3.2.2 Amounts of substances in equations

The balancing numbers give the ratio of moles that react

Definition

Mole

The amount of a substance, measured in mol, where one mole has a mass in grams numerically equal to its relative formula mass.

Definition

Mole ratio

The ratio of reacting amounts shown by the balancing numbers in a chemical equation.

The large numbers in front of the formulae give the mole ratio in which the substances react.
In $2H2+O2→2H2O2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}$ , two moles of hydrogen react with one mole of oxygen to make two moles of water.

Key Idea

A balanced equation is a recipe in moles, so once you know the moles of one substance you can find the moles of any other.

Three steps take you from one mass to another

Definition

Relative formula mass

The sum of the relative atomic masses of all the atoms shown in a chemical formula.

Change the mass you are given into moles using $\dfrac{m}{M_r}$ .
Use the mole ratio from the balanced equation to find the moles of the substance you want.
Change those moles back into a mass using $\times M_r$ .

Exam technique

Always convert to moles before using the ratio, as you cannot apply the balancing numbers directly to masses.
Set out each stage on its own line, because staged calculations earn marks even if the final answer slips.

Worked example: mass of product from mass of reactant

Find the mass of magnesium oxide made when $6 g6\ \text{g}$ $6 g$ of magnesium burns in $2Mg+O2→2MgO2\text{Mg} + \text{O}_2 \rightarrow 2\text{MgO}$ $2 Mg + O_{2} \to 2 MgO$ .
1. Moles of magnesium $\dfrac{6}{24} = 0.25\ \text{mol}$ .
2. The ratio of magnesium to magnesium oxide is $2 : 2$ , so moles of magnesium oxide $0.25\ \text{mol}$ .
3. Mass of magnesium oxide $\times 40 = 10\ \text{g}$ .

Self review

What does the mole ratio in a balanced equation tell you?
Why must you change a mass into moles before using the ratio?
In $2Mg+O2→2MgO2\text{Mg} + \text{O}_2 \rightarrow 2\text{MgO}$ , how many moles of oxygen react with $mol0.25\ \text{mol}$ of magnesium?
Find the mass of water made from $g4\ \text{g}$ of hydrogen in $2H2+O2→2H2O2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}$ .

A balanced chemical equation shows the ratio of moles in which substances react. The large numbers in front of the formulae are called balancing numbers, or coefficients.

For example, in $2H2+O2→2H2O2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}$ , the mole ratio is hydrogen : oxygen : water $= 2 : 1 : 2$ . This means that $mol2\ \text{mol}$ of hydrogen reacts with $mol1\ \text{mol}$ of oxygen to produce $mol2\ \text{mol}$ of water.

A mole is an amount of substance measured in $mol\text{mol}$ . A balanced equation is a recipe in moles, so the ratio cannot usually be applied directly to masses.

What do the large numbers in front of formulae show in a balanced equation?