Balanced Equations and State Symbols

Chemical equations are the language of chemistry. A balanced equation tells you exactly what reacts, what is produced, and in what proportions. Getting comfortable with writing and balancing equations is essential for every area of A-Level Chemistry.

Why Equations Must Be Balanced

Atoms cannot be created or destroyed in a chemical reaction — this is the law of conservation of mass. A balanced equation has the same number of each type of atom on both sides of the arrow. An unbalanced equation violates this fundamental law.

For example, the unbalanced equation for the combustion of methane is:

CH₄ + O₂ → CO₂ + H₂O (unbalanced)

Counting atoms: Left side has 1C, 4H, 2O. Right side has 1C, 2H, 3O. This is not balanced.

The balanced equation is:

CH₄ + 2O₂ → CO₂ + 2H₂O

Now: Left = 1C, 4H, 4O. Right = 1C, 4H, 4O. Balanced.

Systematic Balancing Method

For most equations, follow this approach:

flowchart TD
    A["Write correct formulae for all species"] --> B["Balance metals first"]
    B --> C["Balance non-metals (except H and O)"]
    C --> D["Balance hydrogen"]
    D --> E["Balance oxygen last"]
    E --> F["Check all atoms balance"]
    F --> G{"All balanced?"}
    G -- No --> B
    G -- Yes --> H["Ensure smallest whole-number coefficients"]
    H --> I["Add state symbols"]

Critical rule: Never change a formula during balancing — only change coefficients (the numbers in front of formulae).

Worked Example 1

Balance the equation for the reaction of aluminium with hydrochloric acid.

Unbalanced: Al + HCl → AlCl₃ + H₂

Step 1: Balance Al — already 1 on each side. Step 2: Balance Cl — 1 on left, 3 on right, so put 3 in front of HCl. Al + 3HCl → AlCl₃ + H₂

Step 3: Balance H — 3 on left, 2 on right. We need a common multiple. Put 6HCl and 3H₂: Al + 6HCl → AlCl₃ + 3H₂

Step 4: Now Cl — 6 on left, 3 on right. Put 2AlCl₃: Al + 6HCl → 2AlCl₃ + 3H₂

Step 5: Balance Al — 1 on left, 2 on right. Put 2Al: 2Al + 6HCl → 2AlCl₃ + 3H₂

Check: Al = 2:2, H = 6:6, Cl = 6:6

Worked Example 2

Balance: Fe₂O₃ + CO → Fe + CO₂

Step 1: Balance Fe — 2 on left, 1 on right → put 2Fe. Fe₂O₃ + CO → 2Fe + CO₂

Step 2: Balance O — 3 + 1 = 4 on left, 2 on right. Try 3CO and 3CO₂: Fe₂O₃ + 3CO → 2Fe + 3CO₂

Check: Fe = 2:2, C = 3:3, O = 3 + 3 = 6 on left and 6 on right.

Fe₂O₃ + 3CO → 2Fe + 3CO₂

Worked Example 3 — A Harder Equation

Balance: C₂H₅OH + O₂ → CO₂ + H₂O

Step 1: Balance C — 2 on left → 2CO₂. C₂H₅OH + O₂ → 2CO₂ + H₂O

Step 2: Balance H — 6 on left → 3H₂O. C₂H₅OH + O₂ → 2CO₂ + 3H₂O

Step 3: Balance O — Left: 1 (from OH) + 2x (from O₂). Right: 4 + 3 = 7. So 1 + 2x = 7, x = 3. C₂H₅OH + 3O₂ → 2CO₂ + 3H₂O

Check: C = 2:2, H = 6:6, O = 1 + 6 = 7 : 4 + 3 = 7.

State Symbols

State symbols are written after each formula in brackets to show the physical state:

Symbol	State	Example
(s)	solid	NaCl(s)
(l)	liquid	H₂O(l)
(g)	gas	CO₂(g)
(aq)	aqueous (dissolved in water)	NaCl(aq)

State symbols are expected in all equations at A-Level. For example:

2Na(s) + 2H₂O(l) → 2NaOH(aq) + H₂(g)

Common State Symbol Rules

Most metals are (s) at room temperature (except mercury, which is (l)).
Water in a reaction mixture is (l); water as steam is (g).
If a substance is dissolved in water, it is (aq).
Gases produced that escape the solution are (g).
Precipitates formed in solution are (s).

Ionic Equations

Many reactions in aqueous solution involve ions. A full ionic equation shows all ions present, while a net ionic equation removes the spectator ions (ions that appear unchanged on both sides).

Worked Example 4

Write the full and net ionic equations for the reaction of silver nitrate with sodium chloride.

Full equation: AgNO₃(aq) + NaCl(aq) → AgCl(s) + NaNO₃(aq)

Full ionic equation: Ag⁺(aq) + NO₃⁻(aq) + Na⁺(aq) + Cl⁻(aq) → AgCl(s) + Na⁺(aq) + NO₃⁻(aq)

Spectator ions: Na⁺ and NO₃⁻ (they appear on both sides).

Net ionic equation: Ag⁺(aq) + Cl⁻(aq) → AgCl(s)

Worked Example 5

Write the net ionic equation for the neutralisation of hydrochloric acid with sodium hydroxide.

Full equation: HCl(aq) + NaOH(aq) → NaCl(aq) + H₂O(l)

Full ionic: H⁺(aq) + Cl⁻(aq) + Na⁺(aq) + OH⁻(aq) → Na⁺(aq) + Cl⁻(aq) + H₂O(l)

Spectator ions: Na⁺ and Cl⁻.

Net ionic equation: H⁺(aq) + OH⁻(aq) → H₂O(l)

This is the net ionic equation for any strong acid–strong base neutralisation.

Half-Equations

Half-equations show either the oxidation or the reduction part of a redox reaction separately. They are balanced for both atoms and charge.

Rules for Writing Half-Equations

Write the species being oxidised or reduced on each side.
Balance atoms other than O and H first.
Balance O by adding H₂O.
Balance H by adding H⁺.
Balance charge by adding electrons (e⁻).

Worked Example 6

Write the half-equation for the reduction of dichromate(VI) ions in acidic solution.

Cr₂O₇²⁻ → 2Cr³⁺

Balance O: add 7H₂O to the right. Cr₂O₇²⁻ → 2Cr³⁺ + 7H₂O

Balance H: add 14H⁺ to the left. Cr₂O₇²⁻ + 14H⁺ → 2Cr³⁺ + 7H₂O

Balance charge: Left = −2 + 14 = +12. Right = +6. Add 6e⁻ to the left. Cr₂O₇²⁻ + 14H⁺ + 6e⁻ → 2Cr³⁺ + 7H₂O

Combining Half-Equations

To combine two half-equations into one overall equation, the number of electrons lost must equal the number gained. Multiply the half-equations by appropriate factors, then add them together and cancel the electrons.

Worked Example 7

Combine these half-equations:

Fe²⁺ → Fe³⁺ + e⁻
MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O

Step 1: The first half-equation involves 1 electron; the second involves 5 electrons. Multiply the first by 5: 5Fe²⁺ → 5Fe³⁺ + 5e⁻

Step 2: Add the half-equations: MnO₄⁻ + 8H⁺ + 5e⁻ + 5Fe²⁺ → Mn²⁺ + 4H₂O + 5Fe³⁺ + 5e⁻

Step 3: Cancel electrons: MnO₄⁻ + 8H⁺ + 5Fe²⁺ → Mn²⁺ + 4H₂O + 5Fe³⁺

Common Mistakes When Balancing Equations

Mistake	Example	Fix
Changing a formula	Writing H₃O instead of H₂O to balance	Only change coefficients
Forgetting to balance charge in ionic equations	Net charge ≠ on both sides	Count total charge on each side
Not using smallest whole-number ratios	4H₂ + 2O₂ → 2H₂O	Divide all coefficients by 2
Omitting state symbols	Not penalised in some marks but required	Add (s), (l), (g), (aq)
Mixing up products	Writing wrong products for a reaction type	Learn common reaction types

Summary: Types of Chemical Equations You Need

Type	What it shows	Example
Word equation	Names of substances	Sodium + water → sodium hydroxide + hydrogen
Balanced symbol equation	Formulae with state symbols	2Na(s) + 2H₂O(l) → 2NaOH(aq) + H₂(g)
Full ionic equation	All ions written separately	Na⁺(aq) + OH⁻(aq) + H⁺(aq) + Cl⁻(aq) → Na⁺(aq) + Cl⁻(aq) + H₂O(l)
Net ionic equation	Spectator ions removed	H⁺(aq) + OH⁻(aq) → H₂O(l)
Half-equation	One half of a redox reaction	Fe²⁺ → Fe³⁺ + e⁻

Being fluent in all five types is essential for success across both the amounts of substance and the redox chemistry sections of the specification.

Using Equations for Mole Calculations

Balanced equations are not just theoretical — they are the foundation of every mole calculation. The coefficients in a balanced equation tell you the mole ratio.

Worked Example 8

What mass of carbon dioxide is produced when 10.0 g of calcium carbonate reacts with excess hydrochloric acid?

CaCO₃(s) + 2HCl(aq) → CaCl₂(aq) + H₂O(l) + CO₂(g)

Step 1: Moles of CaCO₃ = 10.0 / 100.0 = 0.100 mol Step 2: From the equation, 1 mol CaCO₃ → 1 mol CO₂. So moles of CO₂ = 0.100 mol. Step 3: Mass of CO₂ = 0.100 × 44.0 = 4.40 g

Without the balanced equation, you would not know the 1:1 ratio. For a reaction like 2Al + 3H₂SO₄ → Al₂(SO₄)₃ + 3H₂, the ratio is 2:3:1:3, and getting this wrong would give you the wrong mass by a factor of 1.5 or more.

Common Equations You Should Know

Reaction	Balanced equation
Metal + acid	Mg(s) + 2HCl(aq) → MgCl₂(aq) + H₂(g)
Carbonate + acid	Na₂CO₃(s) + 2HCl(aq) → 2NaCl(aq) + H₂O(l) + CO₂(g)
Neutralisation	NaOH(aq) + HCl(aq) → NaCl(aq) + H₂O(l)
Combustion of alkane	CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l)
Thermal decomposition	CaCO₃(s) → CaO(s) + CO₂(g)

A-Level Deep Dive: Balanced Equations and State Symbols

Spec mapping

Edexcel 9CH0 specification Topic 5 — Formulae, Equations and Amounts of Substance, sub-strand on chemical equations, requires students to write balanced full and ionic equations, including state symbols (s, l, g, aq), and to construct ionic equations by cancelling spectator ions (refer to the official specification document for exact wording). The skill is examined ubiquitously across all three papers — every reaction students describe must be writeable as a balanced equation, and ionic equations appear specifically in displacement, neutralisation, redox and precipitation contexts. The data sheet does not supply equations; balancing is a memorised competence.

Worked example with full mark scheme

Question (8 marks):

(a) Balance the following equation and add state symbols throughout:

$\text{C}_3\text{H}_8 + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O}$ (combustion at 1000 K). (3)

(b) When solid magnesium is added to aqueous copper(II) sulfate, a single-displacement reaction occurs. Write the full balanced equation with state symbols, and the ionic equation, identifying spectator ions. (5)

Solution with mark scheme:

(a) Step 1 — balance C, then H, then O.

$\text{C}_3\text{H}_8(g) + 5\text{O}_2(g) \rightarrow 3\text{CO}_2(g) + 4\text{H}_2\text{O}(g)$