Difficulty: Intermediate to Advanced | Prerequisites: Nomenclature and the Mole (Ch. 9–10)
This is where chemistry becomes quantitative. You learn to write and balance chemical equations, classify reactions by type, and use stoichiometry to predict how much product a reaction will make. Gas laws describe how pressure, volume and temperature interact for gases. Solutions introduce concentration (molarity), and redox reactions show how electron transfer drives many processes from rusting to batteries. These topics account for a large share of most final exams.
Chemical equations must be balanced to satisfy the law of conservation of mass. Reactions fall into five types: combination, decomposition, single replacement, double replacement and combustion. Stoichiometry uses mole ratios from balanced equations to convert between reactants and products. Gas behaviour follows Boyle's law (P and V inversely proportional), Charles's law (V and T directly proportional) and Dalton's law (total pressure = sum of partial pressures). Real gases deviate from ideal behaviour at high pressures and low temperatures. Molarity measures solution concentration. In redox reactions, oxidation is loss of electrons and reduction is gain of electrons.
Stoichiometry
The calculation of quantities (moles, grams, litres) in chemical equations using mole ratios from balanced equations.
Theoretical yield
The maximum amount of product that can be formed from given amounts of reactants, calculated from the balanced equation.
Actual yield
The amount of product actually obtained from an experiment.
Boyle's law
At constant temperature, the volume of a gas varies inversely with pressure. P₁V₁ = P₂V₂.
Charles's law
At constant pressure, the volume of a gas is directly proportional to its temperature in kelvins. V₁/T₁ = V₂/T₂.
Dalton's law of partial pressures
The total pressure of a gas mixture equals the sum of the partial pressures of each gas.
Molarity (M)
Moles of solute per litre of solution. M = mol / L.
Oxidation
Loss of electrons. An increase in oxidation number.
Reduction
Gain of electrons. A decrease in oxidation number.
Redox reaction
A reaction in which electrons are transferred from one substance to another. Oxidation and reduction always occur together.
The delta symbol (Δ) above or below the arrow means heat is supplied to the reaction.
An upward arrow (↑) indicates a gas is formed.
A double arrow (⇌) indicates the reaction is reversible.
In H₂O₂(aq) → H₂O(l) + O₂(g), O₂ is a product.
Equations must be balanced to satisfy the law of conservation of mass: atoms of each element must be equal on both sides.
In every balanced equation, each side has the same number of atoms of each element (not molecules or moles necessarily).
AlCl₃ + NaOH → Al(OH)₃ + NaCl balances with coefficients 1, 3, 1, 3.
Fe + Cl₂ → FeCl₃ balances as 2Fe + 3Cl₂ → 2FeCl₃; the coefficient for Cl₂ is 3.
Al₂(SO₄)₃ + KOH → Al(OH)₃ + K₂SO₄ balances with coefficients 1, 6, 2, 3.
Combination (synthesis): A + B → AB. Rubidium + bromine → RbBr (Rb is +1, Br is -1).
Decomposition: AB → A + B. PbO₂ → Pb + O₂ must balance as PbO₂ → Pb + O₂.
Single replacement: A + BC → AC + B. One element displaces another from a compound. In the activity series, only metals above hydrogen will displace hydrogen from an acid.
Double replacement: AB + CD → AD + CB. Two compounds exchange ions.
Combustion: A hydrocarbon + O₂ → CO₂ + H₂O.
Use mole ratios from the balanced equation to convert between substances.
2Al + 3FeO → 3Fe + Al₂O₃: to react with 1.2 mol FeO, moles of Al = 1.2 x (2/3) = 0.8 mol.
2Al + 3H₂SO₄ → Al₂(SO₄)₃ + 3H₂: 15.0 mol Al requires 15.0 x (3/2) = 22.5 mol H₂SO₄.
For mass-to-mass problems: grams → moles (÷ molar mass) → mole ratio → moles of target → grams (x molar mass).
Iron(III) oxide from 16.7 g Fe: 16.7 g / 55.85 g/mol = 0.299 mol Fe; 0.299 x (2/4) x 159.7 = 23.9 g Fe₂O₃.
The theoretical yield is the calculated maximum product from a balanced equation. The actual yield is what you measure in the lab.
Kinetic molecular theory:
Gas particles move constantly and collide elastically.
Gas flows from high pressure to low pressure (aerosol cans work this way).
Compressing a gas increases its temperature.
Doubling the Kelvin temperature of an enclosed gas makes particles move faster (higher average kinetic energy).
Boyle's law (constant T):
Volume and pressure are inversely proportional: P₁V₁ = P₂V₂.
A gas at 2.4 L and 14.1 kPa compressed to 84.6 kPa: V₂ = (2.4 x 14.1) / 84.6 = 0.40 L.
Charles's law (constant P):
Volume and temperature (in kelvins) are directly proportional: V₁/T₁ = V₂/T₂.
A sealed syringe plunged into cold water: the gas cools, volume decreases, piston slides in.
17 mL at -112 °C (161 K) to 70 °C (343 K): V₂ = 17 x (343/161) = 36 mL.
Gay-Lussac's law (constant V):
Pressure and temperature are directly proportional. As temperature of a fixed volume increases, pressure increases.
Ideal vs real gases:
At high pressures, real gas volume is greater than ideal gas volume (molecules have actual volume).
Real gases behave most like ideal gases at high temperature and low pressure.
Dalton's law of partial pressures:
P_total = P₁ + P₂ + P₃ + ...
A diving mixture at 101.4 kPa with P_He = 82.5 kPa and P_CO₂ = 0.4 kPa: P_O₂ = 101.4 - 82.5 - 0.4 = 18.5 kPa.
Diffusion and effusion:
Diffusion is the tendency of molecules to move toward areas of lower concentration.
Effusion is the escape of gas through a tiny opening.
Lighter gases effuse faster. Of bromine, chlorine, ammonia and hydrogen, hydrogen effuses most rapidly (lowest molar mass).
If adding a crystal to a solution causes many particles to precipitate out, the original solution was supersaturated.
For most solids, solubility increases as temperature increases.
Molarity = moles of solute / litres of solution.
6 moles in 2 litres = 3 M.
7.0 moles in 569 mL (0.569 L) = 7.0 / 0.569 = 12 M (approximately).
Oxidation = loss of electrons (increase in oxidation number). "OIL" = Oxidation Is Loss.
Reduction = gain of electrons (decrease in oxidation number). "RIG" = Reduction Is Gain.
In a redox reaction, if one atom is reduced, another must be oxidised (they always occur together).
Another name for an oxidation-reduction reaction is a redox reaction.
Cu → Cu²⁺ + 2e⁻ is oxidation (electrons are lost).
Sn²⁺ → Sn⁴⁺ is oxidation (oxidation number increased, electrons lost).
Elements in their free state = 0 (e.g. bromine in Br₂ gas has oxidation number 0).
Hydrogen in most compounds = +1 (except in metal hydrides, where it is -1).
Oxygen in most compounds = -2 (except in peroxides = -1).
Magnesium in MgCl₂ = +2 (each Cl is -1; two Cl = -2; Mg must be +2 to balance).
Students think Boyle's law means volume increases with pressure. Volume and pressure are inversely proportional at constant temperature.
Real gases at high pressure take up more space than ideal gas calculations predict, not less. The molecules themselves occupy volume.
Diffusion and effusion are different. Diffusion is movement through a mixture toward lower concentration. Effusion is escape through a tiny hole.
Oxidation is loss of electrons, not gain. The mnemonic OIL RIG helps: Oxidation Is Loss, Reduction Is Gain.
An element in its free state (like Br₂) always has oxidation number 0, not -1 or -2.
⚠️ Know how to balance equations, especially multi-step ones like Al₂(SO₄)₃ + KOH.
⚠️ Stoichiometry problems require a balanced equation first. Convert grams → moles → mole ratio → moles → grams.
⚠️ Be comfortable applying Boyle's and Charles's laws to numerical problems. Always convert temperature to kelvins for Charles's law.
⚠️ Real gases behave most ideally at high temperature and low pressure.
⚠️ Molarity = mol / L. Watch for mL that need converting to L.
⚠️ Hydrogen effuses fastest because it has the lowest molar mass.
⚠️ Know oxidation number rules: free element = 0, H = +1 (usually), O = -2 (usually).
True or False: Boyle's law says volume varies directly with pressure.
Fill in the blank: The calculation of quantities in chemical equations is called ______.
True or False: Oxidation is a gain of electrons.
Fill in the blank: Real gases behave most like ideal gases at ______ temperature and ______ pressure.
True or False: The oxidation number of an element in its free state is always 0.
Q: How many moles of Al are needed to react with 1.2 mol FeO in the reaction 2Al + 3FeO → 3Fe + Al₂O₃?
A: 0.8 mol (1.2 x 2/3).
Q: A gas occupies 2.4 L at 14.1 kPa. What volume will it occupy at 84.6 kPa?
A: 0.40 L (Boyle's law: V₂ = 2.4 x 14.1 / 84.6).
Q: What is the partial pressure of oxygen in a mixture at 101.4 kPa if P_He = 82.5 kPa and P_CO₂ = 0.4 kPa?
A: 18.5 kPa (101.4 - 82.5 - 0.4).
Q: What is the molarity of a solution with 6 moles of solute in 2 litres?
A: 3 M (6 / 2).
Q: Cu → Cu²⁺ + 2e⁻ represents what type of half-reaction?
A: Oxidation (electrons are lost).
Q: What is the oxidation number of bromine in Br₂ gas?
A: 0 (element in its free state).
Q: Which gas effuses most rapidly: bromine, chlorine, ammonia or hydrogen?
A: Hydrogen (lowest molar mass).
Stoichiometry connects to every quantitative topic in chemistry, including solution chemistry, thermochemistry and equilibrium. Gas laws apply directly in industrial chemistry and environmental science (e.g. breathing mixtures for divers, atmospheric pressure). Redox reactions underpin electrochemistry (batteries, electroplating), corrosion and biological energy transfer.
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