Balanced Equations
Learning Objectives (OCR Spec 2.1.3)
- Construct balanced chemical equations using state symbols
- Write balanced ionic equations, including half-equations
- Apply the law of conservation of mass to chemical equations
- Balance equations involving gases, ions and spectator species
- Write half-equations for oxidation and reduction
- Combine half-equations to produce overall redox equations
Why Equations Must Balance
Chemical reactions obey the law of conservation of mass: matter is neither created nor destroyed, only rearranged. A balanced equation must have:
- Equal numbers of each type of atom on both sides
- Equal total charge on both sides (for ionic equations)
- Correct state symbols where required
The French chemist Antoine Lavoisier (1743–1794) established conservation of mass through precise measurements of combustion reactions in sealed containers in the 1770s and 1780s. Before this, many chemists believed that burning destroyed matter — Lavoisier showed this was wrong and laid the foundation for modern quantitative chemistry.
State Symbols
OCR expects state symbols in almost every equation answer. They are:
| Symbol | Meaning |
|---|
| (s) | Solid |
| (l) | Pure liquid |
| (g) | Gas |
| (aq) | Aqueous (dissolved in water) |
Tip: Missing state symbols are a common reason for losing 1 mark on a 2-mark equation question.
Common state symbol rules:
- Water in a neutralisation is (l), the pure product, not (aq)
- NaOH dissolved in water is (aq)
- Solid NaOH from the bottle is (s)
- Molten NaOH (for electrolysis) is (l)
- Precipitates in solution reactions are (s), even though the solution is aqueous
- Gases evolved in test tube reactions are (g)
A Systematic Method for Balancing
- Write the correct formulae for reactants and products (never change these)
- Count atoms of each element on each side
- Add whole-number coefficients (never fractions in final answer, except for energetics)
- Balance one element at a time — leave H and O until last
- Do a final atom count check
- Add state symbols
Worked Example 1: Combustion of Methane
Unbalanced: CH₄(g) + O₂(g) → CO₂(g) + H₂O(l)
- C: 1 = 1 ✓
- H: 4 on left, 2 on right → put coefficient 2 before H₂O
- CH₄ + O₂ → CO₂ + 2H₂O
- O: 2 on left, 2 + 2 = 4 on right → put coefficient 2 before O₂
- Final: CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l) ✓
Worked Example 2: Combustion of Propane
Unbalanced: C₃H₈(g) + O₂(g) → CO₂(g) + H₂O(l)
- C: 3 on left → 3CO₂
- H: 8 on left → 4H₂O
- C₃H₈ + O₂ → 3CO₂ + 4H₂O
- O: 10 on right → 5O₂
- Final: C₃H₈(g) + 5O₂(g) → 3CO₂(g) + 4H₂O(l) ✓
Worked Example 3: Reaction of Aluminium with Oxygen
Unbalanced: Al(s) + O₂(g) → Al₂O₃(s)
- Al: start with 2Al₂O₃ → 4Al, 6O
- Place 4 before Al, 3 before O₂ (6 O atoms)
- Final: 4Al(s) + 3O₂(g) → 2Al₂O₃(s) ✓
Worked Example 4: Reaction of Sodium with Water
Unbalanced: Na(s) + H₂O(l) → NaOH(aq) + H₂(g)
- Na: 1 on each side — seems fine but H is odd on right, so double
- 2Na + 2H₂O → 2NaOH + H₂
- Final: 2Na(s) + 2H₂O(l) → 2NaOH(aq) + H₂(g) ✓
Worked Example 5: Combustion of Butane
Unbalanced: C₄H₁₀(g) + O₂(g) → CO₂(g) + H₂O(l)
- C: 4 → 4CO₂
- H: 10 → 5H₂O
- O on right: 8 + 5 = 13; O₂ coefficient = 13/2
- Multiply everything by 2 to clear the fraction:
- Final: 2C₄H₁₀(g) + 13O₂(g) → 8CO₂(g) + 10H₂O(l) ✓
Worked Example 6: Thermite Reaction
Fe₂O₃ + Al → Al₂O₃ + Fe
- Al: 2 on right → 2Al
- Fe: 2 on left → 2Fe
- O: 3 on both sides ✓
- Final: Fe₂O₃(s) + 2Al(s) → Al₂O₃(s) + 2Fe(l) ✓
Note the state symbol for Fe — the reaction is so exothermic that iron is produced as a liquid, which is why thermite is used for welding rail tracks.
Ionic Equations
For reactions in aqueous solution, many ions are spectators — they appear on both sides unchanged. An ionic equation removes them, showing only the species that actually react.
Procedure
- Write the full balanced equation with state symbols
- Expand aqueous ionic compounds into their constituent ions
- Cancel any ions that appear identically on both sides (spectators)
- Keep solids, liquids, gases and covalent molecules as they are
Worked Example 7: Precipitation of Silver Chloride
Full equation: AgNO₃(aq) + NaCl(aq) → AgCl(s) + NaNO₃(aq)
Expanded:
Ag⁺(aq) + NO₃⁻(aq) + Na⁺(aq) + Cl⁻(aq) → AgCl(s) + Na⁺(aq) + NO₃⁻(aq)