# Moles and masses - Higher

There is a relationship between a (Ar) or (Mr), and the of one of a substance:

The mass of 1 mol of a substance is its Ar or Mr in grams (g).

Some examples are given in the table below.

SubstanceFormulaAr or MrMass of 1 mol (g)
CalciumCa40.140.1
OxygenO22 × 16.0 = 32.032.0
Calcium carbonateCaCO340.1 + 12.0 + (3 × 16.0) = 100.1100.1

This relationship is useful because it makes it possible to work out the mass of reactants needed to make a particular mass of product. It is also possible to work out which reactant will be used up.

## Calculating number of moles

The number of moles of a given mass substance is calculated using:

number of moles = $$\frac{mass~(g)}{relative~formula~mass (g)}$$

Use Ar instead of Mr for metals or separate .

Question

Calculate the number of moles of carbon atoms in 6.0 g of carbon. (Relative atomic mass: C = 12.0)

number of moles = $$\frac{mass}{A_r}$$

number of moles = $$\frac{6.0}{12.0}$$

= 0.50 mol

## Calculating masses

To calculate the mass if given the number of moles and the relative formula mass, the equation must be rearranged to make mass the subject.

The mass of a given number of moles of substance is calculated using: mass (g) = relative formula mass (g) × number of moles

One way to remember this is ‘mass equals mister mole’.

Question

Calculate the mass of 0.25 mol of carbon dioxide molecules. (Relative formula mass: CO2 = 44.0)

mass = 44.0 × 0.25

= 11 g

The calculation is the same if a substance is a metal or exists as separate atoms, but its Ar is used instead of an Mr.

### Example

Question

Calculate the mass of 0.125 moles of iron. (Relative atomic mass: Fe = 55.8)

mass = 55.8 × 0.125

= 6.98 g (to 3 significant figures)