Topic 1 · page 3 of 10

Writing equations

A balanced equation is a recipe in moles. It must balance in atoms and, for ionic equations, in charge, and it must say what state each substance is in.

12 min read1.3

Read first: Relative mass and the mole

Balanced full equations 1.3

The numbers in front of each formula (the coefficients) give the mole ratio. Read this equation aloud as "one mole of magnesium reacts with two moles of hydrochloric acid to give one mole of magnesium chloride and one mole of hydrogen":

\ce{Mg(s) + 2HCl(aq) -> MgCl2(aq) + H2(g)}

MethodBalancing an equation

Write the correct formula of every reactant and product. Get these right first; they never change afterwards.
Balance one element at a time by changing coefficients only.
Leave elements that appear on their own (O₂, H₂, a metal) until last, because changing them disturbs nothing else.
Check every element, and the total charge if there are ions.
Add state symbols.

Worked exampleCombustion of propane

Unbalanced: C₃H₈ + O₂ → CO₂ + H₂O

Carbon: 3 on the left, so 3CO₂.
Hydrogen: 8 on the left, so 4H₂O.
Oxygen: the right now has 3(2) + 4(1) = 10 atoms, so 5O₂.

\ce{C3H8(g) + 5O2(g) -> 3CO2(g) + 4H2O(l)}

If oxygen ends up needing an odd number of atoms, double everything. For ethane: 2C₂H₆ + 7O₂ → 4CO₂ + 6H₂O.

State symbols 1.3

Symbol	Meaning	Typical examples
(s)	solid	metals, precipitates, insoluble carbonates and oxides
(l)	liquid	water at room temperature, ethanol
(g)	gas	H₂, O₂, CO₂, Cl₂
(aq)	aqueous: dissolved in water	acids, alkalis, soluble salts in solution

Ionic equations 1.3

Many reactions in solution involve ions that are not changed at all. These spectator ions are present on both sides and are left out. An ionic equation shows only the species that actually react.

MethodFrom full equation to ionic equation

Write the balanced full equation with state symbols.
Split every aqueous ionic substance into its ions. Strong acids count: HCl(aq) is H⁺(aq) + Cl⁻(aq).
Cross out ions that appear unchanged on both sides.
Write what is left, and check it balances in atoms and charge.

Worked exampleSilver nitrate and sodium chloride

Full: $\ce{AgNO3(aq) + NaCl(aq) -> AgCl(s) + NaNO3(aq)}$
Split: $\ce{Ag+(aq) + NO3^-(aq) + Na+(aq) + Cl^-(aq) -> AgCl(s) + Na+(aq) + NO3^-(aq)}$
Na⁺ and NO₃⁻ are spectators.
Ionic: $\ce{Ag+(aq) + Cl^-(aq) -> AgCl(s)}$ . Charge: 0 on each side.

Ionic equations show that different reactions are really the same chemistry. Any strong acid with any alkali:

\ce{H+(aq) + OH^-(aq) -> H2O(l)}

Worked exampleCalcium carbonate and hydrochloric acid

Full: $\ce{CaCO3(s) + 2HCl(aq) -> CaCl2(aq) + H2O(l) + CO2(g)}$

Calcium carbonate is a solid, so it stays whole. Only Cl⁻ is a spectator:

\ce{CaCO3(s) + 2H+(aq) -> Ca^2+(aq) + H2O(l) + CO2(g)}

Charge check: 2+ on the left, 2+ on the right.

Check yourself

Balance: Fe₂O₃(s) + CO(g) → Fe(s) + CO₂(g)
Balance: Al(s) + O₂(g) → Al₂O₃(s)
Write the full equation, with state symbols, for sodium hydroxide solution reacting with nitric acid. Then write the ionic equation.
Write the ionic equation for barium chloride solution reacting with sodium sulfate solution to form a white precipitate of barium sulfate.
A student writes Ca²⁺(aq) + CO₃²⁻(aq) + 2H⁺(aq) → Ca²⁺(aq) + H₂O(l) + CO₂(g) for solid calcium carbonate reacting with acid. What is wrong?
Check whether this equation balances in charge: Fe²⁺(aq) + Cl₂(aq) → Fe³⁺(aq) + 2Cl⁻(aq). Correct it if needed.

Answers cover these until you have tried the questions

$\ce{Fe2O3(s) + 3CO(g) -> 2Fe(s) + 3CO2(g)}$
$\ce{4Al(s) + 3O2(g) -> 2Al2O3(s)}$
Full: $\ce{NaOH(aq) + HNO3(aq) -> NaNO3(aq) + H2O(l)}$ . Ionic: $\ce{H+(aq) + OH^-(aq) -> H2O(l)}$
$\ce{Ba^2+(aq) + SO4^2-(aq) -> BaSO4(s)}$
Calcium carbonate is a solid, so it must not be split into ions. Correct: $\ce{CaCO3(s) + 2H+(aq) -> Ca^2+(aq) + H2O(l) + CO2(g)}$
Left: 2+ and 0, total 2+. Right: 3+ and 2(1−), total 1+. It does not balance. Correct: $\ce{2Fe^2+(aq) + Cl2(aq) -> 2Fe^3+(aq) + 2Cl^-(aq)}$ , with 4+ on the left and 6+ − 2 = 4+ on the right.