Using moles and balanced equations (HT)
Once you can convert between mass and moles, balanced equations let you predict the mass of product made from a known mass of reactant — or the mass of reactant needed to make a target product.
The four-step method
For any reaction question, follow this routine:
- Write the balanced equation.
- Convert known mass → moles (moles = mass ÷ M_r).
- Use the equation to find moles of the unknown (mole ratio).
- Convert moles → mass (mass = moles × M_r).
✦Worked example— Worked example 1 — simple ratio
What mass of magnesium oxide is produced when 6 g of magnesium burns in oxygen?
Equation: 2Mg + O₂ → 2MgO
A_r: Mg = 24; M_r MgO = 40.
- moles Mg = 6 ÷ 24 = 0.25 mol.
- From the equation: 2 mol Mg → 2 mol MgO. Ratio 1:1, so moles MgO = 0.25 mol.
- mass MgO = 0.25 × 40 = 10 g.
✦Worked example— Worked example 2 — non-1:1 ratio
What mass of carbon dioxide is produced when 5.6 g of iron(III) oxide is reduced by carbon monoxide?
Equation: Fe₂O₃ + 3CO → 2Fe + 3CO₂
A_r: Fe = 56; O = 16. M_r Fe₂O₃ = 160; M_r CO₂ = 44.
- moles Fe₂O₃ = 5.6 ÷ 160 = 0.035 mol.
- Mole ratio Fe₂O₃ : CO₂ = 1 : 3, so moles CO₂ = 0.035 × 3 = 0.105 mol.
- mass CO₂ = 0.105 × 44 = 4.62 g.
✦Worked example— Worked example 3 — find a coefficient
When iron reacts with oxygen, 11.2 g iron forms 16.0 g iron oxide. Determine the formula of the oxide.
A_r Fe = 56; A_r O = 16.
- moles Fe = 11.2 ÷ 56 = 0.2 mol.
- mass O combined = 16.0 − 11.2 = 4.8 g.
- moles O = 4.8 ÷ 16 = 0.3 mol.
- ratio Fe : O = 0.2 : 0.3 = 2 : 3 → Fe₂O₃.
✦Worked example— Worked example 4 — finding the balancing number
Sodium reacts with oxygen: Na + O₂ → Na₂O.
If 4.6 g of Na reacts completely:
- moles Na = 4.6 ÷ 23 = 0.2 mol.
To form Na₂O, 2 Na are needed per O atom (so per ½ O₂). Na : O₂ ratio is 4 : 1.
So 4Na + O₂ → 2Na₂O is the balanced equation.
moles O₂ = 0.2 ÷ 4 = 0.05; moles Na₂O = 0.2 ÷ 2 = 0.1; mass Na₂O = 0.1 × 62 = 6.2 g.
⚠Common mistakes
- Skipping the balanced equation. Always write it first — coefficients are essential.
- Using mass ratios instead of mole ratios. The equation gives mole ratios.
- Forgetting to multiply by the coefficient. In 2Mg + O₂ → 2MgO, the Mg : MgO ratio is 1 : 1; in Fe₂O₃ + 3CO → 2Fe + 3CO₂, ratio Fe₂O₃ : Fe is 1 : 2.
- Wrong M_r in step 4. Convert to the correct compound's M_r.
Links
Required for C3.6 (limiting reactants), C3.7 (concentration), C3.8 (yield/atom economy) and C3.9 (gas volumes).
AI-generated · claude-opus-4-7 · v3-deep-chemistry