3.6 Reacting masses from equations

Using the balanced equation

A balanced equation tells you the ratio in which substances react. You can use it to calculate the mass of a product from the mass of a reactant (or the other way round).

The mole method

1. Moles of the substance you know: moles = mass ÷ M_\mathrm{r}
2. Use the ratio from the balanced equation to find the moles of the substance you want.
3. Mass of the substance you want: mass = moles × M_\mathrm{r}

Example: what mass of carbon dioxide is made when 25 g of calcium carbonate is heated?

CaCO₃ → CaO + CO₂ (M_\mathrm{r}: CaCO₃ = 100, CO₂ = 44)

1. moles of CaCO₃ = 25 ÷ 100 = 0.25 mol
2. ratio 1 : 1, so 0.25 mol of CO₂
3. mass of CO₂ = 0.25 × 44 = 11 g

The proportion method

Use the M_\mathrm{r} values and the numbers in the equation as reacting masses, then scale.

Example: 2Mg + O₂ → 2MgO. 48 g of Mg makes 80 g of MgO, so 6.0 g of Mg makes 6.0 × 80 ÷ 48 = 10 g.

Working out the equation from masses

You can work backwards: convert each mass to moles, then find the simplest whole-number ratio.

Example: 4.8 g of Mg reacts with 3.2 g of O₂ to make 8.0 g of MgO.

• Mg: 4.8 ÷ 24 = 0.2 mol; O₂: 3.2 ÷ 32 = 0.1 mol; MgO: 8.0 ÷ 40 = 0.2 mol
• divide by 0.1 → 2 : 1 : 2, so 2Mg + O₂ → 2MgO