3.2.3 Using moles to balance equations

Measured masses can reveal the balancing numbers

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.

Higher tier only: balancing from masses is assessed on the higher tier.
If you know the mass of each substance that reacts, you can work out the balancing numbers of the equation.
The method is to turn each mass into moles and then find the simplest ratio of those moles.

Key Idea

The simplest whole-number ratio of the moles is exactly the set of balancing numbers in the equation.

First change every mass into moles

Definition

Relative formula mass

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

Work out the moles of each reactant and product using $\dfrac{m}{M_r}$ .
Keep every value in moles, since only moles can be compared as a ratio.

Example

$g48\ \text{g}$ of magnesium ( $A_r = 24$ ) is $mol\dfrac{48}{24} = 2\ \text{mol}$ .
$g32\ \text{g}$ of oxygen ( $M_r = 32$ ) is $mol\dfrac{32}{32} = 1\ \text{mol}$ .

Then reduce the moles to the simplest whole-number ratio

Definition

Mole ratio

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

Divide every mole value by the smallest one to get the simplest ratio.
Round the ratio to whole numbers, which then become the balancing numbers.

Exam technique

Divide by the smallest number of moles first, as it makes the ratio easiest to read.
A ratio like $1 : 0.5$ is not finished, so double both numbers to reach whole numbers such as $2 : 1$ .

Worked example: building the equation for burning magnesium

$48 g48\ \text{g}$ $48 g$ of magnesium reacts with $32 g32\ \text{g}$ $32 g$ of oxygen to make $80 g80\ \text{g}$ $80 g$ of magnesium oxide.
1. The moles are $2$ for magnesium, $1$ for oxygen and $8040=2\dfrac{80}{40} = 2$ for magnesium oxide.
2. The ratio $2 : 1 : 2$ gives the balanced equation $2Mg+O2→2MgO2\text{Mg} + \text{O}_2 \rightarrow 2\text{MgO}$ .

Self review

What two steps turn reacting masses into balancing numbers?
Why must the masses be changed into moles before comparing them?
How do you deal with a mole ratio that comes out as $1 : 0.5$ ?
$mol2\ \text{mol}$ of hydrogen reacts with $mol1\ \text{mol}$ of oxygen; what is the simplest ratio?

When measured masses represent the amounts of reactants actually consumed and products formed in the same reaction, with no excess reactant, unreacted material, side products, or incomplete yield, they can be used to find the balancing numbers in a chemical equation. This is a higher-tier method.

First convert every mass into moles. Then find the simplest whole-number ratio of the moles, which gives the balancing numbers in the equation.

The key formula is:

\frac{m}{M_r}

Here, $n$ is the amount in moles, $m$ is the mass in grams, and $M_r$ is the relative formula mass.

Why must reacting masses be converted into moles before comparison?