Balancing equations

A chemical equation shows what reacts and what is made. A word equation uses names; a symbol equation uses formulae. Atoms are only rearranged in a reaction, never made or destroyed, so a symbol equation must have the same number of each kind of atom on both sides. You balance it by putting numbers in front of the formulae, never by changing the formulae themselves.

Key facts

  • Reactants are on the left of the arrow; products are on the right: magnesium + oxygen → magnesium oxide.
  • A balanced equation has the same number of atoms of each element on both sides. This is why mass is conserved.
  • Balance by changing the big numbers in front (2H2O), never the small numbers in a formula: H2O2 would be a different substance.
  • A number in front multiplies the whole formula: 2H2O has 4 hydrogen atoms and 2 oxygen atoms.
  • A good method: count each element on both sides, balance one element at a time (leave elements that appear on their own, like O2, until last), then check every element again.
  • State symbols: (s) solid, (l) liquid, (g) gas, (aq) dissolved in water.
  • An ionic equation shows only the ions that change; spectator ions are left out. Every neutralisation is H⁺(aq) + OH⁻(aq) → H2O(l).

Worked examples

Example 1

Balance: H2 + O2 → H2O

  1. Count the atoms: hydrogen 2 and 2; oxygen 2 on the left but only 1 on the right.
  2. Put a 2 in front of H2O to make 2 oxygen atoms on the right. Now there are 4 hydrogen atoms on the right. H2 + O2 → 2H2O
  3. Put a 2 in front of H2 to make 4 hydrogen atoms on the left. Check: H 4 = 4, O 2 = 2. 2H2 + O2 → 2H2O

Answer: 2H2 + O2 → 2H2O

Example 2

Balance the equation for methane burning: CH4 + O2 → CO2 + H2O

  1. Carbon: 1 on each side. Already balanced.
  2. Hydrogen: 4 on the left, so you need 2H2O on the right. CH4 + O2 → CO2 + 2H2O
  3. Oxygen: now 2 + 2 = 4 on the right, so you need 2O2 on the left. CH4 + 2O2 → CO2 + 2H2O

Answer: CH4 + 2O2 → CO2 + 2H2O

Example 3

Silver nitrate solution is added to sodium chloride solution and a white solid forms. Write the equation with state symbols and the ionic equation.

  1. Both starting solutions are (aq). The white solid is silver chloride, a precipitate: (s). Sodium nitrate stays dissolved: (aq). AgNO3(aq) + NaCl(aq) → AgCl(s) + NaNO3(aq)
  2. Split the dissolved ionic compounds into ions. Na⁺ and NO3⁻ are the same on both sides: they are spectator ions.
  3. Leave them out to get the ionic equation. Ag⁺(aq) + Cl⁻(aq) → AgCl(s)

Answer: AgNO3(aq) + NaCl(aq) → AgCl(s) + NaNO3(aq); Ag⁺(aq) + Cl⁻(aq) → AgCl(s)