Chemistry

The mole

# Calculating molar volume

• The molar volume is the volume occupied by one mole of a gas.
• The units used for the molar volume are l mol-1 (litres per mole).

## Calculating molar volume from mass

### Example:

976 cm3 of oxygen was found to have a mass of 1.3 g

Calculate the molar volume of oxygen, under these conditions.

Remember that, the molar volume is the volume occupied by one mole of oxygen, O2.

GFM of oxygen, O2, is 32.0 g.

Volume of 1 g = 976 ÷ 1.3

Hence, 32 g = (976 ÷ 1.3) × 32 = 24024 cm3

Answer: 24.0 is the volume of 32.0 g of O2. So, the molar volume of oxygen is 24.0 l mol-1, under these conditions.

The above can be carried out for other gases, under the same conditions of temperature and pressure. The molar volume is the same for all gases, at the same temperature and pressure.

## Calculating molar volume from density

The molar volume of a gaseous element can be calculated from its density.

The SQA data booklet shows the densities of selected elements.

Density figures are quoted using the units, g cm-3, and are measured at standard temperature and pressure (0°C and one atmosphere).

Question
Calculate the molar volume of argon, at standard temperature and pressure (s.t.p), using the density value quoted on page 3 of the SQA data booklet.

Density of argon = 0.0018 g cm-3.

GFM of argon = 40.0 g

Find: m litres from 40.0 g of Ar

Link: 1 cm3 ↔ 0.0018 g

Convert: 0.001 litre ↔ 0.0018 g

Proportion: 0.0018 g of Ar has a volume of 0.001 litre. Hence, 40 g has a volume of:

m = (0.001 × 40.0) ÷ 0.0018

m = 22.2

Answer: 22.2 litres is the volume of 40.0 g of argon. So, the molar volume of argon is 22.2 l mol-1, under these conditions.

In this example, the molar volume of argon was calculated as 22.2 l mol-1, under conditions of standard temperature and pressure (0°C and one atmosphere pressure). If measurements had been made under different conditions, the actual value for the molar volume of argon calculated would be different.

The actual value for the molar volume of a gas depends on the conditions of temperature and pressure used when making the measurement.

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