moles of second substance → mass of second substance: use the molar mass of the second substance.

Example: Given the equation Fe₂O₃ + 3SO₃ → Fe₂(SO₄)₃, if you have 3.59 mol of Fe₂O₃, how many grams of SO₃ can react?

• Step 1: Convert 3.59 mol Fe₂O₃ to moles of SO₃ using the ratio 3 mol SO₃ / 1 mol Fe₂O₃ = 10.77 mol SO₃.
• Step 2: Convert 10.77 mol SO₃ to grams using molar mass 80.06 g/mol = 862 g SO₃.

✏️ Single-line vs stepwise

• You can perform both steps separately and round at each stage.
• Or you can combine all conversion factors into one continuous calculation.
• The excerpt notes that both methods give essentially the same answer, though slight differences may appear due to rounding at intermediate steps.

🔁 The mass-mass calculation sequence

🔁 What mass-mass calculations do

Mass-mass calculations: a stoichiometry calculation converting between the mass of one substance and the mass of a different substance in a chemical reaction.

• You start with a known mass of one substance.
• You end with the mass of a different substance.
• This requires three conversion steps.

📏 The three-step sequence

The excerpt describes this order:

1. Mass of first substance → moles of first substance: use the molar mass of the first substance.
2. Moles of first substance → moles of second substance: use the molar ratio from the balanced equation.
3. Moles of second substance → mass of second substance: use the molar mass of the second substance.

Example: For the reaction CH₄ + 4Cl₂ → CCl₄ + 4HCl, how many grams of HCl are produced from 100.0 g of CH₄?

• Step 1: Convert 100.0 g CH₄ to moles using molar mass 16.05 g/mol = 6.231 mol CH₄.
• Step 2: Convert to moles HCl using ratio 4 mol HCl / 1 mol CH₄ = 24.92 mol HCl.
• Step 3: Convert to grams HCl using molar mass 36.46 g/mol = 908.5 g HCl.

⚠️ Critical rule: always go through moles

• You cannot skip the mole-to-mole conversion step.
• The balanced equation gives ratios in moles, not in grams.
• Don't confuse: you must convert mass to moles before applying the molar ratio from the equation.

🔑 Key tools and concepts

🔑 Molar mass as a conversion factor

• Molar mass connects mass (grams) and amount (moles) for a single substance.
• When converting mass → moles, invert the molar mass so gram units cancel.
• When converting moles → mass, use molar mass directly.

🔑 Molar ratio from balanced equations

• The coefficients in a balanced equation give the ratio of moles between substances.
• This ratio is the only way to convert from moles of one substance to moles of another.
• The excerpt emphasizes: "We have established that a balanced chemical equation is balanced in terms of moles as well as atoms or molecules."

🔑 Significant figures

• Limit intermediate answers to the proper number of significant figures if calculating stepwise.
• If combining all steps in one line, only the final answer needs to be rounded.
• The excerpt shows that both approaches give "essentially the same" result, with only minor differences.

📊 Summary comparison

Calculation type	Starting point	Ending point	Number of steps
Mole-mass	Moles of substance A	Mass of substance B	2
Mass-mass	Mass of substance A	Mass of substance B	3

Common pattern: Both types require using the molar ratio from the balanced equation; the difference is whether you start with moles (2 steps) or mass (3 steps).

🧭 Overview

🧠 One-sentence thesis

Energy, defined as the ability to do work, is measured in joules or calories and is transferred between objects as heat when temperature differences exist.

📌 Key points (3–5)

• What energy is: the ability to do work; when you feel energetic, you can perform more work.
• Heat as energy transfer: heat is energy moving from one object to another due to temperature differences.
• Units and conversions: energy, work, and heat share the same units—joules (J) and calories (cal), with 1 cal = 4.184 J.
• Common confusion: nutritional Calories (capital C) vs. calories—1 Cal = 1,000 cal = 1 kcal.
• Why it matters: understanding energy units is essential for interpreting food energy content, exercise expenditure, and chemical processes.

🔋 What energy and heat are

🔋 Energy as the ability to do work

Energy: the ability to do work.

• Think of feeling "energetic"—you feel ready to jump up and get something done.
• When you have a lot of energy, you can perform a lot of work; when you lack energy, you have little desire to do anything.
• This applies not only to people but to all physical and chemical processes.
• The quantity of work that can be done is directly related to the quantity of energy available.

🔥 Heat as energy transfer

Heat: the transfer of energy from one part of the universe to another due to temperature differences.

• Energy can be transferred between objects if they have different temperatures.
• Example: holding an ice cube—energy (as heat) flows from your warm hand to the cold ice, melting the ice and making your hand feel cold.
• Heat is not "hotness" itself; it is the movement of energy caused by temperature differences.
• Because of their interrelationships, energy, work, and heat all have the same units.

📏 Units of energy and heat

📏 The joule (SI unit)

Joule (J): the SI unit of energy, work, and heat.

• A joule is a tiny amount of energy.
• Example: it takes about 4 J to warm 1 mL of water by 1°C.
• Many processes involve thousands of joules, so the kilojoule (kJ) is also common.

🍎 The calorie (everyday and health professions)

Calorie (cal): a unit of energy widely used in the health professions and everyday life.

• Originally defined as the amount of energy needed to warm 1 g of water by 1°C.
• In modern times, the calorie is directly related to the joule: 1 cal = 4.184 J.
• Because a calorie is small, nutritional energies are usually expressed in kilocalories (kcal), also called Calories (capital C).
• Don't confuse: 1 Cal (capital C, nutritional Calorie) = 1,000 cal = 1 kcal.

🔄 Converting between units

From	To	Conversion
Calories (Cal)	calories (cal)	1 Cal = 1,000 cal
calories (cal)	joules (J)	1 cal = 4.184 J
joules (J)	kilojoules (kJ)	1,000 J = 1 kJ
kilocalories (kcal)	kilojoules (kJ)	1 kcal = 4.184 kJ

• Example: A candy bar provides 120 Cal of energy, which equals 120,000 cal.
• Example: 70.0 Cal of bread = 70,000 cal = 293,000 J = 293 kJ.

🍽️ Nutritional energy

🍽️ Food energy content

• The energy values of foods are reported in kilocalories (kcal) or Calories (Cal).
• Proteins and carbohydrates supply 4 kcal/g.
• Fat supplies 9 kcal/g (more than twice the energy per gram).
• Example: one cup of honey contains 1,030 Cal = 1,030,000 cal = about 4.3 million joules.

🏃 Energy expenditure during exercise

• Exercise expends energy, also reported in kilocalories per hour.
• Energy expenditures vary widely depending on the activity:
  • Walking at 4 mph: about 440 kcal/h
  • Mountain biking at 20 mph: about 1,870 kcal/h
  • Basketball: 940 kcal/h
  • Yoga: 280 kcal/h
• After obtaining energy from food, we need to expend it through activity, or our bodies will store it in unhealthy ways.
• Most health professionals agree that exercise is a valuable component of a healthy lifestyle—it strengthens the body, develops muscle tone, and expends energy.

🧭 Overview

🧠 One-sentence thesis

Heat transfer is proportional to mass and temperature change through a substance-specific constant called specific heat, which determines how much energy is needed to change a substance's temperature.

📌 Key points (3–5)

• What heat is: energy that flows due to temperature differences between objects or systems.
• The heat equation: heat equals mass times temperature change times specific heat (heat = mcΔT).
• Specific heat definition: the amount of energy needed to change 1 gram of a substance by 1 degree.
• Direction matters: positive ΔT and heat mean energy flows in; negative values mean energy flows out.
• Common confusion: don't confuse specific heat (energy per gram per degree) with total heat transferred (which also depends on mass and temperature change).

🌡️ Temperature differences and heat flow

🌡️ What drives heat transfer

• Heat flows because of temperature differences between objects.
• Energy moves from hotter objects to cooler ones.
• Example: touching a hot object → energy flows into your fingers; holding ice → energy flows out of your hand.

🔄 What happens to the receiving system

• Generally, the system's temperature changes when it gains or loses heat.
• Greater original temperature difference → greater heat transfer → greater temperature change.
• The relationship is proportional: heat ∝ ΔT (where ΔT = T_final − T_initial).

🧮 The heat transfer equation

🧮 Building the equation

The excerpt develops the equation in steps:

1. Temperature proportionality: heat ∝ ΔT
2. Mass matters: more mass requires more heat for the same temperature change → heat ∝ mΔT
3. The proportionality constant: to make it an equality, add specific heat (c) → heat = mcΔT

📏 What each variable means

Variable	Meaning	Notes
heat	Energy transferred	Positive = energy in; negative = energy out
m	Mass of substance	In grams
c	Specific heat	Characteristic of each substance
ΔT	Temperature change	T_final − T_initial

🔢 Specific heat definition

Specific heat: the amount of energy that must be transferred to or from 1 g of a substance to change its temperature by 1°.

• Symbol: c
• Units: cal/g·°C or cal/g·K
• Every substance has its own characteristic value.
• Also called "specific heat capacity" (the term "heat capacity" alone is incorrect).

📊 Specific heat values and patterns

📊 Substance comparison

The excerpt provides a table showing specific heats vary widely:

• Highest: hydrogen (3.419 cal/g·°C)
• Water: 1.00 cal/g·°C (reference value)
• Lowest in table: mercury (0.033 cal/g·°C)

🔍 What the values tell you

• Lower specific heat → less energy needed for the same temperature change → larger temperature change for the same heat input.
• Higher specific heat → more energy needed → smaller temperature change for the same heat input.
• Example: if 1.00 g of each substance absorbed 100 cal, mercury would experience the largest temperature change (lowest c), and hydrogen would experience the smallest (highest c).

🧪 Applying the equation

🧪 Calculating heat transferred

When you know mass, temperature change, and specific heat:

• Determine ΔT = T_final − T_initial
• Look up specific heat for the substance
• Substitute into heat = mcΔT
• Check units cancel properly (grams and °C should cancel, leaving calories)

Example from excerpt: 150.0 g iron heated from 25.0°C to 73.3°C

• ΔT = 73.3°C − 25.0°C = 48.3°C
• c for iron = 0.108 cal/g·°C
• heat = (150.0 g)(0.108 cal/g·°C)(48.3°C) = 782 cal
• Direction: temperature increased, so energy flowed into the metal

🔬 Finding specific heat from data

When you know heat, mass, and temperature change:

• Calculate ΔT
• Rearrange equation: c = heat / (m × ΔT)
• Pay attention to signs (heat lost = negative value)

Example from excerpt: 10.3 g metal gave off 71.7 cal, temperature dropped from 97.5°C to 22.0°C

• ΔT = 22.0°C − 97.5°C = −75.5°C
• Heat lost, so heat = −71.7 cal
• c = −71.7 cal / [(10.3 g)(−75.5°C)] = 0.0923 cal/g·°C
• This matches copper's specific heat, identifying the metal

⚠️ Sign conventions

Don't confuse the direction of heat flow:

• Energy into object: total energy increases → heat and ΔT are positive
• Energy out of object: total energy decreases → heat and ΔT are negative
• The equation itself doesn't show direction; you determine it from the sign of the values

🧭 Overview

🧠 One-sentence thesis

Phase changes occur at characteristic temperatures (melting and boiling points) where substances transition between solid, liquid, and gas phases without changing temperature, requiring specific amounts of heat energy per gram or mole of material.

📌 Key points (3–5)

• What phase changes are: physical processes where substances transition between solid, liquid, and gas phases at specific temperatures (melting point or boiling point).
• Isothermal nature: temperature remains constant during a phase change; added heat changes the phase, not the temperature.
• Two phases coexist: at the melting or boiling point, both phases can exist simultaneously (e.g., ice and liquid water both at 0°C).
• Heat requirements: each substance has characteristic heats of fusion (for melting/freezing) and vaporization (for boiling/condensing) that determine how much energy is needed per gram or mole.
• Common confusion: heat going in vs. out—adding heat causes solid→liquid→gas transitions; removing heat causes gas→liquid→solid transitions.

🌡️ Phase change temperatures and definitions

🌡️ Melting point

The melting point is the temperature at which a substance goes from a solid to a liquid (or from a liquid to a solid).

• This is a fixed temperature for each pure substance.
• Example: water has a melting point of 0°C on the Celsius scale.
• At this temperature, solid and liquid phases can coexist.

🌡️ Boiling point

The boiling point is the temperature at which a substance goes from a liquid to a gas (or from a gas to a liquid).

• Also a characteristic fixed temperature for each substance.
• Example: water has a boiling point of 100°C.
• Both liquid and gas phases can exist together at this temperature.

🔄 Direction matters

• Heat going in: solid → liquid (melting) or liquid → gas (vaporization).
• Heat going out: gas → liquid (condensation) or liquid → solid (solidification/freezing).
• The direction of heat transfer determines which phase change occurs.

🧊 Key principle: isothermal phase changes

🧊 Temperature stays constant

Phase changes are isothermal (isothermal means "constant temperature").

• When a substance is at its melting or boiling point, adding or removing heat does not change the temperature.
• Instead, the heat energy goes into changing the phase.
• Example: ice at 0°C that receives heat will melt into liquid water also at 0°C; the temperature does not rise until all the ice has melted.

🔀 Two phases coexist

• At the melting point, solid and liquid can both be present at the same temperature.
• At the boiling point, liquid and gas can both be present at the same temperature.
• Example: at 100°C, liquid water and steam (gaseous water) coexist.
• Only after the phase change is complete does further heat addition change the temperature.

🔥 Heat of fusion and heat of vaporization

🔥 Heat of fusion (ΔHfus)

The heat of fusion is the amount of heat per gram (or per mole) required for a phase change that occurs at the melting point.

• This is the energy needed to melt a solid into a liquid (or released when a liquid freezes into a solid).
• Each substance has its own characteristic heat of fusion.
• Example: water has a heat of fusion of 79.9 cal/g.

Calculation formulas:

• heat = n × ΔHfus (where n is the number of moles)
• heat = m × ΔHfus (where m is the mass in grams)

💨 Heat of vaporization (ΔHvap)

The heat of vaporization is the amount of heat per gram (or per mole) required for a phase change that occurs at the boiling point.

• This is the energy needed to vaporize a liquid into a gas (or released when a gas condenses into a liquid).
• Example: water has a heat of vaporization of 540 cal/g.

Calculation formulas:

• heat = n × ΔHvap (where n is the number of moles)
• heat = m × ΔHvap (where m is the mass in grams)

📊 Comparison table

Substance	ΔHfus (cal/g)	ΔHvap (cal/g)
Water (H₂O)	79.9	540
Aluminum (Al)	94.0	2,602
Gold (Au)	15.3	409
Iron (Fe)	63.2	1,504
Sodium chloride (NaCl)	123.5	691
Ethanol (C₂H₅OH)	45.2	200.3
Benzene (C₆H₆)	30.4	94.1

Note: Vaporization typically requires much more energy than fusion for the same substance.

❄️ Special case: sublimation

❄️ Direct solid-to-gas transition

Sublimation is a phase change where a solid goes directly to a gas: solid → gas.

• This skips the liquid phase entirely.
• Each substance has a characteristic heat of sublimation (ΔHsub).
• Example: water has a heat of sublimation of 620 cal/g.

🧊 Practical examples

• Dry ice: solid carbon dioxide (CO₂) sublimes at −78.5°C, going directly from solid to gas without becoming liquid.
• Frozen water: even below 0°C, ice and snow slowly sublime over time.
• Ice cubes in freezers: get smaller over time as solid water sublimes and redeposits on cooling elements.
• Freezer burn: water sublimes from frozen foods, creating an unattractive appearance (not actual burning; the food is still safe but looks unappetizing).

Don't confuse: Dry ice is called "dry" because it does not pass through a liquid phase; it goes directly from solid to gas. Carbon dioxide can exist as a liquid, but only under high pressure.

🧭 Overview

🧠 One-sentence thesis

Atoms bond together because doing so releases energy and moves them to a lower, more stable energy state, and chemical reactions always involve energy changes because bonds break and form with different characteristic energies.

📌 Key points (3–5)

• Why atoms bond: atoms combine to form compounds because bonded atoms have lower energy than separated atoms, and energy is released (usually as heat) when bonds form.
• Bond energy definition: the characteristic amount of energy needed to break a bond between specific atoms, which is the same amount released when that bond forms.
• Energy always changes in reactions: when reactants rearrange into products, the total bond energy changes, so every chemical reaction absorbs or releases energy.
• Exothermic vs endothermic: exothermic reactions release energy (products have lower energy than reactants); endothermic reactions absorb energy (products have higher energy than reactants).
• Common confusion: bond breaking requires energy (endothermic), but bond making releases energy (exothermic)—the net effect determines whether the overall reaction absorbs or releases energy.

⚛️ Why atoms form bonds

⚛️ Atoms move toward lower energy

• The excerpt uses an analogy: a basketball on a slide always rolls down (to lower gravitational potential energy) unless someone does work to push it up.
• Atoms behave similarly: they spontaneously move to positions of minimum energy.
• General principle: all objects tend to move spontaneously to minimum energy unless acted on by another force.

🔗 Bonding releases energy

When atoms combine to make a compound, energy is always given off, and the compound has a lower overall energy.

• Bonded atoms have lower energy than the same atoms separated.
• The energy difference between bonded and separated states is released (usually as heat) when the bond forms.
• Example: when two atoms bond, they "roll downhill" energetically, just like the basketball.

🔄 Breaking bonds requires energy input

• Reversing the process (breaking bonds) requires putting energy back in, just as lifting the basketball back up the slide requires work.
• The amount of energy needed to break a bond equals the amount released when that bond formed.

🔢 Bond energy values

🔢 What bond energy means

Bond energy: the strength of interactions between atoms that make covalent bonds.

• Bond energy describes how much energy is needed to break a specific type of covalent bond.
• For ionic compounds, the term lattice energy is used instead (for attractions between opposite charges).

📊 Characteristic energies for different bonds

• Each molecule has its own exact bond energy, but bonds between the same pair of elements have roughly the same value across different molecules.
• Example: all C–H bonds have bond energy around 100 kcal/mol, regardless of which molecule they are in.
• The excerpt provides a table of approximate values:

Bond type	Approximate energy (kcal/mol)	Notes
C–H	100	Single bond
C–C	85	Single bond
C=C	145	Double bond (stronger)
C≡C	200	Triple bond (strongest)
C–O	86	Single bond
C=O	190	Double bond
C–N	70	Single bond
N–H	93	Single bond
H–H	105	Single bond

• Pattern: multiple bonds (double, triple) are stronger and require more energy to break than single bonds between the same atoms.

🔥 Energy changes in chemical reactions

🔥 Why reactions always involve energy change

When chemical reactions occur, the atoms in the reactants rearrange their chemical bonds to make products. The new arrangement of bonds does not have the same total energy as the bonds in the reactants. Therefore, when chemical reactions occur, there will always be an accompanying energy change.

• Reactants have one set of bonds with a certain total energy.
• Products have a different arrangement of bonds with a different total energy.
• The difference must be absorbed from or released to the surroundings.

⬇️ Exothermic reactions

Exothermic: a process that gives off energy.

• What happens: the energy of products is lower than the energy of reactants.
• Result: substances lose energy to the surrounding environment during the reaction.
• Most common form: energy is given off as heat (though a few reactions give off light).
• How to recognize: energy appears as a product in the equation.
• Example from the excerpt: 2H₂(g) + O₂(g) → 2H₂O(ℓ) + 135 kcal — energy is a product, so this is exothermic.

⬆️ Endothermic reactions

Endothermic: a process that absorbs energy.

• What happens: products have higher energy than reactants.
• Result: reactants must absorb energy from their environment to react.
• How to recognize: energy appears as a reactant in the equation.
• Example from the excerpt: N₂(g) + O₂(g) + 45 kcal → 2NO(g) — energy is a reactant, so this is endothermic.

🧩 Energy as reactant or product

• Exothermic reactions: think of energy as a product (the reaction "produces" energy).
• Endothermic reactions: think of energy as a reactant (the reaction "consumes" energy).
• This mental model helps identify the type of reaction from a chemical equation.

🧬 Energy in biochemical reactions

🧬 Glucose oxidation as an energy source

• The human body (and all living organisms) follows the same energy principles as other chemical reactions.
• Key reaction: oxidation of glucose provides energy for the body.
  • C₆H₁₂O₆(s) + 6O₂(g) → 6CO₂(g) + 6H₂O(ℓ) + 670 kcal
• One mole of glucose (about 115 mL volume) releases 670 kcal, making it a compact energy source.

🍽️ Dietary energy sources

Carbohydrates: one of the three main dietary components; all carbohydrates supply approximately 4 kcal/g.

• Carbohydrates (like glucose and other sugars): supply about 4 kcal per gram.
  • You can verify this by dividing the heat of reaction (670 kcal/mol) by glucose's molar mass.
• Proteins (building blocks of muscle and skin): also supply about 4 kcal per gram.
• Fats (largely hydrocarbon chains): mentioned as other important energy sources (the excerpt cuts off before giving their energy value).

🔑 Don't confuse: bond breaking vs bond making

• Bond breaking is endothermic (requires energy input).
• Bond making is exothermic (releases energy).
• The overall reaction can be either exothermic or endothermic depending on whether more energy is released by new bonds forming or consumed by old bonds breaking.
• Example: even though breaking bonds in reactants costs energy, if forming new bonds in products releases more energy, the net reaction is exothermic.

🧭 Overview

🧠 One-sentence thesis

Biochemical reactions in the human body follow the same energy principles as other chemical reactions, with energy coming primarily from the oxidation of glucose and the conversion of ATP to ADP, while dietary carbohydrates and proteins supply about 4 kcal/g and fats supply about 9 kcal/g.

📌 Key points (3–5)

• Energy source for the body: The oxidation of glucose (C₆H₁₂O₆) is an important reaction that provides energy, releasing 670 kcal per mole.
• ATP to ADP conversion: Breaking an O–P bond in ATP and forming new bonds releases about 7.5 kcal/mol, which fuels other cellular reactions.
• Dietary energy content: Carbohydrates and proteins each supply approximately 4 kcal/g, while fats provide about 9 kcal/g.
• Common confusion: Even though 7.5 kcal/mol from ATP seems small compared to glucose oxidation (670 kcal/mol), it is sufficient to power many biochemical reactions in cells.
• Core principle: Complex biological reactions must obey the basic rules of chemistry, including energy change principles.

🍬 Energy from dietary components

🍬 Carbohydrates as energy sources

Carbohydrates: One of the three main dietary components of a human diet, like glucose and other sugars, that supplies energy for the body.

• All carbohydrates supply approximately 4 kcal/g.
• Glucose is a compact source of energy: 1 mol of glucose (about 115 mL volume) releases 670 kcal when oxidized.
• You can verify the 4 kcal/g value by dividing the heat of reaction for glucose oxidation by its molar mass.

🥩 Proteins as energy sources

Proteins: Building blocks of structural tissues, like muscle and skin.

• Proteins also supply about 4 kcal/g, the same as carbohydrates.
• They serve dual roles: structural function and energy provision.

🥑 Fats as energy sources

Fats: A compound, composed largely of hydrocarbon chains, that supplies energy for the body.

• Fats are largely hydrocarbon chains.
• They provide even more energy per gram: about 9 kcal/g.
• This is more than twice the energy density of carbohydrates or proteins.

Comparison table:

Dietary component	Energy content	Chemical nature
Carbohydrates	~4 kcal/g	Sugars like glucose
Proteins	~4 kcal/g	Structural tissue building blocks
Fats	~9 kcal/g	Hydrocarbon chains

⚡ Key biochemical energy reactions

⚡ Glucose oxidation reaction

The oxidation of glucose is an important reaction that provides energy for our bodies:

• Reaction: C₆H₁₂O₆ (solid) + 6O₂ (gas) → 6CO₂ (gas) + 6H₂O (liquid) + 670 kcal
• Energy released: 670 kcal per mole of glucose.
• Why it matters: This is one of the primary ways the body extracts energy from food.
• Efficiency: Considering that 1 mol of glucose has a volume of about 115 mL, glucose is a compact source of energy.

Example: When you eat foods containing glucose or other sugars, your body oxidizes them through this reaction to power cellular activities.

🔋 ATP to ADP conversion

Another important reaction is the conversion of adenosine triphosphate (ATP) to adenosine diphosphate (ADP):

• Energy released: About 7.5 kcal/mol of ATP under physiological conditions.
• What happens chemically: Breaking an O–P bond and forming an O–P bond and two O–H bonds.
• Why it matters: This energy fuels other biochemically important chemical reactions in our cells.

Don't confuse: The 7.5 kcal/mol from ATP may not seem like much compared to the 670 kcal from glucose oxidation, but it is enough energy to power many cellular processes. The body uses glucose oxidation to generate ATP, which then powers individual cellular reactions.

🔄 Reversibility of ATP/ADP

• If ATP → ADP gives off 7.5 kcal/mol, then the reverse process ADP → ATP requires 7.5 kcal/mol to proceed.
• This means the body must invest energy (from glucose or other sources) to regenerate ATP from ADP.
• The cycle allows energy to be stored (in ATP) and released (to ADP) as needed.

🧬 Fundamental principle

🧬 Biochemical reactions follow chemistry rules

The excerpt emphasizes a key principle:

Note: Even complex biological reactions must obey the basic rules of chemistry.

• The chemistry of the human body, or any living organism, is very complex.
• However: The chemical reactions found in the human body follow the same principles of energy that other chemical reactions follow.
• This means concepts like exothermic/endothermic reactions, bond energies, and energy conservation apply to biological systems just as they do to simpler chemical reactions.

Why this matters: Understanding basic chemistry principles allows us to understand how energy flows through living systems, even when the specific reactions are complicated.

🧭 Overview

🧠 One-sentence thesis

The strength of intermolecular interactions between particles determines the temperatures at which substances transition between solid, liquid, and gas phases, with stronger interactions requiring higher temperatures to overcome.

📌 Key points (3–5)

• What phases are: A phase is a form of matter with consistent physical properties throughout (solid, liquid, or gas).
• What determines phase transitions: The strength of intermolecular interactions dictates melting and boiling points—stronger interactions require more thermal energy (higher temperature) to change phases.
• Types of intermolecular forces: From strongest to weakest: covalent network bonding, ionic interactions, hydrogen bonding, dipole-dipole interactions, and dispersion forces.
• Common confusion—polar vs. nonpolar molecules: A molecule can have polar covalent bonds but still be nonpolar overall if the bond dipoles cancel due to molecular geometry (e.g., CO₂).
• Why it matters: Understanding intermolecular interactions explains the wide variability in melting and boiling points across different substances.

🔬 What are phases and what controls them

🔬 Definition of a phase

Phase: A certain form of matter that includes a specific set of physical properties; the atoms, molecules, or ions make up the phase in a consistent manner throughout.

• The excerpt recognizes three stable phases: solid, liquid, and gas.
• Solid phase: Individual particles are in contact and held in place.
• Liquid phase: Individual particles are in contact but moving with respect to each other.
• Gas phase: Individual particles are separated by relatively large distances.

🌡️ Temperature and pressure effects

• Temperature is the primary factor determining which phase a substance adopts.
• Example: H₂O exists as ice when very cold, liquid water when warmer, and steam at even higher temperatures.
• Pressure can also affect phase presence (e.g., carbon dioxide does not exhibit a liquid phase unless pressure exceeds about six times normal atmospheric pressure), but its effects are less obvious in everyday conditions.

📏 Melting and boiling points

Melting point: The temperature that separates a solid and a liquid.

Boiling point: The temperature that separates a liquid and a gas.

• Different substances have vastly different temperature ranges for their phases.
• Example comparison from the excerpt:

Substance	Solid Phase Below	Liquid Phase Above	Gas Phase Above
Hydrogen (H₂)	−259°C	−259°C	−253°C
Water (H₂O)	0°C	0°C	100°C
Sodium chloride (NaCl)	801°C	801°C	1413°C

• This extreme variability depends entirely on the strength of intermolecular interactions.

💪 Types of intermolecular interactions

💪 What intermolecular interactions are

Intermolecular interactions: A force of attraction between different molecules (the term is also used to include interactions between ions in ionic compounds).

• Substances with strong intermolecular interactions require higher temperatures to become liquids and gases.
• Substances with weak intermolecular interactions need less energy (lower temperature) to become liquids and gases.

🔗 Covalent network bonding (strongest)

Covalent network bonding: A type of interaction in which all the atoms in a sample are covalently bonded to other atoms.

• This is actually a covalent bond, not just an intermolecular force.
• The entire sample is essentially one large molecule.
• These substances are solid over a large temperature range because disrupting all covalent bonds at once requires enormous energy.
• Example: Diamond (pure carbon) finally vaporizes only at temperatures over 3,500°C.
• Don't confuse: This is different from discrete molecules held together by weaker forces; here, every atom is covalently bonded to neighbors throughout the sample.

⚡ Ionic interactions (very strong)

Ionic interactions: An attraction due to ions of opposite charges.

• The strongest force between any two particles is the ionic bond (two ions of opposing charge attracted to each other).
• Substances with ionic interactions are relatively strongly held together, so they typically have high melting and boiling points.
• Example: Sodium chloride (NaCl) has a melting point of 801°C and boiling point of 1413°C.

🧲 Hydrogen bonding (strong dipole-dipole)

Hydrogen bonding: A particularly strong type of dipole-dipole interaction caused by a hydrogen atom being bonded to a very electronegative element.

• Occurs in molecules with H–F, O–H, or N–H bonds.
• These bonds are strongly polar, creating particularly strong dipole-dipole interactions (as strong as 10% of a true covalent bond).
• Example: Water molecules experience hydrogen bonding between the O–H bonds, which strongly affects water's physical properties.
• The excerpt shows hydrogen bonding allows molecules to interact through their oppositely charged ends.

🔄 Dipole-dipole interactions (moderate)

Dipole-dipole interaction: An attraction between polar molecules.

• Occurs when molecules have polar covalent bonds with unequal electron sharing.
• Polar covalent bond: A covalent bond with unequal sharing of electrons (one atom attracts electrons more strongly).
• Polar molecule: A molecule with a net unequal distribution of electrons in its covalent bonds.
• Example: In HF, fluorine attracts electrons more strongly than hydrogen, creating a partial negative charge (δ−) on the fluorine side and partial positive charge (δ+) on the hydrogen side.
• Oppositely charged ends of different polar molecules attract each other.

🌫️ Dispersion forces (weakest)

Dispersion forces (or London forces): A force caused by the instantaneous imbalance of electrons about a molecule.

• These forces exist between all molecules, caused by electrons being in different places at any moment, creating a temporary charge separation that disappears almost instantly.
• Very weak intermolecular interactions.
• Substances experiencing only dispersion forces are typically soft in the solid phase and have relatively low melting points.
• However, larger molecules with many electrons can experience substantial dispersion forces.
• Example: Waxes are long hydrocarbon chains that are solid at room temperature because the molecules have so many electrons that the resulting dispersion forces are strong enough to hold them in the solid phase.

🔀 Polar vs. nonpolar molecules

🔀 When polar bonds don't make a polar molecule

Nonpolar covalent bond: A covalent bond that has an equal sharing of electrons (same atom on each side).

Nonpolar molecule: A molecule where the individual polar bonds cancel each other out due to spatial orientation.

• Some molecules have polar covalent bonds, but the bonds are oriented in space such that they cancel each other out.
• The individual bonds are polar, but the overall molecule is not polar.
• Such molecules experience little or no dipole-dipole interactions.

📐 Examples of nonpolar molecules with polar bonds

• Carbon dioxide (CO₂): Has polar C=O bonds, but they point in opposite directions and cancel out.
• Carbon tetrachloride (CCl₄): Has polar C–Cl bonds, but their spatial arrangement causes the dipoles to cancel.
• Don't confuse: Having polar bonds does not automatically mean the molecule is polar—geometry matters.

📊 Summary comparison of intermolecular forces

Type of Interaction	Relative Strength	Example Substance	Key Characteristic
Covalent network bonding	Strongest	Diamond (C)	All atoms covalently bonded throughout sample
Ionic interactions	Very strong	Sodium chloride (NaCl)	Oppositely charged ions attract
Hydrogen bonding	Strong (10% of covalent bond)	Water (H₂O)	H bonded to F, O, or N
Dipole-dipole interactions	Moderate	Hydrogen fluoride (HF)	Polar molecules attract via opposite partial charges
Dispersion forces	Weakest	Waxes, Br₂	Temporary electron imbalances; present in all molecules

🎯 How to predict phase behavior

• Identify the strongest intermolecular interaction present in a substance.
• Stronger interactions → higher melting and boiling points → substance remains solid or liquid at higher temperatures.
• Weaker interactions → lower melting and boiling points → substance becomes liquid or gas at lower temperatures.
• Example: Hydrogen (H₂) has only weak dispersion forces, so it becomes a gas at −253°C; sodium chloride has strong ionic interactions, so it doesn't become a gas until 1413°C.

🧭 Overview

🧠 One-sentence thesis

Solids and liquids are condensed phases whose particles remain in virtual contact, but solids hold particles in fixed positions with definite shape while liquids allow particles to move about each other and take the shape of their container.

📌 Key points (3–5)

• Condensed phases: solids and liquids are collectively called condensed phases because their particles are in virtual contact, unlike gases.
• Key difference in particle motion: solids have particles in fixed positions (not enough thermal energy to overcome intermolecular interactions), while liquids have particles that can move about each other (enough energy to partially overcome interactions).
• Shape and volume: solids have definite shape and volume; liquids have definite volume but indefinite shape; gases have neither.
• Common confusion: both solids and liquids have definite volume, but only solids have definite shape—don't confuse "in contact" with "fixed in place."
• Intermolecular interaction strength: solids have the strongest intermolecular interactions, liquids moderate, and gases weak.

🧊 The solid state

🔒 Fixed particle positions

Solid: the individual particles of a substance are in fixed positions with respect to each other because there is not enough thermal energy to overcome the intermolecular interactions between the particles.

• Particles cannot move around each other; they are locked in place.
• This fixed arrangement gives solids a definite shape and volume.
• Most solids are hard, but some (like waxes) are relatively soft.
• Many solids composed of ions can be quite brittle.

💎 Crystalline vs amorphous solids

Crystal: a regular, three-dimensional array of alternating positive and negative ions.

• Crystalline solids: particles arranged in a regular, repeating three-dimensional pattern.
  • Many solids composed of ions form crystals.
  • The regular arrangement is sometimes visible macroscopically (you can see the crystal structure with your eyes).
  • Example: Some large crystals show their structure because of the regular arrangement of atoms or ions.

Amorphous solid: a solid with no regular structure (literally, "without form").

• Amorphous solids: no regular crystal structure.
  • Especially common in solids composed of large molecules that cannot easily organize into regular patterns.
  • Example: Glass is an amorphous solid.

💧 The liquid state

🌊 Particles in contact but mobile

• In liquids, particles have enough energy to partially overcome intermolecular interactions.
• Particles can move about each other while remaining in contact.
• This explains why liquids have:
  • Definite volume (particles still touch, so the substance doesn't expand freely).
  • No definite shape (particles can slide past each other, so the liquid takes the shape of its container).

🔄 How liquids differ from solids and gases

• vs. Solids: Liquids have weaker intermolecular interactions than solids, allowing particle movement.
• vs. Gases: Liquids have stronger intermolecular interactions than gases, keeping particles in contact.
• Don't confuse: "in contact" (liquids and solids) vs. "fixed in place" (solids only).

📊 Comparing the three states

📋 Summary table

Characteristic	Solid	Liquid	Gas
Shape	Definite	Indefinite	Indefinite
Volume	Definite	Definite	Indefinite
Intermolecular interaction strength	Strong	Moderate	Weak
Particle positions	In contact and fixed in place	In contact but not fixed	Not in contact, random positions

🔥 Energy and phase transitions

• Solid → Liquid: Particles gain enough thermal energy to partially overcome intermolecular interactions and move about each other.
• Liquid → Gas: Particles gain enough energy to completely overcome intermolecular interactions and separate from each other.
• The change from solid to liquid usually does not significantly change volume.
• The change from liquid to gas significantly increases volume, by a factor of 1,000 or more.

⚖️ Why intermolecular strength matters

• Stronger interactions → particles held more tightly → solid state likely at higher temperatures.
• Weaker interactions → particles can separate more easily → liquid or gas state likely at lower temperatures.
• Example: Substances with strong intermolecular interactions are likely to be solids at higher temperatures because their interactions are strong enough to hold particles in place.

🌍 Special case: water

💦 Unique properties of water

The excerpt includes a "Looking Closer" section on water as the most important liquid:

• Universal solvent: Water is an excellent solvent; it dissolves many substances and allows them to react in solution.
• Unusually high melting and boiling points: 0°C and 100°C, respectively, for such a small molecule.
  • Similar-sized molecules like methane (BP = −162°C) and ammonia (BP = −33°C) have boiling points more than 100° lower.
  • Water molecules experience relatively strong intermolecular interactions that maintain the liquid phase at higher temperatures than expected.
• Ice floats: The solid form of water is less dense than its liquid form, allowing ice to float.
  • In colder weather, lakes and rivers freeze from the top, allowing animals and plants to live underneath.
• High energy requirement for temperature change: Water requires an unusually large amount of energy to change temperature.
  • 100 J of energy changes 1 g of Fe by 230°C, but only changes 1 g of H₂O by 100°C.
  • Water changes temperature slowly as heat is added or removed, impacting weather and storm systems like hurricanes.

🌊 Why water matters

• Earth is the only known body in our solar system with liquid water freely on its surface.
• Life on Earth would not be possible without liquid water.
• Water's properties have a major impact on the world around us.

🧭 Overview

🧠 One-sentence thesis

The kinetic theory of gases allows us to model all gases similarly regardless of their chemical identity, and the pressure they exert arises from constant collisions of gas particles with container walls.

📌 Key points (3–5)

• Why gases are unique: simple models can predict the physical behavior of all gases independent of their identities, unlike solids and liquids.
• Kinetic theory foundation: gases consist of tiny, widely separated particles in constant motion with no intermolecular attractions, making their identity irrelevant to certain physical properties.
• What pressure is: the force generated by gas particles colliding with container walls, divided by the area of those walls.
• Common confusion: ideal vs. real gases—ideal gases follow kinetic theory perfectly; real gases show slight deviations but the theory remains important.
• Multiple pressure units: pressure can be expressed in pascals, bars, atmospheres, torr, or millimeters of mercury, and converting between them is a useful skill.

🔬 The kinetic theory of gases

🔬 Core statements of the theory

Kinetic theory of gases: the fundamental theory of the behavior of gases.

The theory consists of four key statements:

• Gases are composed of tiny particles separated by large distances.
• Gas particles are constantly moving, experiencing collisions with other gas particles and the walls of their container.
• The velocity of gas particles is related to the temperature of a gas.
• Gas particles do not experience any force of attraction or repulsion with each other.

Why this matters: None of these statements relates to the identity of the gas, meaning all gases should behave similarly.

🎯 Ideal vs. real gases

Ideal gas: a gas that follows the kinetic theory statements perfectly.

Real gases: gases that show slight deviations from the kinetic theory statements.

• Most gases are real gases, but the deviations are small enough that the kinetic theory remains useful.
• The theory assumes gas particles are so far apart that individual particles don't "feel" each other, allowing us to treat them as tiny bits of matter whose identity isn't important to certain physical properties.
• Don't confuse: the existence of real gases does not diminish the importance of the kinetic theory.

📜 Historical significance

• The development of understanding gas behavior represents the historical dividing point between alchemy and modern chemistry.
• Initial advances were made in the mid-1600s by Robert Boyle, who founded the Royal Society.
• Example: This was one of the world's oldest scientific organizations.

💥 Gas pressure and collisions

💥 How pressure arises

Pressure: force divided by area.

• Gas particles are constantly moving and constantly colliding with each other and with the walls of their container.
• Forces are generated as gas particles bounce off the container walls.
• The force generated by gas particles divided by the area of the container walls yields pressure.
• Pressure is a property we can measure for a gas, but we typically do not consider pressure for solids or liquids.

📏 Units of pressure

The basic unit of pressure is the newton per square meter (N/m²), but several other units are commonly used:

Unit	Definition	Relationship
Pascal (Pa)	Redefined N/m²	Basic unit; 1 Pa is not very large
Bar	100,000 Pa	More useful than pascal
Atmosphere (atm)	Originally average pressure of Earth's atmosphere at sea level	Exactly 760 torr = 1 atm
Millimeters of mercury (mmHg)	Pressure generated by a column of mercury 1 mm high	1 mmHg = 1 torr
Torr	Named after Evangelista Torricelli	Same as 1 mmHg

Key relationships:

• 1 bar = 100,000 Pa
• 1 atm = 760 torr (exactly)
• 1 bar = 1.01325 atm
• 1 mmHg = 1 torr

🔄 Converting pressure units

The ability to convert from one pressure unit to another is a useful skill.

Example: To convert 1,547 mmHg to atmospheres:

• First recognize that 1 mmHg equals 1 torr, so 1,547 mmHg = 1,547 torr.
• Use the conversion factor: 1 atm = 760 torr.
• Calculate: 1,547 torr × (1 atm / 760 torr) = 2.04 atm.
• Note how the torr units cancel algebraically.

Don't confuse: When converting, ensure the units you're converting from cancel out algebraically, leaving only the desired unit.

🧭 Overview

🧠 One-sentence thesis

Gas laws are mathematical relationships that allow us to predict how the physical properties of gases—pressure, volume, temperature, and amount—change under different conditions or relate to one another at any given moment.

📌 Key points (3–5)

• Boyle's law: pressure and volume are inversely related when temperature and amount stay constant (increase pressure → decrease volume).
• Charles's law: volume and absolute temperature are directly proportional when pressure and amount stay constant (increase temperature → increase volume).
• Combined gas law: brings together pressure, volume, and temperature relationships for changing conditions.
• Ideal gas law: relates all four properties (P, V, n, T) under any conditions using the constant R, not just changes.
• Common confusion: temperature must always be in Kelvin for gas law calculations, not Celsius; units must match across similar quantities.

🔄 Boyle's Law: Pressure and Volume

🔄 The inverse relationship

Boyle's law: the relationship between the pressure and volume of a gas when temperature and amount remain constant, expressed as P₁V₁ = P₂V₂.

• When pressure increases, volume decreases; when pressure decreases, volume increases.
• The product of pressure and volume stays constant for a fixed amount of gas at constant temperature.
• Example: If initial pressure is 1.56 atm and initial volume is 7.02 L, and pressure drops to 0.987 atm, the final volume becomes 11.1 L—the volume increases because pressure decreased.

⚠️ Unit consistency requirement

• Both pressure values must use the same unit (both in atm, or both in torr, etc.).
• Both volume values must use the same unit.
• If units don't match, convert one quantity to the other's unit before calculating.
• Example: 1.56 atm can be converted to 1,190 torr by multiplying by 760 torr/1 atm.

🫁 Real-world application: Breathing

• Breathing is an application of Boyle's law in the human body.
• When the diaphragm moves down, lung volume expands → pressure inside lungs decreases slightly (by ~3 torr) → air rushes in (inhalation).
• When the diaphragm relaxes, lung volume decreases → pressure increases slightly (by 1–2 torr) → air is forced out (exhalation).
• Each breath involves only 0.5–1.0 L of air and very small pressure changes (~0.4% of atmospheric pressure).

🌡️ Charles's Law: Volume and Temperature

🌡️ The direct relationship

Charles's law: the relationship between volume and absolute temperature of a gas when pressure and amount remain constant, expressed as V₁/T₁ = V₂/T₂.

• As temperature increases, volume increases proportionally.
• As temperature decreases, volume decreases proportionally.
• The ratio of volume to temperature stays constant.

🔢 The Kelvin requirement

• Gas volumes relate directly to Kelvin temperature, not Celsius.
• Conversion formula: Kelvin = Celsius + 273.
• The Kelvin scale is the absolute scale with zero at absolute zero (the coldest possible temperature).
• Example: 20°C converts to 293 K; 60°C converts to 333 K.
• Don't confuse: Always convert Celsius to Kelvin before using Charles's law, even if the problem gives temperatures in Celsius.

📐 Calculation example

• A gas at 20°C (293 K) with volume 20.0 L is heated to 60°C (333 K).
• Using Charles's law: (20.0 L)/(293 K) = V₂/(333 K).
• Solving: V₂ = 22.7 L.
• The volume increased because temperature increased, which makes sense for a direct relationship.

🔗 Combined and Ideal Gas Laws

🔗 Combined gas law

Combined gas law: relates pressure, volume, and temperature changes together, expressed as (P₁V₁)/T₁ = (P₂V₂)/T₂.

• Brings Boyle's and Charles's laws together.
• The amount of gas must remain constant.
• Temperature must be in Kelvin; similar quantities must have matching units.
• Example: A balloon in Cleveland (22°C, 1.09 atm, 1,070 mL) is transported to Denver (11°C, 655 torr). After converting units and applying the law, the new volume is 1,300 mL.

⚗️ Ideal gas law

Ideal gas law: PV = nRT, where P is pressure, V is volume, n is amount in moles, T is absolute temperature, and R is the ideal gas law constant.

• Unlike other gas laws, this relates properties under any conditions, not just changes.
• R = 0.08205 (L·atm)/(mol·K) when volume is in liters and pressure in atmospheres.
• Example: To find volume of 1.45 mol N₂ at 298 K and 3.995 atm, substitute into PV = nRT and solve for V = 8.87 L.

📏 Standard Temperature and Pressure (STP)

STP: standard conditions defined as 273 K (0°C) and 1.00 atm pressure.

• At STP, 1 mol of any gas occupies about 22.4 L.
• This provides a convenient conversion: 1 mol gas = 22.4 L at STP.
• Example: A 100.0 L sample at STP contains (100.0 L) × (1 mol/22.4 L) = 4.46 mol of gas.

🧮 Problem-Solving Strategy

🧮 Identifying the right law

Situation	Which law to use	What stays constant
Pressure and volume change	Boyle's law	Temperature, amount
Volume and temperature change	Charles's law	Pressure, amount
Pressure, volume, and temperature all change	Combined gas law	Amount
Need to find one property given the others	Ideal gas law	Nothing (any conditions)

✅ Key steps for calculations

1. Convert temperature to Kelvin if given in Celsius.
2. Check units for matching quantities (both pressures in same unit, both volumes in same unit).
3. Convert if needed before substituting into equations.
4. Substitute values into the appropriate gas law equation.
5. Cancel units algebraically to verify the answer will have correct units.
6. Solve for the unknown variable.
7. Check if the answer makes sense based on the relationships (inverse for Boyle's, direct for Charles's).

🎯 Common pitfalls

• Forgetting to convert Celsius to Kelvin (always add 273).
• Mixing units (e.g., one pressure in atm, another in torr) without converting.
• Using the wrong gas law for the situation.
• Not recognizing that the ideal gas law applies to static conditions, not changes.

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🧭 Overview

🧠 One-sentence thesis

Solutions are homogeneous mixtures whose concentrations can be expressed in multiple units (percent, molarity, ppm/ppb), and these concentration measures enable precise stoichiometric calculations and dilution adjustments in chemistry.

📌 Key points (3–5)

• What a solution is: a homogeneous mixture of solute (minority component) dissolved in solvent (majority component); solutions can be solid, liquid, or gas.
• Concentration vs. solubility: solubility is the maximum amount that can dissolve; concentration is the actual amount dissolved (which may be less).
• Multiple concentration units: mass/mass %, volume/volume %, mass/volume %, ppm, ppb, molarity (mol/L), and equivalents—each suited to different contexts.
• Common confusion: dilute/concentrated are relative terms; precise concentration units are needed for calculations.
• Why it matters: molarity links concentration directly to moles, enabling stoichiometry in solution reactions and accurate dilution calculations.

🧪 What solutions are

🧪 Definition and components

Solution: a homogeneous mixture.

• A solvent is the majority component; a solute is the minority component.
• Solutions are not limited to liquids—air is a gaseous solution, and some alloys are solid solutions.
• A solution can contain more than one solute (e.g., multiple substances dissolved in water).

💉 Examples in the body

• Blood plasma, stomach acid, and urine are all solutions containing various solutes.
• Blood plasma contains ions like Na⁺ (0.138 M), K⁺ (0.005 M), Cl⁻ (0.110 M), and others.
• Stomach acid is approximately 0.10 M HCl.

🔬 Solubility vs. concentration

🔬 Solubility limit

Solubility: the limit of how much solute can be dissolved in a given amount of solvent.

• Solubility varies with temperature and is often reported per 100 mL of water at a specific temperature.
• Example: NaCl solubility is 36.0 g per 100 mL H₂O at 25°C.

📊 Saturation states

State	Definition	Stability
Saturated	Solute concentration at the solubility limit	Stable
Unsaturated	Solute concentration below the limit	Stable
Supersaturated	Solute concentration exceeds the limit	Unstable; excess can recrystallize

• Most everyday solutions are unsaturated, so solubility alone doesn't tell you the actual concentration.
• Don't confuse: "dilute" and "concentrated" are relative terms; they don't specify exact amounts.

📏 Concentration units: percent and trace

📏 Mass/mass percent (% m/m)

• Formula: (mass of solute / mass of solution) × 100
• Both masses must use the same units.
• Example: 36.5 g NaCl in 355 g solution = 10.3% m/m.

📏 Volume/volume percent (% v/v)

• Formula: (volume of solute / volume of solution) × 100
• Used for liquid or gas solutions.
• Example: 45.0% v/v ethanol means 45 mL ethanol per 100 mL solution.

📏 Mass/volume percent (% m/v)

• Formula: (mass of solute in g / volume of solution in mL) × 100
• Commonly used for IV fluids.
• Example: "normal saline" is 0.9% m/v NaCl (9.0 g NaCl per 1,000 mL).

🔍 Parts per million (ppm) and parts per billion (ppb)

• ppm = (mass of solute / mass of solution) × 1,000,000
• ppb = (mass of solute / mass of solution) × 1,000,000,000
• Used for trace elements and pollutants.
• In aqueous solutions: 1 ppm ≈ 1 mg/L; 1 ppb ≈ 1 μg/L.
• Example: cobalt in the human body is about 21 ppb; arsenic toxicity starts around 7,000 ppb.

⚠️ "The dose makes the poison"

• Even essential trace elements (like arsenic at ~50 ppb) become toxic at higher concentrations (7,000+ ppb).
• Water itself can be dangerous if consumed too quickly (water intoxication dilutes essential salts).

🧮 Molarity and stoichiometry

🧮 Molarity definition

Molarity (M): number of moles of solute per liter of solution.

• Formula: M = (moles of solute) / (liters of solution)
• Units: mol/L (often abbreviated M).
• Example: 1.5 mol NaCl in 0.500 L = 3.0 M NaCl.

🔄 Using molarity in calculations

• Molarity connects concentration to moles, enabling stoichiometry.
• Typical workflow for solution stoichiometry:
  1. Convert mass of substance A to moles of A.
  2. Use balanced equation to find moles of substance B.
  3. Use molarity to find volume of solution B (or vice versa).
• Example: To react 185 g NaOH with HCl (2.75 M), first convert NaOH to moles (4.63 mol), then use 1:1 ratio to find moles HCl needed (4.63 mol), then solve for volume: 4.63 mol ÷ 2.75 M = 1.68 L.

⚡ Equivalents (Eq)

Equivalent: one mole of positive or negative charge.

• 1 mol/L of Na⁺ = 1 Eq/L (charge is 1+).
• 1 mol/L of Ca²⁺ = 2 Eq/L (charge is 2+).
• Blood plasma has about 150 mEq/L total ion concentration.

💧 Dilution

💧 Dilution principle

• Adding solvent changes volume but not the amount (moles) of solute.
• Formula: (concentration × volume)initial = (concentration × volume)final
• Any concentration and volume units work, as long as they match on both sides.

💧 Dilution example

• A 125 mL sample of 0.900 M NaCl diluted to 1,125 mL:
  • (0.900 M × 125 mL) = (concentration × 1,125 mL)
  • Final concentration = (0.900 × 125) ÷ 1,125 = 0.100 M
• Don't confuse: dilution reduces concentration but does not change the total moles of solute.

🧭 Overview

🧠 One-sentence thesis

When a solute dissolves in a solvent, individual solute particles become surrounded by solvent molecules and separate from each other, with ionic solutes dissociating into ions that can conduct electricity while molecular solutes remain as neutral molecules.

📌 Key points (3–5)

• Solvation mechanism: solute particles interact with solvent particles so strongly that they separate and become surrounded by solvent molecules.
• Ionic vs molecular behavior: ionic solutes dissociate into separate cations and anions, while molecular solutes dissolve as intact neutral molecules.
• Electrical conductivity: ionic compounds that dissociate are electrolytes (conduct electricity), while molecular compounds that don't dissociate are nonelectrolytes.
• Common confusion: not all dissolved substances behave the same—ionic solutes split into ions, molecular solutes stay as whole molecules.
• Strength variation: some ionic compounds dissociate completely (strong electrolytes) while others dissociate only partially (weak electrolytes).

🔬 How dissolution works at the molecular level

🧲 The solvation process

Solvation: the process by which solute particles are surrounded by solvent particles.

• When a soluble solute enters a solvent, solvent particles interact with solute particles.
• These interactions are strong enough to pull individual solute particles away from each other.
• Each separated solute particle becomes surrounded by solvent molecules.
• The "like dissolves like" rule applies—substances need similar intermolecular forces to form solutions.

💧 Hydration (special case)

Hydration: solvation by water molecules.

• When the solvent is specifically water, the process is called hydration rather than solvation.
• The mechanism is the same, but the term distinguishes water as the solvent.

⚡ Ionic solutes and dissociation

🔌 What happens to ionic compounds

Dissociation: the process of cations and anions of an ionic solute separating when the solute dissolves.

• Ionic solutes don't just separate as whole formula units—they split into individual ions.
• Cations and anions separate from each other completely.
• Each ion becomes surrounded by solvent particles independently.
• Example: When sodium chloride dissolves, Na⁺ ions and Cl⁻ ions separate and are each surrounded by water molecules.

Don't confuse with: molecular dissolution, where molecules stay intact and don't split into charged particles.

⚡ Electrolytes and electrical conductivity

Electrolyte: an ionic compound that dissolves in water.

• Dissolved ionic compounds conduct electricity because their separated ions can move freely.
• The ions carry electrical charge through the solution.
• This property distinguishes ionic solutions from molecular solutions.

Type	Definition	Conductivity	Example
Strong electrolyte	Ionizes completely when dissolved	High	Sodium chloride (NaCl)
Weak electrolyte	Ionizes only partially when dissolved	Low	Acetic acid (CH₃COOH)
Nonelectrolyte	Does not ionize at all when dissolved	None	Table sugar (C₁₂H₂₂O₁₁)

🧪 Molecular solutes

🔬 How molecular compounds dissolve

• Molecular solutes like glucose dissolve as individual intact molecules.
• No dissociation into ions occurs.
• Each molecule separates from other molecules but remains a complete neutral particle.
• Example: When fructose dissolves, each C₆H₁₂O₆ molecule stays as one unit surrounded by water molecules.

🚫 Nonelectrolytes

Nonelectrolyte: a compound that does not ionize at all when it dissolves.

• Molecular compounds are typically nonelectrolytes.
• They don't conduct electricity because they produce no charged particles.
• The solution contains only neutral molecules, not ions.
• Example: Isopropyl alcohol dissolves into individual molecules but creates no ions, so it doesn't conduct electricity.

🏥 Practical distinction

🔍 How to classify a dissolved substance

Step 1: Determine if the compound is ionic or molecular

• Ionic compounds (metal + nonmetal, or polyatomic ions) → likely electrolyte
• Molecular compounds (covalent bonding throughout) → likely nonelectrolyte

Step 2: Check the bonding type

• If ionic: it will dissociate into ions (electrolyte)
• If molecular: it will dissolve as whole molecules (nonelectrolyte)

Example classification:

• Potassium chloride (KCl): ionic compound → dissociates into K⁺ and Cl⁻ → electrolyte
• Fructose (C₆H₁₂O₆): molecular compound → stays as whole molecules → nonelectrolyte
• Magnesium hydroxide [Mg(OH)₂]: ionic compound → dissociates into Mg²⁺ and OH⁻ → electrolyte

Medical note: In medicine, "electrolyte" refers to important ions dissolved in body fluids, including Na⁺, K⁺, Ca²⁺, Mg²⁺, and Cl⁻.

🧭 Overview

🧠 One-sentence thesis

Solutions exhibit colligative properties—vapor pressure depression, boiling point elevation, freezing point depression, and osmotic pressure—that depend only on the number of dissolved particles, not their chemical identity, and these properties have critical applications in everyday life and biological systems.

📌 Key points (3–5)

• What colligative properties are: characteristics of solutions that depend only on the number of dissolved particles, not what those particles are.
• Four main colligative properties: vapor pressure depression, boiling point elevation, freezing point depression, and osmotic pressure.
• Ionic vs molecular solutes: ionic compounds produce more particles per mole when they dissolve (e.g., NaCl → 2 particles) than molecular compounds (e.g., glucose → 1 particle), so ionic solutes have a larger effect on colligative properties.
• Common confusion: 1 M NaCl and 1 M glucose do not have the same effect on colligative properties because NaCl produces two particles per formula unit while glucose produces only one.
• Why it matters: these properties explain practical phenomena like antifreeze in car engines, salting roads in winter, and osmotic balance in living cells.

🔬 What makes colligative properties special

🔬 Dependence on particle count, not identity

Colligative properties: characteristics of solutions that depend only on the number of dissolved particles.

• The key word is number—not the type, size, or charge of the particles.
• Whether you dissolve salt, sugar, or any other solute, the effect on vapor pressure, boiling point, freezing point, and osmotic pressure is determined by how many particles end up in solution.
• Example: dissolving 1 mole of glucose (which stays as individual molecules) produces 1 mole of particles; dissolving 1 mole of NaCl (which separates into Na⁺ and Cl⁻) produces 2 moles of particles, so NaCl has twice the effect.

🧪 Ionic vs molecular solutes

Solute type	What happens when it dissolves	Particles per mole	Effect on colligative properties
Molecular (e.g., glucose C₆H₁₂O₆)	Separates into individual molecules	1 mole of particles	Baseline effect
Ionic (e.g., NaCl)	Separates into constituent ions (Na⁺ + Cl⁻)	2 moles of particles	Twice the effect of molecular solute
Ionic (e.g., CaCl₂)	Separates into three ions (Ca²⁺ + 2 Cl⁻)	3 moles of particles	Three times the effect of molecular solute

• Don't confuse: equal molarities of NaCl and glucose do not produce equal effects—NaCl produces more particles.

💨 Vapor pressure depression

💨 How solute lowers vapor pressure

Vapor pressure: the pressure of a vapor that is in equilibrium with its liquid phase.

Vapor pressure depression: the lowering of the vapor pressure of a solution versus the pure solvent.

• Pure liquids evaporate until the rate of evaporation equals the rate of condensation; the pressure at that point is the vapor pressure.
• When a solid solute is dissolved, solute particles block some liquid particles from evaporating.
• Result: the solution evaporates more slowly and has a lower vapor pressure than the pure solvent.
• Exception: if the solute itself is a liquid or gas, it can also evaporate and contribute to vapor pressure (not covered in this excerpt).

🌡️ Boiling point elevation and freezing point depression

🌡️ Boiling point elevation

Boiling point elevation: the raising of the boiling point of a solution versus the pure solvent.

• Because solute particles lower vapor pressure, more heat (higher temperature) is needed to make the solution boil.
• Quantitative rule from the excerpt: for every mole of particles dissolved in a liter of water, the boiling point increases by about 0.5°C.
• Example: a 1 M NaCl solution (which produces 2 moles of particles per liter) raises the boiling point by about 1.0°C.
• Practical application: water-ethylene glycol mixtures in car radiators have boiling points above 100°C, preventing overheating.

❄️ Freezing point depression

Freezing point depression: the lowering of the freezing point of a solution versus the pure solvent.

• When a solution freezes, only solvent particles form the solid; solute particles interfere with this process.
• More energy must be removed (lower temperature) for the solvent to freeze.
• Quantitative rule from the excerpt: for every mole of particles in a liter of water, the freezing point decreases by about 1.9°C.
• Example: a 1 M CaCl₂ solution (which produces 3 moles of particles per liter) lowers the freezing point by about 5.7°C.
• Practical applications:
  • Salts like NaCl and CaCl₂ are spread on roads and sidewalks in winter to prevent ice formation.
  • CaCl₂ is more effective than NaCl mole-for-mole because it produces three particles instead of two.

🧂 Comparing ionic salts

• The excerpt gives an example: which has a greater effect on freezing point, 1 M NaCl or 1 M CaCl₂?
• Answer: CaCl₂, because it separates into three ions (one Ca²⁺ and two Cl⁻) while NaCl separates into only two (Na⁺ and Cl⁻).
• Mole for mole, CaCl₂ has 50% more impact on freezing point depression than NaCl.

🍝 Common misconception: salting pasta water

• Some people claim that adding salt to pasta water makes it boil faster because the boiling point is higher.
• The excerpt clarifies: the amount of salt typically used is so small that the boiling point is practically unchanged.

🧬 Osmotic pressure and biological systems

🧬 What osmosis is

Osmosis: the process by which solvent molecules can pass through certain membranes but solute particles cannot.

Semipermeable membranes: membranes that allow solvent molecules to pass but block solute particles.

Osmotic pressure: the tendency for solvent molecules to move from the more dilute solution to the more concentrated solution until the concentrations of the two solutions are equal.

• When two solutions of different concentration are separated by a semipermeable membrane, solvent flows from the dilute side to the concentrated side.
• External pressure can be applied to stop this flow; the pressure needed to halt osmosis equals the osmotic pressure of the solution.

🧮 Osmolarity: measuring osmotic pressure

Osmolarity (osmol): a way of reporting the total number of particles in a solution to determine osmotic pressure; defined as the molarity of a solute times the number of particles a formula unit makes when it dissolves (represented by i).

Formula: osmol = M × i

• M = molarity of the solution
• i = number of particles produced per formula unit
• Example: 0.50 M NaCl → osmol = 0.50 × 2 = 1.0 osmol
• Example: 0.30 M Ca(NO₃)₂ → osmol = 0.30 × 3 = 0.90 osmol (one Ca²⁺ and two NO₃⁻)
• If multiple solutes are present, add their individual osmolarities to get the total.

🔄 Predicting solvent flow

• Solutions with the same osmolarity have the same osmotic pressure.
• If solutions of different osmolarity are on opposite sides of a semipermeable membrane, solvent transfers from the lower-osmolarity side to the higher-osmolarity side.
• Example from the excerpt: 0.50 M NaCl (osmol = 1.0) and 0.30 M Ca(NO₃)₂ (osmol = 0.90) → water flows from the Ca(NO₃)₂ side to the NaCl side.

🌊 Reverse osmosis

Reverse osmosis: applying pressure higher than the osmotic pressure to force solvent from the high-osmolarity solution to the low-osmolarity solution.

• Used to make fresh water from saltwater in areas where fresh water is scarce.

🩸 Osmosis in biological systems

🩸 Dialysis and kidney function

• The kidneys filter blood to remove wastes and excess water, which are expelled as urine.
• When kidneys fail, dialysis can remove waste materials and excess water from the blood.
• Hemodialysis: blood is passed through tubing with a semipermeable membrane immersed in a sterile solution (water, glucose, amino acids, electrolytes).
• Osmotic pressure forces waste molecules and excess water through the membrane into the sterile solution; red and white blood cells are too large to pass through.
• Typically, 5–10 pounds of waste-containing fluid is removed per session; sessions last 2–8 hours and must be performed several times a week.
• Dialysis is a temporary solution; a kidney transplant is more permanent.

🔴 Red blood cells and osmotic balance

• Cell walls are semipermeable membranes, so osmotic pressure affects cells.
• Three scenarios:

Solution type	Osmolarity relative to cell interior	What happens	Process name
Hypotonic	Lower than inside the cell	Water enters cells; cells swell and burst	Hemolysis
Hypertonic	Higher than inside the cell	Water leaves cells; cells shrivel and die	Crenation
Isotonic	Same as inside the cell	No net water movement; cells unaffected	(Normal)

• Isotonic solutions for blood plasma: approximately 0.31 M glucose or 0.16 M NaCl.
• Note: NaCl concentration is half that of glucose because NaCl produces two particles per formula unit, while glucose produces one, so their osmolarities are equal.

🌊 Why not drink seawater?

• Seawater has an osmolarity about three times higher than bodily fluids (hypertonic).
• Drinking seawater would draw water out of your cells to dilute the salty water you ingested, making you thirstier and ultimately killing cells.
• The body handles hypotonic solutions better: excess water is collected by the kidneys and excreted.

🥒 Food industry applications

• Osmotic pressure is used to make pickles from cucumbers and to brine meat for corned beef.
• It also plays a role in transporting water from tree roots to the tops of trees.

🧭 Overview

🧠 One-sentence thesis

Acids and bases are fundamental chemical classes defined by their ability to increase hydrogen or hydroxide ion concentrations in aqueous solutions, and they react together in neutralization reactions to form salts and water.

📌 Key points (3–5)

• Arrhenius definitions: acids increase H⁺ concentration; bases increase OH⁻ concentration in aqueous solution.
• Naming conventions: binary acids use "hydro-" prefix and "-ic acid" suffix; bases are typically named as hydroxide compounds.
• Neutralization reactions: acids and bases react to produce water and a salt, and these reactions must be balanced for stoichiometry calculations.
• Common confusion: not all bases contain hydroxide in their formula—ammonia (NH₃) is a base because it reacts with water to produce hydroxide ions.
• Everyday prevalence: acids and bases are common in daily life, from stomach acid (hydrochloric acid) to cleaning products.

🔬 Arrhenius acid-base definitions

🧪 What makes a compound an acid

Arrhenius acid: a compound that increases the concentration of hydrogen ion (H⁺) in aqueous solution.

• Many acids release a hydrogen cation when they dissolve in water.
• Acids share common characteristics: sour taste, turn litmus red, dissolve certain metals while producing hydrogen gas.
• Example: hydrochloric acid (HCl) dissolves in water and releases H⁺ ions.

🧴 What makes a compound a base

Arrhenius base: a compound that increases the concentration of hydroxide ion (OH⁻) in aqueous solution.

• Many bases are ionic compounds containing hydroxide ions that are released when dissolved.
• Bases share common characteristics: slippery texture, bitter taste, turn litmus blue.
• Example: sodium hydroxide (NaOH) is both an ionic compound and releases OH⁻ when dissolved.

💧 The ammonia exception

• Ammonia (NH₃) does not contain hydroxide in its formula but still qualifies as a base.
• It reacts with water molecules: ammonia takes a hydrogen ion from water, producing an ammonium ion (NH₄⁺) and a hydroxide ion (OH⁻).
• This reaction increases hydroxide concentration, satisfying the Arrhenius base definition.
• Don't confuse: a base doesn't need to contain hydroxide in its formula; it only needs to increase hydroxide concentration in solution.

📝 Naming acids and bases

🏷️ Binary acid names

• Binary acids contain hydrogen and one other element.
• Naming pattern: "hydro-" + element root + "-ic acid"
• Examples from the excerpt:
  • HCl(aq) → hydrochloric acid
  • H₂S(aq) → hydrosulfuric acid
  • HBr(aq) → hydrobromic acid

🏷️ Polyatomic acid names

• These acids contain hydrogen, oxygen, and another element.
• Suffixes depend on oxygen atom count: "-ic acid" or "-ous acid"
• Additional prefixes like "per-" and "hypo-" appear in some names.
• The excerpt notes there is no strict rule for oxygen numbers; names are best memorized.
• Examples: HNO₃ (nitric acid), H₂SO₄ (sulfuric acid), HClO₃ (chloric acid)

🏷️ Base names

• Most bases follow normal ionic compound naming rules.
• Named as hydroxide compounds when hydroxide appears in the formula.
• Examples: NaOH (sodium hydroxide), Ca(OH)₂ (calcium hydroxide), Mg(OH)₂ (magnesium hydroxide)

⚗️ Neutralization reactions

🔄 The general neutralization pattern

Neutralization: the reaction of acid and base to make water and a salt.

• General equation: acid + base → water + salt
• A salt is any ionic compound formed from an acid and a base.
• These reactions must be properly balanced like any chemical equation.

⚖️ Balancing neutralization equations

• Coefficients must balance the number of hydrogen ions from the acid with hydroxide ions from the base.
• Example with 1:1 ratio: NaOH(aq) + HCl(aq) → NaCl(aq) + H₂O(ℓ)
• Example with 2:1 ratio: 2NaOH(aq) + H₂SO₄(aq) → Na₂SO₄(aq) + 2H₂O(ℓ)
• The excerpt shows that sulfuric acid requires two sodium hydroxide molecules because it can release two hydrogen ions.

🧮 Stoichiometry applications

• Once balanced, neutralization equations can be used for stoichiometry calculations.
• The excerpt mentions calculating masses and volumes needed for complete neutralization.
• Example setup: given grams of acid, calculate grams of base needed to neutralize it.

🏥 Real-world context: stomach acid

🩺 Stomach acid composition

• Stomach acid can be approximated as 0.05 M hydrochloric acid solution.
• This concentration is strong enough to dissolve some metals in a laboratory setting.
• Special cells in the stomach wall secrete this acid along with enzymes for digestion.

🛡️ Protection mechanisms

• The stomach lining is coated with mucus containing bicarbonate ions (HCO₃⁻).
• Bicarbonate reacts with hydrochloric acid to produce water, carbon dioxide, and harmless chloride ions.
• The gastric epithelium (surface layer of stomach cells) is constantly shed and replaced if damaged by acid.

🩹 Ulcer formation and treatment

• Ulcers occur when the gastric epithelium is destroyed faster than it can be replaced.
• Severe ulcers can expose blood vessels and cause bleeding.
• Ulcers can also result from Helicobacter pylori bacteria (mechanism not fully understood).
• Two main treatments: (1) antacids to react with excess acid, (2) antibiotics to destroy H. pylori bacteria.

🧭 Overview

🧠 One-sentence thesis

The Brønsted-Lowry definition expands acid-base chemistry beyond the Arrhenius framework by focusing on proton transfer, allowing water and other substances to act as either acids or bases depending on the reaction context.

📌 Key points (3–5)

• Core definitions: A Brønsted-Lowry acid is a proton (H⁺) donor; a Brønsted-Lowry base is a proton (H⁺) acceptor.
• Broader scope: All Arrhenius acids and bases are also Brønsted-Lowry acids and bases, but not all Brønsted-Lowry acids and bases qualify under the Arrhenius definition.
• Hydronium ion reality: In aqueous solution, H⁺ ions do not exist as bare protons—they attach to water molecules to form H₃O⁺ (hydronium ions).
• Common confusion: Water can act as either a Brønsted-Lowry acid or base depending on what it reacts with; this dual behavior is called being amphiprotic.
• Practical applications: Pharmaceutical drugs containing nitrogen atoms can be converted to more water-soluble hydrochloride or hydrobromide salts through Brønsted-Lowry acid-base reactions.

🔄 Proton transfer mechanism

🔄 What proton transfer means

Brønsted-Lowry acid: a compound that supplies a hydrogen ion (H⁺) in a reaction; a proton donor.

Brønsted-Lowry base: a compound that accepts a hydrogen ion (H⁺) in a reaction; a proton acceptor.

• The key idea is movement of H⁺ from one molecule to another.
• Unlike Arrhenius definitions (which focus on producing H⁺ or OH⁻ in water), Brønsted-Lowry definitions focus on the transfer process itself.
• Example: When ammonia (NH₃) dissolves in water, the water molecule donates a hydrogen ion to ammonia. Water is the Brønsted-Lowry acid; ammonia is the Brønsted-Lowry base.

💧 The hydronium ion (H₃O⁺)

• A hydrogen ion is a single proton (the hydrogen atom minus its electron).
• Bare protons do not float freely in aqueous solution—they attach to water molecules.
• The H⁺ ion attaches to H₂O to form H₃O⁺, the hydronium ion.
• For most purposes, H⁺ and H₃O⁺ represent the same species, but writing H₃O⁺ shows understanding that protons are attached to solvent molecules.
• Don't confuse: A proton in solution may be surrounded by multiple water molecules (e.g., H₅O₂⁺ or H₉O₄⁺), but H₃O⁺ is the simplest representation.

🔬 Brønsted-Lowry vs. Arrhenius

🔬 How HCl behaves in both frameworks

When HCl dissolves in water:

HCl + H₂O(ℓ) → H₃O⁺(aq) + Cl⁻(aq)

• Arrhenius view: HCl is an acid because it produces H⁺ in water.
• Brønsted-Lowry view: HCl donates a hydrogen ion to H₂O, making HCl the acid and H₂O the base.
• The Brønsted-Lowry definition classifies this as a reaction between an acid and a base, whereas the Arrhenius definition would not label H₂O a base here.

📊 Relationship between the two definitions

Aspect	Arrhenius	Brønsted-Lowry
Acid definition	Produces H⁺ in water	Donates H⁺ (proton donor)
Base definition	Produces OH⁻ in water	Accepts H⁺ (proton acceptor)
Scope	Only aqueous solutions	Any solvent; broader applicability
Overlap	All Arrhenius acids/bases are Brønsted-Lowry acids/bases	Not all Brønsted-Lowry acids/bases are Arrhenius acids/bases

🌍 Beyond water: reactions in other solvents

Example: Sodium amide (NaNH₂) in methanol (CH₃OH):

NH₂⁻(solv) + CH₃OH(ℓ) → NH₃(solv) + CH₃O⁻(solv)

• The label (solv) indicates the species are dissolved in some solvent (not necessarily water).
• NH₂⁻ accepts a proton from CH₃OH, so NH₂⁻ is the Brønsted-Lowry base and CH₃OH is the Brønsted-Lowry acid.
• The Brønsted-Lowry framework works for non-aqueous reactions, unlike the Arrhenius definition.

🔀 Amphiprotic substances: water's dual role

🔀 Water as both acid and base

Amphiprotic compound: a substance that can either donate or accept a proton, depending on the circumstances.

• Water (H₂O) can act as a Brønsted-Lowry acid or a Brønsted-Lowry base.
• As a base: When HCl dissolves, water accepts a proton from HCl to form H₃O⁺.
• As an acid: When ammonia dissolves, water donates a proton to NH₃ to form OH⁻ and NH₄⁺.

💦 Autoionization of water

Water can react with itself:

H₂O(ℓ) + H₂O(ℓ) → H₃O⁺(aq) + OH⁻(aq)

• About 6 in every 100 million water molecules undergo this reaction.
• This process is called autoionization of water and occurs in every sample of water, pure or in solution.
• One water molecule acts as the acid (proton donor), the other as the base (proton acceptor).
• Autoionization occurs to some extent in any amphiprotic liquid (e.g., liquid ammonia, though much less frequently—about 1 in a million billion molecules).

🧪 Identifying water's role in reactions

Example 1: Water as acid

H₂O(ℓ) + NO₂⁻(aq) → HNO₂(aq) + OH⁻(aq)

• Water donates a proton to NO₂⁻, so water is the Brønsted-Lowry acid.

Example 2: Water as base

HC₂H₃O₂(aq) + H₂O(ℓ) → H₃O⁺(aq) + C₂H₃O₂⁻(aq)

• Water accepts a proton from HC₂H₃O₂, so water is the Brønsted-Lowry base.

Don't confuse: The same substance (water) can be an acid in one reaction and a base in another—it depends on what it reacts with.

💊 Pharmaceutical applications

💊 Making drugs water-soluble

• Many complex organic drugs are not soluble or only slightly soluble in water.
• Drugs containing proton-accepting nitrogen atoms can be reacted with dilute hydrochloric acid.
• The nitrogen atoms (acting as Brønsted-Lowry bases) accept hydrogen ions from the acid to form ions, which are much more soluble in water.

🧂 Hydrochloride and hydrobromide salts

General reaction:

RN(sl aq) + H⁺(aq) → RNH⁺(aq) → RNHCl(s)

(where RN represents an organic compound containing nitrogen; "sl aq" means "slightly aqueous" or slightly soluble)

• The modified drug molecules are isolated as hydrochloride salts (when HCl is used) or hydrobromide salts (when HBr is used).
• Example: Codeine is commonly administered as codeine hydrochloride; dextromethorphan (a cough medicine ingredient) is dispensed as dextromethorphan hydrobromide.
• This Brønsted-Lowry acid-base reaction increases drug effectiveness by improving water solubility.

🔄 The dissolution process

When a hydrochloride salt dissolves in water:

• It separates into chloride ions (Cl⁻) and the appropriate cation.
• Example: Cocaine hydrochloride (C₁₇H₂₂ClNO₄) dissolves and can donate a proton to a water molecule.
• This is the reverse of the salt-formation reaction—the drug cation can act as a Brønsted-Lowry acid in solution.

🧭 Overview

🧠 One-sentence thesis

The Brønsted-Lowry definition expands acid-base chemistry beyond the Arrhenius framework by classifying acids as proton donors and bases as proton acceptors, allowing reactions to be understood as proton transfers even in non-aqueous solvents.

📌 Key points (3–5)

• Core definitions: A Brønsted-Lowry acid donates a hydrogen ion (proton); a Brønsted-Lowry base accepts a hydrogen ion (proton).
• Proton transfer mechanism: Brønsted-Lowry acid-base reactions are essentially proton transfer reactions between donor and acceptor.
• Broader scope than Arrhenius: All Arrhenius acids and bases are also Brønsted-Lowry acids and bases, but not all Brønsted-Lowry acids and bases qualify under the Arrhenius definition.
• Common confusion: Water can act as either an acid or a base depending on the reaction—it's a base when accepting a proton from HCl, but an acid when donating a proton to ammonia.
• Works in non-aqueous solvents: The Brønsted-Lowry framework applies to reactions in solvents other than water, unlike the Arrhenius definition.

🔄 Core definitions and proton transfer

🔬 What defines a Brønsted-Lowry acid

A Brønsted-Lowry acid: a compound that supplies a hydrogen ion (H⁺) in a reaction; a proton donor.

• The key action is donating a hydrogen ion to another species.
• The hydrogen ion (H⁺) is essentially a proton—a hydrogen atom with its electron removed.
• Example: HCl donates a proton to water, making HCl the acid in that reaction.

🔬 What defines a Brønsted-Lowry base

A Brønsted-Lowry base: a compound that accepts a hydrogen ion (H⁺) in a reaction; a proton acceptor.

• The key action is accepting a hydrogen ion from another species.
• Example: Ammonia (NH₃) accepts a proton from water, making ammonia the base.

⚡ Proton transfer as the central mechanism

• Every Brønsted-Lowry acid-base reaction involves one species giving up a proton and another species receiving it.
• The excerpt emphasizes: "Brønsted-Lowry acid-base reactions are essentially proton transfer reactions."
• This framing shifts focus from "what dissolves in water" to "what transfers protons."

💧 Water's dual role and the hydronium ion

💧 Water as a base

• When HCl dissolves in water, the reaction is: HCl + H₂O → H₃O⁺ + Cl⁻
• Water accepts a proton from HCl, so water acts as a Brønsted-Lowry base.
• The Arrhenius definition would not label water a base in this case, but the Brønsted-Lowry definition does.

💧 Water as an acid

• When ammonia dissolves in water, the reaction is: NH₃ + H₂O → NH₄⁺ + OH⁻
• Water donates a proton to ammonia, so water acts as a Brønsted-Lowry acid.
• Ammonia is the base because it accepts the proton.

🧪 The hydronium ion (H₃O⁺)

• Bare protons (H⁺) do not actually float freely in aqueous solution.
• Instead, the proton attaches to a water molecule to form the hydronium ion (H₃O⁺).
• For most purposes, H⁺ and H₃O⁺ represent the same species, but writing H₃O⁺ shows understanding that protons are attached to solvent molecules.
• Don't confuse: The excerpt notes that protons may be surrounded by multiple water molecules (e.g., H₅O₂⁺ or H₉O₄⁺), but H₃O⁺ is the simpler representation.

🔀 Relationship to Arrhenius definitions

🔀 Overlap and extension

Aspect	Arrhenius	Brønsted-Lowry
Scope	Only aqueous solutions	Any solvent
Acid definition	Produces H⁺ in water	Donates H⁺ (proton donor)
Base definition	Produces OH⁻ in water	Accepts H⁺ (proton acceptor)
Relationship	All Arrhenius acids/bases are also Brønsted-Lowry acids/bases	Not all Brønsted-Lowry acids/bases are Arrhenius acids/bases

🔀 Why the expansion matters

• The excerpt shows that ammonia acts as a base in both the Arrhenius sense (produces OH⁻) and the Brønsted-Lowry sense (accepts H⁺).
• HCl is an acid in both frameworks, but the Brønsted-Lowry view reveals the proton transfer to water.
• The Brønsted-Lowry framework captures reactions the Arrhenius definition misses, such as water acting as a base when dissolving HCl.

🧪 Applications beyond water

🧪 Non-aqueous solvent reactions

• The Brønsted-Lowry definitions work in solvents other than water.
• Example from the excerpt: Sodium amide (NaNH₂) in methanol (CH₃OH):
  • Reaction: NH₂⁻ + CH₃OH → NH₃ + CH₃O⁻
  • NH₂⁻ accepts a proton from methanol, so NH₂⁻ is the base.
  • Methanol donates a proton, so CH₃OH is the acid.
• The label "(solv)" indicates dissolved in some solvent, contrasting with "(aq)" for aqueous solutions.

💊 Pharmaceutical applications

• Many drugs contain nitrogen atoms that can accept protons (act as Brønsted-Lowry bases).
• These drugs can be reacted with dilute hydrochloric acid to form hydrochloride salts, which are much more water-soluble.
• The nitrogen atom accepts a hydrogen ion from HCl, forming an ion that dissolves better.
• Example: Codeine is commonly administered as codeine hydrochloride; dextromethorphan is dispensed as dextromethorphan hydrobromide.
• This proton-transfer reaction improves drug effectiveness by increasing solubility.

🧭 Overview

🧠 One-sentence thesis

Water can act as either a Brønsted-Lowry acid or a Brønsted-Lowry base depending on the chemical circumstances, making it an amphiprotic compound.

📌 Key points (3–5)

• Water as a base: H₂O can accept a proton from an acid (e.g., when HCl dissolves in water).
• Water as an acid: H₂O can donate a proton to a base (e.g., when reacting with amide ion).
• Amphiprotic definition: a substance that can either donate or accept a proton depending on circumstances.
• Autoionization: even in pure water, about 6 in 100 million water molecules spontaneously react with each other to form hydronium and hydroxide ions.
• Common confusion: water's role is not fixed—it depends on what other substance is present in the reaction.

💧 Water's dual behavior

💧 Acting as a Brønsted-Lowry base

• When water accepts a proton, it becomes a base.
• Example: HCl + H₂O → H₃O⁺ + Cl⁻
  • The water molecule accepts a proton from HCl
  • Water becomes hydronium ion (H₃O⁺)
  • HCl is the acid (proton donor), water is the base (proton acceptor)

💧 Acting as a Brønsted-Lowry acid

• When water donates a proton, it becomes an acid.
• Example: H₂O + NH₂⁻ → OH⁻ + NH₃
  • The water molecule donates a proton to the amide ion
  • Water becomes hydroxide ion (OH⁻)
  • NH₂⁻ is the base (proton acceptor), water is the acid (proton donor)

🔄 What determines water's role

• The role depends on the other substance present in the reaction.
• If the other substance is a stronger acid, water acts as a base.
• If the other substance is a stronger base, water acts as an acid.
• Don't confuse: water itself doesn't change—its behavior changes based on its reaction partner.

🔬 Amphiprotic compounds

🔬 Definition and significance

Amphiprotic compound: a substance that can either donate or accept a proton, depending on the circumstances.

• Water is the most common and most important example.
• Other substances can also be amphiprotic, but water is encountered most frequently.
• This dual capability makes water unique and central to acid-base chemistry.

🔬 Other amphiprotic substances

• Water is not the only amphiprotic substance.
• Any amphiprotic liquid can undergo similar behavior.
• Example mentioned: liquid ammonia also shows amphiprotic behavior (though to a much lesser extent).

⚡ Autoionization of water

⚡ What autoionization means

Autoionization of water: the process by which water ionizes into hydronium ions and hydroxide ions as it acts as an acid and a base.

• Water molecules can react with each other even in pure water.
• One water molecule acts as an acid, the other as a base.
• Chemical equation: H₂O + H₂O → H₃O⁺ + OH⁻

⚡ How often it happens

• Approximately 6 in every 100 million (6 in 10⁸) water molecules undergo this reaction.
• This is a very small fraction but occurs in every water sample.
• It happens whether the water is pure or part of a solution.

⚡ Comparison to other liquids

• Autoionization occurs to some extent in any amphiprotic liquid.
• Liquid ammonia also autoionizes, but much less frequently.
• Only about 1 molecule in a million billion (1 in 10¹⁵) ammonia molecules react with another ammonia molecule.
• Water autoionizes much more readily than ammonia (about 10 million times more).

🎯 Identifying water's role in reactions

🎯 Step-by-step approach

To determine whether water is acting as an acid or base:

1. Look at what water becomes in the products
2. If water becomes H₃O⁺ (gains a proton) → water is a base
3. If water becomes OH⁻ (loses a proton) → water is an acid

🎯 Practice scenarios

Reaction	Water becomes	Water's role	Why
H₂O + NO₂⁻ → HNO₂ + OH⁻	OH⁻	Acid	Water donated a proton
HC₂H₃O₂ + H₂O → H₃O⁺ + C₂H₃O₂⁻	H₃O⁺	Base	Water accepted a proton
H₂O + NH₄⁺ → H₃O⁺ + NH₃	H₃O⁺	Base	Water accepted a proton
CH₃⁻ + H₂O → CH₄ + OH⁻	OH⁻	Acid	Water donated a proton

🎯 Key reminder

• Don't confuse the product with the role: if water becomes H₃O⁺, it accepted a proton (base behavior), not donated one.
• The direction of proton transfer determines the role, not the final charge.

🧭 Overview

🧠 One-sentence thesis

Acids and bases vary in strength based on their degree of ionization in solution, with strong acids and bases ionizing essentially 100% while weak acids and bases ionize only partially and reach a dynamic equilibrium between forward and reverse reactions.

📌 Key points (3–5)

• Strong vs weak distinction: strong acids/bases ionize ~100% in solution; weak acids/bases ionize much less (sometimes only 1–5%).
• Very few strong acids and bases exist: only a handful of compounds (like HCl, HNO₃, NaOH, KOH) are strong; most others are weak.
• Chemical equilibrium: weak acid/base ionization is reversible—forward and reverse reactions occur simultaneously at equal rates, creating a dynamic balance.
• Common confusion: equilibrium does not mean reactions stop; both directions continue but cancel each other out (dynamic equilibrium).
• pH scale application: pH quantifies acidity/basicity—below 7 is acidic, 7 is neutral, above 7 is basic—and helps compare solution strengths.

💪 Strong acids and bases

💪 What makes an acid or base "strong"

Strong acid: a compound that is essentially 100% ionized in aqueous solution.

Strong base: a compound that is essentially 100% ionized in aqueous solution.

• "Essentially 100%" means nearly every molecule separates into ions when dissolved.
• Example: when HCl dissolves in water, every HCl molecule separates into hydronium ion (H₃O⁺) and chloride ion (Cl⁻).
• The reaction goes essentially to completion in one direction.

📋 The short list of strong acids and bases

Strong Acids	Strong Bases
HCl	LiOH
HBr	NaOH
HI	KOH
HNO₃	Mg(OH)₂
H₂SO₄	Ca(OH)₂
HClO₄

• There are very few strong acids and bases.
• If an acid is not on this list, it is likely weak.
• Similarly, if a base is not on this list, it is likely weak.

🔄 Weak acids and bases

🔄 What makes an acid or base "weak"

Weak acid: a compound that is not 100% ionized in aqueous solution.

Weak base: a compound that is not 100% ionized in aqueous solution.

• Only a small fraction of molecules ionize.
• Example: acetic acid (HC₂H₃O₂) ionizes only 1–5% depending on concentration.
• The ionization reaction: HC₂H₃O₂(aq) + H₂O(ℓ) → H₃O⁺(aq) + C₂H₃O₂⁻(aq)
• Most of the acid remains in molecular form.

🏠 Common household examples

Weak acids:

• Vinegar (acetic acid, HC₂H₃O₂)
• Vitamin C (ascorbic acid, HC₆H₇O₆)
• Many food products are slightly acidic due to weak acids

Weak bases:

• Ammonia (NH₃) in cleaning products
• Soaps (contain compounds that accept protons from water, forming excess hydroxide ions—this is why soap solutions feel slippery)

Strong acids/bases in the home:

• Muriatic acid (HCl) for pool cleaning
• Lye (sodium hydroxide, NaOH) in drain cleaners—extremely caustic and dangerous

Don't confuse: If food products contained strong acids instead of weak acids, they would be inedible due to extreme acidity.

⚖️ Chemical equilibrium

⚖️ What happens with weak acids and bases

Chemical equilibrium (or equilibrium): the condition in which the extent of a chemical reaction does not change any further.

• Weak acid/base ionization does not simply stop when some molecules ionize.
• The reverse process (reformation of molecular form) also occurs.
• Eventually, the forward and reverse reactions occur at the same rate.

🔁 Dynamic equilibrium in action

For acetic acid:

• Forward reaction: HC₂H₃O₂(aq) + H₂O(ℓ) → H₃O⁺(aq) + C₂H₃O₂⁻(aq)
• Reverse reaction: H₃O⁺(aq) + C₂H₃O₂⁻(aq) → HC₂H₃O₂(aq) + H₂O(ℓ)
• At equilibrium: HC₂H₃O₂(aq) + H₂O(ℓ) ⇌ H₃O⁺(aq) + C₂H₃O₂⁻(aq)

The double arrow (⇌) shows both reactions occurring simultaneously.

⚠️ Common misconception about equilibrium

• Wrong idea: reactions stop at equilibrium.
• Correct understanding: reactions continue in both directions but balance each other out—this is called dynamic equilibrium.
• There is no net change because forward and reverse effects cancel out.
• Example: water autoionization is also an equilibrium: H₂O(ℓ) + H₂O(ℓ) ⇌ H₃O⁺(aq) + OH⁻(aq)

📏 The pH scale

📏 What pH measures

pH scale: a logarithmic scale that relates the concentration of the hydrogen ion in solution.

• pH is a quantitative measure of acidity or basicity.
• Based on the concentration of hydronium (or hydrogen) ion in aqueous solution.
• Provides a succinct way to communicate how acidic or basic a solution is.

🎯 Interpreting pH values

pH Value	Meaning
pH = 7	Neutral (equal H⁺ and OH⁻ concentrations)
pH < 7	Acidic (lower pH = more acidic)
pH > 7	Basic (higher pH = more basic)

• A neutral solution has the same concentration of hydrogen and hydroxide ions.
• Lower pH values correspond to increasingly acidic solutions.
• Higher pH values correspond to increasingly basic solutions.

🧪 pH of common substances

Substance	pH	Category
Battery acid	0.3	Extremely acidic
Stomach acid	1–2	Very acidic
Lemon/lime juice	2.1	Acidic
Vinegar	2.8–3.0	Acidic
Coffee	5	Slightly acidic
Milk	6	Slightly acidic
Pure water	7	Neutral
Blood	7.3–7.5	Slightly basic
Sea water	8	Basic
Ammonia (1 M)	11.6	Very basic
Bleach	12.6	Very basic
NaOH (1 M)	14.0	Extremely basic

Key observations:

• Many food products are slightly acidic (contain weak acids).
• Some biological fluids (like stomach acid and blood) are nowhere near neutral.
• If food acids were strong instead of weak, the food would likely be inedible.

🧭 Overview

🧠 One-sentence thesis

Buffers resist dramatic pH changes by containing paired solutes (a weak acid plus its salt or a weak base plus its salt) that react with added strong acids or bases to minimize pH shifts, a mechanism critical for biological systems like blood.

📌 Key points (3–5)

• What a buffer is: a solution that resists dramatic changes in pH when strong acids or bases are added.
• What makes a buffer: either a weak acid plus a salt derived from that weak acid, or a weak base plus a salt derived from that weak base.
• How buffers work: the weak acid component reacts with added strong base, and the salt's anion reacts with added strong acid, preventing large pH swings.
• Common confusion: buffers cannot be made from strong acids/bases; only weak acids/bases paired with their salts can buffer.
• Buffer capacity: buffers work only for limited amounts of added strong acid or base; once one component is consumed, the buffer is exhausted and pH changes rapidly.

🧪 What buffers are and why they matter

🧪 The problem buffers solve

• Strong acids and bases can change pH very quickly, even in tiny amounts.
• Example: 1 mL of stomach acid (approximated as 0.05 M HCl) added to bloodstream would shift pH from about 7.4 to about 4.9—a pH incompatible with life—if no correcting mechanism existed.
• The body needs a mechanism to minimize such dramatic pH changes.

🛡️ Definition and composition

Buffer: a solution that resists dramatic changes in pH.

A buffer is composed of certain pairs of solutes:

• Either a weak acid plus a salt derived from that weak acid
• Or a weak base plus a salt derived from that weak base

Examples:

• Acetic acid (HC₂H₃O₂, a weak acid) + sodium acetate (NaC₂H₃O₂, a salt from that acid)
• Ammonia (NH₃, a weak base) + ammonium chloride (NH₄Cl, a salt from that base)

⚙️ How buffers work with acids and bases

⚙️ Reacting with strong bases

When a strong base (source of OH⁻ ions) is added to a buffer:

• The hydroxide ions react with the weak acid component.
• Example (acetic acid–sodium acetate buffer):
  • HC₂H₃O₂(aq) + OH⁻(aq) → H₂O(ℓ) + C₂H₃O₂⁻(aq)
• Rather than making the solution basic and changing pH dramatically, the added hydroxide ions react to make water.
• The pH does not change much.

⚙️ Reacting with strong acids

When a strong acid (source of H⁺ ions) is added to a buffer:

• The hydrogen ions react with the anion from the salt.
• Because the weak acid is not ionized much, lots of hydrogen ions and acetate ions (from sodium acetate) come together to make acetic acid:
  • H⁺(aq) + C₂H₃O₂⁻(aq) → HC₂H₃O₂(aq)
• Rather than making the solution acidic and changing pH dramatically, the added hydrogen ions react to make molecules of a weak acid.

⚙️ Weak base buffers work similarly

For a buffer containing NH₃ and NH₄Cl:

• With strong acid: ammonia molecules react with excess hydrogen ions:
  • NH₃(aq) + H⁺(aq) → NH₄⁺(aq)
• With strong base: the ammonium ion reacts with hydroxide ions:
  • NH₄⁺(aq) + OH⁻(aq) → NH₃(aq) + H₂O(ℓ)

🔍 Identifying valid buffer combinations

🔍 What makes a valid buffer

A buffer requires:

• A weak acid or base (not strong)
• Plus a salt derived from that weak acid or base

Don't confuse: Strong acids/bases cannot form buffers. HCl + NaCl is not a buffer because HCl is a strong acid. NH₃ + NaOH is not a buffer because NaOH is a strong base.

🔍 Examples from the excerpt

Combination	Valid buffer?	Reason
HCHO₂ + NaCHO₂	✅ Yes	Formic acid (weak acid) + formate salt
HCl + NaCl	❌ No	HCl is a strong acid
CH₃NH₂ + CH₃NH₃Cl	✅ Yes	Methylamine (weak base) + its salt
NH₃ + NaOH	❌ No	NaOH is a strong base
H₃PO₄ + NaH₂PO₄	✅ Yes	Phosphoric acid (weak) + phosphate salt

📏 Buffer capacity and limits

📏 What capacity means

Buffer capacity: the amount of strong acid or base a buffer can counteract.

• Buffers work well only for limited amounts of added strong acid or base.
• Once either solute is all reacted, the solution is no longer a buffer.
• Rapid changes in pH may occur after the buffer is exhausted.

📏 What affects capacity

• Buffers that have more solute dissolved in them to start with have larger capacities.
• Example: The excerpt compares two buffer solutions with the same concentrations—the one made from phosphoric acid and sodium phosphate should have larger capacity than one made from hydrocyanic acid and sodium cyanide (because phosphoric acid is a stronger weak acid).

🩸 Biological buffer systems

🩸 Blood buffering

• Human blood has a buffering system to minimize extreme changes in pH.
• One buffer in blood is based on the presence of HCO₃⁻ and H₂CO₃ (another way to write CO₂(aq)).
• With this buffer present, even if some stomach acid were to find its way directly into the bloodstream, the change in blood pH would be minimal.

🩸 Cellular buffering

• Inside many of the body's cells, there is a buffering system based on phosphate ions.
• The complete phosphate buffer system is based on four substances: H₃PO₄, H₂PO₄⁻, HPO₄²⁻, and PO₄³⁻.
• Different buffer solutions can be made by combining: H₃PO₄ + H₂PO₄⁻, H₂PO₄⁻ + HPO₄²⁻, and HPO₄²⁻ + PO₄³⁻.

🩸 Buffered aspirin

• Many people are aware of buffers from buffered aspirin.
• Buffered aspirin contains aspirin (itself a weak acid) plus magnesium carbonate, calcium carbonate, magnesium oxide, or some other salt.
• The salt acts like a base, forming a buffer system.

🧭 Overview

🧠 One-sentence thesis

Radioactive decay occurs when unstable atomic nuclei spontaneously emit particles or radiation, transforming into different isotopes through processes that follow predictable patterns such as half-life.

📌 Key points (3–5)

• Three major types of radioactive emissions: alpha particles (helium nuclei), beta particles (electrons from the nucleus), and gamma rays (high-energy electromagnetic radiation).
• Conservation of matter in decay: atomic numbers and mass numbers must balance on both sides of nuclear equations; the parent isotope transforms into a daughter isotope.
• Penetration differences: alpha particles are easily stopped by matter, beta particles penetrate a few centimeters, and gamma rays penetrate deeply into tissues.
• Common confusion: beta particles are electrons ejected from the nucleus (not from electron shells), and their emission converts a neutron into a proton.
• Half-life constancy: the time for half of a radioactive isotope to decay is fixed and unaffected by conditions or initial amount.

☢️ The three types of radioactive emissions

⚛️ Alpha particles

Alpha particle: a type of radioactive emission composed of two protons and two neutrons, equivalent to a helium nucleus.

• Symbolized by α or He-4 (sometimes written as ₂⁴He).
• Carries a 2+ charge.
• Effect on the nucleus: when emitted, the parent atom loses 2 protons (atomic number decreases by 2) and 4 nuclear particles total (mass number decreases by 4).
• Example: Uranium-235 decays to thorium-231 by emitting an alpha particle: ₉₂²³⁵U → ₂⁴He + ₉₀²³¹Th.
• Penetration: minimal; easily stopped by matter and will not penetrate skin.

🔵 Beta particles

Beta particle: an electron ejected from the nucleus (not from electron shells) with a 1− charge.

• Symbolized by β or ₋₁⁰e or β−.
• Effect on the nucleus: a neutron is converted to a proton; mass number stays the same, but atomic number increases by one.
• Example: Carbon-14 decays to nitrogen-14 by emitting a beta particle: ₆¹⁴C → ₇¹⁴N + ₋₁⁰e.
• Don't confuse: beta particles come from the nucleus (nuclear transformation), not from the atom's electron shells.
• Penetration: short; will penetrate skin and some tissues slightly, perhaps a few centimeters at most.

🌊 Gamma rays

Gamma rays: a very energetic form of electromagnetic radiation emitted from the nucleus.

• Symbolized by γ.
• No charge or mass number: gamma rays are not particles; they are electromagnetic radiation.
• Often emitted simultaneously with alpha or beta particles.
• Example: Radon-222 emits both an alpha particle and a gamma ray: ₈₆²²²Rn → ₈₄²¹⁸Po + ₂⁴He + γ.
• Energy: the gamma ray from radon-222 decay has 8.2 × 10⁻¹⁴ J per nucleus; if 1 mole decayed, total gamma energy would be 49 million kJ.
• Ionizing radiation: gamma rays can knock electrons out of atoms, making matter electrically charged.
• Penetration: deep; will penetrate tissues deeply and impart large amounts of energy to surrounding matter.

🧮 Writing nuclear equations

🧮 Conservation rules

• Law of conservation of matter: matter cannot be created or destroyed, so the sum of atomic numbers and the sum of mass numbers must be the same on both sides of the equation.
• Identifying the daughter isotope: use subtraction to find the remaining protons and nuclear particles.
• Example: Radon-222 (atomic number 86, mass number 222) emits an alpha particle → daughter has 86 − 2 = 84 protons (polonium) and 222 − 4 = 218 mass number → ₈₆²²²Rn → ₂⁴He + ₈₄²¹⁸Po.

🏷️ Parent and daughter isotopes

• Parent isotope: the original radioactive atom before decay.
• Daughter isotope: the product atom (other than the emitted particle) after decay.
• Example: In uranium-235 decay, ₉₂²³⁵U is the parent and ₉₀²³¹Th is the daughter.

Radioactive decay: when one element changes into another through emission of particles or radiation.

📝 Beta decay details

• The electron is assigned an "atomic number" of −1 (equal to its charge) to balance equations.
• Example: Boron-12 decays by beta emission with simultaneous gamma emission: ₅¹²B → ₆¹²C + ₋₁⁰e + γ.
• The daughter (carbon-12) has one more proton than the parent (boron-12) because a neutron converted to a proton.

💥 Spontaneous fission

💥 What fission is

Spontaneous fission (or fission): the breaking apart of an atomic nucleus into smaller nuclei.

• Found only in large nuclei; the smallest nucleus that exhibits spontaneous fission is lead-208.
• Varied products: daughter isotopes are a mixed set of products, not a specific isotope as with alpha/beta emission.
• Often produces excess neutrons that may be captured by other nuclei, possibly inducing additional radioactive events.

🔬 Uranium-235 fission example

• Uranium-235 undergoes spontaneous fission to a small extent.
• One typical reaction: ₉₂²³⁵U → ₅₆¹³⁹Ba + ₃₆⁹⁴Kr + 2 ₀¹n (where ₀¹n is a neutron).
• As with any nuclear process, sums of atomic numbers and mass numbers must be the same on both sides.
• Application: fission is the radioactive process used in nuclear power plants and one type of nuclear bomb.

⏱️ Half-life

⏱️ Definition and constancy

Half-life: the amount of time it takes for one-half of a radioactive isotope to decay.

• Constant property: the half-life of a specific radioactive isotope is constant; it is unaffected by conditions and independent of the initial amount of that isotope.
• Whether an isotope is radioactive is a characteristic of that particular isotope; some are stable indefinitely, others decay through characteristic emissions.

📉 Decay over time

• As time passes, less and less of the radioactive isotope remains, and the level of radioactivity decreases.
• Example: Start with 100.0 g of tritium (³H, half-life 12.3 years).
  • After 12.3 y: half decays to ³He → 50.0 g of ³H remains.
  • After another 12.3 y (total 24.6 y): half of the remaining decays → 25.0 g of ³H remains.
  • After another 12.3 y (total 36.9 y): half of the remaining decays → 12.5 g of ³H remains.
• Pattern: each half-life period reduces the remaining amount by half, regardless of how much was present at the start of that period.

🛡️ Penetration and protection

🛡️ Comparison table

Emission type	Penetration depth	Shielding / protection
Alpha particles	Minimal (will not penetrate skin)	Easily stopped by matter; appropriate thickness shielding
Beta particles	Short (will penetrate skin and some tissues slightly, a few cm at most)	Shielding of appropriate thickness can protect
Gamma rays	Deep (will penetrate tissues deeply)	Requires dense/thick shielding; imparts large energy to surrounding matter

⚠️ Practical implications

• Alpha: large particles, easily stopped, but can impart significant energy to matter they contact.
• Beta: smaller, penetrate slightly into matter.
• Gamma: no mass or charge, so they penetrate deeply and can cause ionization deep in tissues.
• Don't confuse: gamma rays are not "particles"—they are electromagnetic radiation, so the term "gamma particles" is inappropriate.

🌍 Real-world applications

🔥 Smoke detectors

• Contain americium (a radioactive element with atomic number 95).
• Americium emits alpha particles that ionize air between metal plates, creating a tiny current.
• When smoke particles enter, they interfere with the ions, interrupting the current.
• When current drops below a set value, a circuit triggers a loud alarm.
• Safety: the americium is embedded in plastic and is not harmful unless the package is taken apart (unlikely).
• Impact: although many people have unfounded fear of radioactivity, smoke detectors save thousands of lives every year.

🏥 Broader applications

• Nuclear chemistry applications are more widespread than many realize.
• Beyond nuclear power plants and atomic bombs: medicine, sterilization of food, analysis of ancient artifacts.
• Most chemists focus on the number of protons (which determines element identity), but in nuclear chemistry the composition of the nucleus and changes within it are central.

🧭 Overview

🧠 One-sentence thesis

Half-life is a constant time interval in which exactly half of any radioactive isotope decays, allowing us to predict how much radioactive material remains after any number of half-lives.

📌 Key points (3–5)

• What half-life measures: the time required for one-half of a radioactive isotope to decay—a constant property unaffected by conditions or initial amount.
• How decay progresses: after each half-life period, exactly half of the remaining material decays (not half of the original).
• Calculation method: amount remaining equals initial amount multiplied by one-half raised to the power of the number of half-lives.
• Common confusion: half-life is not "how long the material is radioactive"—it's the time for half to decay; the remainder continues to be radioactive.
• Range of half-lives: isotopes vary enormously, from microseconds to billions of years.

⏱️ The half-life concept

⏱️ Definition and constancy

Half-life: the amount of time it takes for one-half of a radioactive isotope to decay.

• Half-life is a characteristic property of each specific radioactive isotope.
• It remains constant regardless of:
  • External conditions (temperature, pressure, etc.)
  • The initial amount of material present
• Some isotopes are stable indefinitely; others decay with characteristic half-lives.

🔄 How sequential decay works

The excerpt illustrates decay with tritium (hydrogen-3):

• Start: 100.0 g of tritium (half-life = 12.3 years)
• After 12.3 y: 50.0 g remains (half decayed to helium-3)
• After 24.6 y total: 25.0 g remains (half of the 50.0 g decayed)
• After 36.9 y total: 12.5 g remains (half of the 25.0 g decayed)

Key insight: Each half-life period removes half of what is currently present, not half of the original amount.

Example: If you start with any amount, after three half-lives you have one-eighth remaining (½ × ½ × ½ = ⅛), not zero.

⚠️ Common misunderstanding

Don't confuse: "Half-life is how long the element is radioactive."

• Wrong interpretation: After one half-life, the material stops being radioactive.
• Correct interpretation: After one half-life, half the material has decayed; the other half remains radioactive and continues decaying.
• The excerpt emphasizes: "Many people think that the half-life of a radioactive element represents the amount of time an element is radioactive. In fact, it is the time required for half—not all—of the element to decay."

🧮 Calculating remaining amounts

🧮 The half-life formula

The excerpt provides this expression:

amount remaining = initial amount × (1/2) raised to the power n

where n = the number of half-lives that have elapsed.

• This formula works even when n is not a whole number.
• To find n: divide the elapsed time by the half-life duration.

📝 Worked example from the excerpt

Problem: Fluorine-20 has a half-life of 11.0 s. Starting with 5.00 g, how much remains after 44.0 s?

Steps:

1. Calculate number of half-lives: 44.0 s ÷ 11.0 s = 4 half-lives
2. Apply formula: 5.00 g × (1/2)^4
3. Simplify: 5.00 g × 1/16 = 0.313 g

Result: Less than one-third of a gram remains.

📊 Half-life ranges in nature

The excerpt provides a table showing enormous variation:

Isotope	Half-Life	Scale
Seaborgium-260	4 milliseconds	Extremely short
Berkelium-248	23.7 hours	Hours
Iodine-131	8.04 days	Days
Tritium (H-3)	12.3 years	Years
Americium-241	432.7 years	Centuries
Carbon-14	5,730 years	Thousands of years
Uranium-235	7.04 × 10⁸ years	Hundreds of millions
Uranium-238	4.47 × 10⁹ years	Billions of years

Practical implications:

• Very short half-lives (e.g., lawrencium-252 at 0.36 s) challenge scientists to conduct experiments quickly.
• Very long half-lives (e.g., americium-241 in smoke detectors) mean minimal decay over human timescales—less than 4% loss in 10 years.

📏 Units of radioactivity

📏 Activity-based units

The excerpt introduces two units that measure decays per time:

Becquerel (Bq): one radioactive decay per second.

Curie (Ci): 3.7 × 10¹⁰ decays per second (originally based on 1 g of radium).

• These units describe the rate of decay, not mass.
• Common to use smaller units: microcuries (μCi), millicuries (mCi).
• Example from excerpt: americium in a smoke detector has activity of 0.9 μCi.

🔁 Activity decreases over half-lives

The excerpt shows that activity (measured in Ci or Bq) also halves with each half-life:

Example: Radium sample with 16.0 mCi activity and 1,600-year half-life:

• After 1,600 y: 8.0 mCi
• After 3,200 y: 4.0 mCi
• After 4,800 y: 2.0 mCi
• After 6,400 y: 1.0 mCi

The same halving pattern applies whether you measure in grams or in activity units.

👤 Named after pioneers

• Becquerel: named after Henri Becquerel, who discovered radioactivity in 1896.
• Curie: named after Marie Curie, who performed early investigations into radioactive phenomena in the 1900s.

🧭 Overview

🧠 One-sentence thesis

Radioactivity can be quantified using multiple units that measure either the rate of decay (becquerel and curie) or the biological effects of radiation exposure (rad, gray, rem, and sievert), with most human exposure coming from unavoidable natural sources.

📌 Key points (3–5)

• Two categories of units: decay-rate units (becquerel, curie) measure disintegrations per second; absorption units (rad, gray, rem, sievert) measure energy absorbed by tissue and biological damage.
• Activity decreases over half-lives: a sample's activity halves with each half-life period, so multiple half-lives compound the reduction.
• Rem accounts for radiation type: the rem unit multiplies rad by a factor that reflects the type of emission and tissue, because alpha particles and beta particles damage tissue differently.
• Common confusion: rad vs rem—rad measures absorbed energy only; rem adjusts for the biological effectiveness of different radiation types.
• Most exposure is natural: approximately 82% of annual radiation exposure comes from unavoidable natural sources like radon gas, cosmic rays, and radioactive atoms in our own bodies.

⚛️ Units that measure decay rate

⚛️ Becquerel (Bq)

Becquerel: a unit of radioactivity equal to one decay per second.

• Named after Henri Becquerel, who discovered radioactivity in 1896.
• It is the SI unit for activity.
• Example: if a sample has an activity of 60,000 Bq, it undergoes 60,000 disintegrations every second.

⚛️ Curie (Ci)

Curie: a unit of radioactivity equal to 3.7 × 10¹⁰ decays per second.

• Named after Marie Curie, who performed early investigations into radioactive phenomena in the 1900s.
• Originally defined as the number of decays per second in 1 gram of radium.
• Much larger than the becquerel: 1 Ci = 3.7 × 10¹⁰ Bq.
• Commonly used in millicuries (mCi) or microcuries (μCi) for practical samples.
• Example: the americium in an average smoke detector has an activity of 0.9 μCi.

🔄 Activity over time

• Both becquerel and curie can replace grams to describe quantities of radioactive material.
• Activity decreases by half with each half-life.
• Example: a radium sample with 16.0 mCi activity and a half-life of 1,600 years 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 (four half-lives).

🧬 Units that measure tissue absorption

🧬 Rad (radiation absorbed dose)

Rad: a unit of radioactive exposure equal to 0.01 joules per gram of tissue.

• Formula: 1 rad = 0.01 J/g.
• Measures the energy transferred to tissue, either through kinetic energy of particles or electromagnetic energy of gamma rays.
• The transferred energy can damage tissue, similar to thermal energy from boiling water.
• Example: absorption of 1 rad by 70,000 g of water (roughly a 150 lb person) raises temperature by only 0.002°C, but breaks about 1 × 10²¹ molecular carbon-carbon bonds in the body—enough to cause harm.

🧬 Gray (Gy)

Gray: a unit of radiation absorption where 1 Gy = 100 rad.

• An alternative to the rad; the rad is more commonly used.

🩺 Units that account for biological effects

🩺 Rem (roentgen equivalent, man)

Rem: a unit of radioactive exposure that includes a factor to account for the type of radioactivity.

• Formula: rem = rad × factor.
• The factor is greater than or equal to 1 and depends on the type of emission and sometimes the tissue exposed.
• Why the factor matters: different emissions and tissues respond differently to radiation.

Emission type	Tissue	Factor
Beta particles	Most tissues	1
Alpha particles	Most tissues	10
Alpha particles	Eye tissue	30

• Most exposures people receive are on the order of a few dozen millirems (mrem) or less.
• Example: a medical X-ray is about 20 mrem.
• Don't confuse: rad measures absorbed energy; rem adjusts that energy for biological damage based on radiation type.

🩺 Sievert (Sv)

Sievert: a unit defined as 100 rem.

• A related unit to the rem, used in some contexts.

🌍 Sources and levels of exposure

🌍 Natural vs avoidable sources

The excerpt provides a table of average annual radiation exposure:

Source	Amount (mrem)	Percentage of total
Radon gas	200	~56%
Medical sources	53	~15%
Radioactive atoms in the body naturally	39	~11%
Terrestrial sources	28	~8%
Cosmic sources	28	~8%
Consumer products	10	~3%
Nuclear energy	0.05	<1%
Total	358	100%

• 82% of exposure is from natural sources that cannot be avoided.
• 10% comes from our own bodies, largely from carbon-14 and potassium-40.
• Example: flying from New York City to San Francisco adds 5 mrem because the plane flies above much of the atmosphere, which normally protects us from cosmic radiation.

⚠️ Health effects of short-term exposure

The excerpt lists effects at various 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 and other tissues; possible internal bleeding; decrease in white blood cell count
200–300	Visible "burns" on skin, nausea, vomiting, and fatigue
>300	Loss of white blood cells; hair loss
~600	Death

• Actual effects depend on the type of radioactivity, length of exposure, and tissues exposed.

🔬 Detection methods

🔬 Film badge

• Uses a piece of photographic film embedded in a badge or pen.
• The film is developed regularly and checked for exposure.
• Comparing the film's exposure level with standard exposures indicates the amount of radiation a person was exposed to.

🔬 Geiger counter

• An electrical device that detects radioactivity.
• Contains a gas-filled chamber (usually argon) with a thin membrane on one end.
• Radiation enters the chamber and knocks electrons off gas atoms.
• The presence of electrons and positively charged ions causes a small current.
• The current is detected and converted to a signal on a meter or an audio circuit to produce an audible "click."