Quick Simpler Start
You learn how to count atoms and moles, balance equations, work with formulas, and use chemical calculations without panic.
When you revise this chapter, ask yourself: "Can I explain this to a friend in one easy paragraph?" If yes, you are in a good place.
Interactive Simulator
This small tool gives you a quick visual check before you move deeper into the chapter notes.
Mole Calculator
Use the mass and molar mass to check your stoichiometry answer.
Chapter 3: Stoichiometry, Formulas, and Equations
1. Objectives: What you need to know
- Explain the mole as a counting unit for particles.
- Use Avogadro’s constant and molar mass in calculations.
- Apply Boyle’s Law, Charles’s Law, Gay-Lussac’s Law, and Avogadro’s Law.
- Use molar volume at STP to solve gas volume problems.
- HL: Use kinetic theory and the ideal gas equation, PV = nRT.
- Calculate percentage composition, empirical formula, and molecular formula.
- Complete stoichiometric calculations involving limiting reactants, theoretical yield, actual yield, and percentage yield.
2. Big idea: The mole is chemistry’s counting bridge
Atoms and molecules are far too small to count one by one. Chemists use the mole to connect microscopic particles to measurable laboratory quantities such as mass, volume, and concentration.
3. Exam-ready definitions
| Term | Definition | Exam clue |
|---|---|---|
| Mole | The amount of substance containing 6 × 10²³ particles. | Used to count atoms, molecules, or ions. |
| Avogadro’s constant | The number of particles in one mole: approximately 6 × 10²³ mol⁻¹. | Multiply moles by this to get number of particles. |
| Molar mass | The mass of one mole of a substance, usually in g mol⁻¹. | Numerically equal to relative formula mass in grams. |
| Empirical formula | The simplest whole-number ratio of atoms of each element in a compound. | Think: simplest ratio. |
| Molecular formula | The actual number of atoms of each element in one molecule. | Can be a multiple of the empirical formula. |
| Limiting reactant | The reactant that is used up first and limits the amount of product formed. | Controls the theoretical yield. |
| Percentage yield | Actual yield divided by theoretical yield, multiplied by 100. | Always less than or equal to 100% in normal exam questions. |
4. Formula toolbox
n = m / Mr
Use SI units unless the question clearly gives a matching value of R: P in Pa, V in m³, T in K, n in mol.
5. The mole and Avogadro’s constant
One mole of any substance contains the same number of particles: 6 × 10²³. This does not mean all moles have the same mass. One mole of carbon atoms has a mass of 12 g, while one mole of water molecules has a mass of 18 g.
6. Gas laws and gas volumes
Gas law questions test whether you understand how pressure, volume, temperature, and amount of gas are connected. Always convert temperature to Kelvin for gas calculations.
| Law | Relationship | Simple meaning | Formula style |
|---|---|---|---|
| Boyle’s Law | Pressure and volume | At constant temperature, pressure increases when volume decreases. | P₁V₁ = P₂V₂ |
| Charles’s Law | Volume and temperature | At constant pressure, volume increases when temperature increases. | V₁/T₁ = V₂/T₂ |
| Gay-Lussac’s Law | Pressure and temperature | At constant volume, pressure increases when temperature increases. | P₁/T₁ = P₂/T₂ |
| Avogadro’s Law | Volume and moles | At same temperature and pressure, equal volumes contain equal numbers of molecules. | V ∝ n |
7. Higher Level extension: kinetic theory and ideal gases
Kinetic theory of gases: gas particles are far apart, move randomly, collide with container walls, and exert pressure. Increasing temperature increases the average kinetic energy of particles, so particles collide more frequently and more forcefully.
8. Chemical calculations: the ExamsLogic method
Stoichiometry questions look frightening because they contain many numbers. Use the same routine every time.
9. Percentage composition
10. Empirical and molecular formulas
11. Limiting reactants and yield
The limiting reactant is the reactant that runs out first. Once it is used up, the reaction stops, even if the other reactant is still available.
12. Worked examples: full exam method
Calculate the number of moles in 11 g of carbon dioxide, CO₂.
What volume is occupied by 0.50 mol of oxygen gas at STP?
A reaction should produce 10.0 g of product, but only 8.2 g is obtained. Find the percentage yield.
13. Common student mistakes
2. Forgetting to balance the equation before using mole ratios.
3. Using Celsius in gas law questions instead of Kelvin.
4. Rounding empirical formula ratios too early.
5. Confusing theoretical yield with actual yield.
6. Using 22.4 L for gases when the question is not at STP without checking the conditions.
14. Examiner traps
Trap 2: In empirical formula questions, percentages can be treated as masses only if you assume a 100 g sample.
Trap 3: In gas laws, temperature must be in Kelvin. 0°C is not 0 K; it is 273 K.
Trap 4: A balanced equation gives mole ratios, not mass ratios.
15. Practical / application skills
In real experiments, the actual yield is often lower than the theoretical yield because product may be lost during filtration, washing, transferring, evaporation, or because the reaction is incomplete. Good exam answers should link the loss to the experimental method.
If a reaction produces gas, the volume can be measured using a gas syringe or by collecting gas over water. You may be asked to connect the measured gas volume to moles using molar volume or PV = nRT.
16. Exam-style questions
Q1. Calculate the number of moles in 5.85 g of sodium chloride, NaCl. [3 marks]
Q2. A compound contains 24 g of carbon and 4 g of hydrogen. Find its empirical formula. [4 marks]
Q3. Magnesium reacts with hydrochloric acid: Mg + 2HCl → MgCl₂ + H₂. Calculate the volume of hydrogen produced at STP when 0.12 mol of magnesium reacts completely. [4 marks]
Q4. 2Al + 3Cl₂ → 2AlCl₃. If 0.50 mol of aluminium reacts with 0.60 mol of chlorine, identify the limiting reactant. [5 marks]
Q5. HL A gas has a volume of 0.010 m³ at 120,000 Pa and 290 K. Calculate the number of moles. Use R = 8.31 J mol⁻¹ K⁻¹. [4 marks]
17. MCQs with explanations
| Question | Answer and explanation |
|---|---|
| 1. How many particles are in 1 mole of a substance? A 6 × 10²³ B 22.4 C 273 D 8.31 | A. Avogadro’s constant is approximately 6 × 10²³ particles per mole. |
| 2. What is the Mr of H₂SO₄? A 49 B 98 C 100 D 196 | B. H₂SO₄ = 2(1) + 32 + 4(16) = 98. |
| 3. Which formula is used for percentage yield? A theoretical / actual × 100 B actual / theoretical × 100 C mass / Mr D PV = nRT | B. Percentage yield compares what was actually obtained with the maximum theoretical amount. |
| 4. In gas law calculations, temperature should be measured in: A °C B K C g D mol | B. Gas law calculations require Kelvin temperature. |
| 5. The empirical formula of C₆H₁₂O₆ is: A C₆H₁₂O₆ B CHO C CH₂O D C₂H₄O₂ | C. Divide all subscripts by 6: C₁H₂O₁ = CH₂O. |
18. Higher Level Challenge
Question: Explain, using kinetic theory, why the pressure of a fixed mass of gas increases when temperature increases at constant volume.
Answer idea: As temperature increases, gas particles gain average kinetic energy. They move faster and collide with the walls of the container more frequently and with greater force. Since volume is constant, the increased collision rate and force increase pressure.
19. Last-minute revision sheet
✓ Moles = mass / Mr.
✓ 1 mole = 6 × 10²³ particles.
✓ 1 mole of gas at STP = 22.4 L.
✓ Balance the equation before using mole ratios.
✓ Gas law temperatures must be in Kelvin.
✓ Empirical formula = simplest whole-number ratio.
✓ Molecular formula = actual formula.
✓ Limiting reactant runs out first.
✓ Percentage yield = actual / theoretical × 100.
✓ HL: PV = nRT and use SI units.
20. Self-assessment checklist
- I can calculate moles from mass and molar mass.
- I can use Avogadro’s constant to calculate particles.
- I can calculate gas volumes at STP.
- I can explain Boyle’s, Charles’s, Gay-Lussac’s, and Avogadro’s laws.
- I can use PV = nRT for Higher Level gas calculations.
- I can calculate percentage composition.
- I can find empirical and molecular formulas.
- I can solve stoichiometry questions using mole ratios.
- I can identify limiting reactants.
- I can calculate theoretical yield, actual yield, and percentage yield.
21. Mark schemes
Mr NaCl = 23 + 35.5 = 58.5 [1]
n = mass / Mr [1]
n = 5.85 / 58.5 = 0.10 mol [1]
Q2 Empirical formula [4]
C moles = 24 / 12 = 2 [1]
H moles = 4 / 1 = 4 [1]
Ratio C:H = 2:4 [1]
Simplest ratio = 1:2, empirical formula = CH₂ [1]
Q3 Hydrogen gas volume [4]
Balanced equation shows Mg:H₂ ratio = 1:1 [1]
Moles H₂ = 0.12 mol [1]
Volume = 0.12 × 22.4 [1]
Volume = 2.688 L ≈ 2.69 L [1]
Q4 Limiting reactant [5]
Equation: 2Al + 3Cl₂ → 2AlCl₃ [1]
For 0.50 mol Al, Cl₂ needed = 0.50 × 3/2 = 0.75 mol [1]
Only 0.60 mol Cl₂ is available [1]
Therefore Cl₂ runs out first [1]
Limiting reactant = chlorine [1]
Q5 HL ideal gas [4]
PV = nRT [1]
n = PV / RT [1]
n = (120000 × 0.010) / (8.31 × 290) [1]
n = 1200 / 2409.9 = 0.498 mol ≈ 0.50 mol [1]
19. States of Matter and Diffusion
At Higher Level, Chapter 3 also expects you to connect particle theory with stoichiometry and gas behaviour.
| State | Particle arrangement | Motion | Key idea |
|---|---|---|---|
| Solid | Closely packed, regular arrangement | Particles vibrate about fixed positions | Definite shape and volume |
| Liquid | Close together but irregular | Particles slide past one another | Definite volume, no fixed shape |
| Gas | Far apart and random | Rapid motion in all directions | No fixed shape or volume |
20. Structural Formulae and Named Biological Examples
A structural formula shows how the atoms are connected in a molecule. This is more detailed than a molecular formula.
| Substance | Molecular formula | Structural / displayed idea |
|---|---|---|
| Water | H2O | H–O–H |
| Methane | CH4 | Carbon single-bonded to four H atoms |
| Ethanol | C2H6O | CH3CH2OH |
| Glucose | C6H12O6 | Important biological sugar |
| Urea | CH4N2O | CO(NH2)2 |
21. Balancing Chemical Equations
Before doing stoichiometric calculations, make sure the equation is balanced.
Unbalanced: Fe + O2 → Fe2O3
Balanced: 4Fe + 3O2 → 2Fe2O3
22. Ionic Redox Equation Balancing
At Higher Level you may also need to balance ionic redox equations.
Fe2+ → Fe3+ + e−
MnO4− + 8H+ + 5e− → Mn2+ + 4H2O
23. Mandatory Experiment: Relative Molecular Mass of a Volatile Liquid
This experiment is part of the chapter’s practical syllabus. A known volume of vapour is produced, condensed or weighed, and its relative molecular mass is determined.
Aim
To determine the relative molecular mass (Mr) of a volatile liquid by heating it so that it vaporises completely.
Key idea
Measure mass of vapour and use gas data to calculate moles, then find Mr from mass ÷ moles.
| Apparatus | Examples |
|---|---|
| Heating setup | Water bath or boiling water |
| Container | Conical flask or gas syringe arrangement |
| Measurements | Mass, temperature, pressure, volume |