Balancing Chemical Equations

This lesson covers how to balance chemical equations as required by the AQA GCSE Combined Science Trilogy specification (8464). You will learn why equations must be balanced, the rules for balancing, and how to tackle equations of increasing difficulty.

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Why Must Equations Be Balanced?

Because of the law of conservation of mass: no atoms are created or destroyed in a chemical reaction. A balanced equation has the same number of each type of atom on both sides of the arrow.

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Rules for Balancing

1. Never change the formulae of the substances — only adjust the coefficients (the large numbers in front of formulae).
2. Start with the element that appears in the fewest formulae.
3. Balance one element at a time.
4. Leave hydrogen and oxygen until last (they often appear in multiple compounds).
5. Check your answer by counting atoms on both sides.

flowchart TD
    A["Write unbalanced equation\nwith correct formulae"] --> B["Pick an element that\nappears in fewest places"]
    B --> C["Adjust coefficients to\nbalance that element"]
    C --> D["Move to the next\nunbalanced element"]
    D --> E{"Are all elements\nbalanced?"}
    E -->|"No"| B
    E -->|"Yes"| F["Check by counting\nevery atom on both sides"]
    F --> G["Add state symbols\n(s), (l), (g), (aq)"]
    style A fill:#3b82f6,color:#fff,stroke:#2563eb
    style F fill:#f59e0b,color:#000,stroke:#d97706
    style G fill:#22c55e,color:#fff,stroke:#16a34a

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State Symbols

Symbol	Meaning
(s)	Solid
(l)	Liquid
(g)	Gas
(aq)	Aqueous (dissolved in water)

Exam Tip (AQA 8464): AQA expects you to use state symbols in balanced equations. Learn to add them routinely.

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Worked Examples

Example 1 — Magnesium and Hydrochloric Acid

Unbalanced: $\text{Mg} + \text{HCl} \rightarrow \text{MgCl}_2 + \text{H}_2$Mg+HCl→MgCl2​+H2​

Count atoms:

Element	Left	Right
Mg	1	1
H	1	2
Cl	1	2

H and Cl are unbalanced. Put a 2 in front of HCl:

$\text{Mg}(s) + 2\text{HCl}(aq) \rightarrow \text{MgCl}_2(aq) + \text{H}_2(g)$Mg(s)+2HCl(aq)→MgCl2​(aq)+H2​(g)

Check: Mg = 1:1, H = 2:2, Cl = 2:2. Balanced.

Example 2 — Iron and Oxygen

Unbalanced: $\text{Fe} + \text{O}_2 \rightarrow \text{Fe}_2\text{O}_3$Fe+O2​→Fe2​O3​

Start with oxygen: 2 on the left, 3 on the right. The LCM of 2 and 3 is 6. Put 3 in front of $\text{O}_2$O2​ and 2 in front of $\text{Fe}_2\text{O}_3$Fe2​O3​:

$\text{Fe} + 3\text{O}_2 \rightarrow 2\text{Fe}_2\text{O}_3$Fe+3O2​→2Fe2​O3​

Now Fe: left = ?, right = 4. Put 4 in front of Fe:

$4\text{Fe}(s) + 3\text{O}_2(g) \rightarrow 2\text{Fe}_2\text{O}_3(s)$4Fe(s)+3O2​(g)→2Fe2​O3​(s)

Check: Fe = 4:4, O = 6:6. Balanced.

Example 3 — Combustion of Methane

Unbalanced: $\text{CH}_4 + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O}$CH4​+O2​→CO2​+H2​O

• C: 1 on each side. Balanced.
• H: 4 on left, 2 on right. Put 2 in front of $\text{H}_2\text{O}$H2​O: now H = 4:4.
• O: 2 on left, $2 + 2 = 4$2+2=4 on right. Put 2 in front of $\text{O}_2$O2​: now O = 4:4.

$\text{CH}_4(g) + 2\text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\text{H}_2\text{O}(l)$CH4​(g)+2O2​(g)→CO2​(g)+2H2​O(l)

Example 4 — Combustion of Ethane

Unbalanced: $\text{C}_2\text{H}_6 + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O}$C2​H6​+O2​→CO2​+H2​O

• C: 2 on left, 1 on right. Put 2 in front of $\text{CO}_2$CO2​.
• H: 6 on left, 2 on right. Put 3 in front of $\text{H}_2\text{O}$H2​O.
• O: 2 on left, $(2 \times 2) + 3 = 7$(2×2)+3=7 on right. Need 7 O atoms on the left → $\frac{7}{2} = 3.5$27​=3.5 $\text{O}_2$O2​.

Multiply everything by 2 to remove fractions:

$2\text{C}_2\text{H}_6(g) + 7\text{O}_2(g) \rightarrow 4\text{CO}_2(g) + 6\text{H}_2\text{O}(l)$2C2​H6​(g)+7O2​(g)→4CO2​(g)+6H2​O(l)

Check: C = 4:4, H = 12:12, O = 14:14. Balanced.

Example 5 — Sodium and Water

$2\text{Na}(s) + 2\text{H}_2\text{O}(l) \rightarrow 2\text{NaOH}(aq) + \text{H}_2(g)$2Na(s)+2H2​O(l)→2NaOH(aq)+H2​(g)

Check: Na = 2:2, H = 4:4, O = 2:2. Balanced.

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Common Mistakes to Avoid

Mistake	Correction
Changing the formula (e.g. $\text{H}_2\text{O}$H2​O to $\text{H}_2\text{O}_2$H2​O2​)	Never change formulae — only adjust coefficients
Missing state symbols	AQA expects state symbols — always include (s), (l), (g) or (aq)
Not checking the final answer	Always count every atom on both sides to confirm
Leaving fractional coefficients	Multiply through to make all coefficients whole numbers

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Summary

• Chemical equations must be balanced because of conservation of mass.
• Only change the coefficients (big numbers in front), never the formulae.
• Work systematically — balance one element at a time.
• Leave H and O until last.
• Always add state symbols.
• Check by counting atoms on both sides.

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Extended Worked Examples — Balancing with Confidence

Balancing equations is a required skill on both Foundation and Higher AQA papers. The examples below build in difficulty and show how balancing connects to relative formula mass ($M_r$Mr​) and conservation of mass.

Worked Example 6 — Thermal Decomposition of Copper Carbonate

Unbalanced: $\text{CuCO}_3 \rightarrow \text{CuO} + \text{CO}_2$CuCO3​→CuO+CO2​

Count atoms:

Element	Left	Right
Cu	1	1
C	1	1
O	3	$1 + 2 = 3$1+2=3

Already balanced with coefficients of 1. Add states:

$\text{CuCO}_3(s) \rightarrow \text{CuO}(s) + \text{CO}_2(g)$CuCO3​(s)→CuO(s)+CO2​(g)

$M_r$Mr​ check for conservation of mass. Left: $63.5 + 12 + 48 = 123.5$63.5+12+48=123.5. Right: $(63.5 + 16) + (12 + 32) = 79.5 + 44 = 123.5$(63.5+16)+(12+32)=79.5+44=123.5. Same total — mass is conserved.

Worked Example 7 — Aluminium and Chlorine

Unbalanced: $\text{Al} + \text{Cl}_2 \rightarrow \text{AlCl}_3$Al+Cl2​→AlCl3​

• Al: 1 vs 1 (balanced for now).
• Cl: 2 vs 3 — LCM = 6.

Put 3 in front of $\text{Cl}_2$Cl2​ and 2 in front of $\text{AlCl}_3$AlCl3​:

$\text{Al} + 3\text{Cl}_2 \rightarrow 2\text{AlCl}_3$Al+3Cl2​→2AlCl3​

Now Al: 1 vs 2 — put 2 in front of Al:

$2\text{Al}(s) + 3\text{Cl}_2(g) \rightarrow 2\text{AlCl}_3(s)$2Al(s)+3Cl2​(g)→2AlCl3​(s)

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

Worked Example 8 — Combustion of Propane

Unbalanced: $\text{C}_3\text{H}_8 + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O}$C3​H8​+O2​→CO2​+H2​O