Reacting masses and limiting reactants

A balanced equation tells you the ratio in which substances react, in moles. To find a reacting mass, turn the mass you know into moles, use the ratio from the equation, then turn the moles back into a mass. If one reactant runs out first it is the limiting reactant: it decides how much product forms, and the other reactant is in excess.

Key facts

  • Mass is conserved: the total mass of the products equals the total mass of the reactants.
  • The big numbers in a balanced equation give the mole ratio: 2Mg + O2 → 2MgO means 2 mol of Mg react with 1 mol of O2.
  • Three steps: mass → moles (÷ Mᵣ), use the ratio, then moles → mass (× Mᵣ).
  • The limiting reactant is the one that is used up first; the other is in excess.
  • The amount of product depends on the amount of the limiting reactant.
  • If a gas escapes from an open container the mass seems to fall; if a gas from the air joins on, it seems to rise.

Worked examples

Example 1

What mass of magnesium oxide forms when 6 g of magnesium burns? 2Mg + O2 → 2MgO (Aᵣ: Mg = 24, O = 16)

  1. Moles of magnesium. 6 ÷ 24 = 0.25 mol
  2. The ratio Mg : MgO is 2 : 2, which is 1 : 1, so 0.25 mol of MgO forms.
  3. Mass of magnesium oxide (Mᵣ = 24 + 16 = 40). 0.25 × 40 = 10 g

Answer: 10 g

Example 2

What mass of calcium oxide is made by heating 25 g of calcium carbonate? CaCO3 → CaO + CO2 (Aᵣ: Ca = 40, C = 12, O = 16)

  1. Mᵣ of CaCO3 is 100, so find the moles. 25 ÷ 100 = 0.25 mol
  2. The ratio CaCO3 : CaO is 1 : 1, so 0.25 mol of CaO forms.
  3. Mᵣ of CaO is 56. 0.25 × 56 = 14 g
  4. Check: the other 11 g leaves as carbon dioxide, and 14 + 11 = 25 g, so mass is conserved.

Answer: 14 g

Example 3

2.4 g of magnesium is added to 0.1 mol of hydrochloric acid. Mg + 2HCl → MgCl2 + H2. Which reactant is limiting, and what mass of hydrogen forms? (Aᵣ: Mg = 24, H = 1)

  1. Moles of magnesium. 2.4 ÷ 24 = 0.1 mol
  2. 0.1 mol of Mg needs 2 × 0.1 = 0.2 mol of HCl, but there is only 0.1 mol. So the acid runs out first: it is the limiting reactant.
  3. 0.1 mol of HCl makes half as many moles of H2. 0.1 ÷ 2 = 0.05 mol
  4. Mass of hydrogen (Mᵣ = 2). 0.05 × 2 = 0.1 g

Answer: the hydrochloric acid is limiting; 0.1 g of hydrogen