# Mole calculations

This equation shows how , number of and are related:

number of moles = mass ÷ relative formula mass

This can be rearranged to find the mass if the number of moles and molar mass (its relative formula mass in grams) are known. It can also be rearranged to find the molar mass if the mass and number of moles are known.

## Finding the number of moles

Question

Calculate the number of moles of carbon dioxide molecules in 22 g of CO2.

Ar (relative atomic mass) of C = 12, Ar of O = 16

Mr (relative formula mass) of carbon dioxide = 12 + 16 + 16 = 44

number of moles = 22 ÷ 44 = 0.5 mol

## Finding the mass

Question

Calculate the mass of 2 mol of carbon dioxide (CO2).

mass = number of moles × relative formula mass = 2 × 44 = 88 g

## Finding the relative formula mass

Question

10 mol of carbon dioxide has a mass of 440 g. What is the relative formula mass of carbon dioxide?

relative formula mass = mass ÷ number of moles = 440 ÷ 10 = 44

## Reacting masses

You can calculate the mass of a or using the idea of moles, a balanced equation and relevant Ar values.

### Example

Sulfuric acid and sodium hydroxide react together to make sodium sulfate and water:

H2SO4 + 2NaOH → Na2SO4 + 2H2O

Question

Calculate the mass of sodium sulfate made when 20 g of sodium hydroxide reacts with excess sulfuric acid. (Ar of H = 1, Ar of O = 16, Ar of Na = 23, Ar of S = 32)

Mr of NaOH = 23 + 16 + 1 = 40

Mr of Na2SO4 = 23 + 23 + 32 + 16 + 16 + 16 + 16 = 142

Number of moles of NaOH = mass ÷ relative formula mass = 20 ÷ 40 = 0.5 mol

From the equation, 2 mol of NaOH reacts with 1 mol of Na2SO4, so 0.5 mol of NaOH will react with 0.25 mol of Na2SO4.

mass of Na2SO4 = moles × relative formula mass = 0.25 × 142 = 35.5 g

The example above could also be tackled like this:

$mass \enspace of \enspace Na_{2}SO_{4} = \frac{20}{2 \times 40} \times 142 = 35.5g$