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3.12 Volumes of gases

The volume of one mole of any gas at room temperature and pressure, how to calculate gas volumes from masses and equations, and how to use Avogadro's law to find the volumes of gases that react.

Higher only Separate only AQA Edexcel OCR 1 min read

Molar volume

Key terms

  • Room temperature and pressure (RTP): 20 °C and 1 atmosphere pressure.
  • Molar volume: the volume of one mole of a gas. At RTP it is 24 dm3 (24 000 cm3) for any gas.

At the same temperature and pressure, one mole of any gas takes up the same volume, whatever the gas. This is because the molecules are very far apart compared with their size.

Three equal balloons, each 24 dm3, containing 1 mole of hydrogen (2 g), oxygen (32 g) and carbon dioxide (44 g), showing equal numbers of molecules but different masses
Three equal balloons, each 24 dm3, containing 1 mole of hydrogen (2 g), oxygen (32 g) and carbon dioxide (44 g), showing equal numbers of molecules but different masses
volume of gas (dm^3) = moles × 24

So moles of gas = volume (dm3) ÷ 24, or volume (cm3) ÷ 24 000.

Calculating gas volumes

Example 1: volume of 8.8 g of carbon dioxide (M_\mathrm{r} = 44) at RTP.

moles = 8.8 ÷ 44 = 0.20 mol, so volume = 0.20 × 24 = 4.8 dm3

Example 2: volume of carbon dioxide made when 10 g of calcium carbonate reacts with excess acid.

CaCO3 + 2HCl → CaCl2 + H2O + CO2

  • moles of CaCO3 = 10 ÷ 100 = 0.10 mol
  • ratio 1 : 1, so 0.10 mol of CO2
  • volume = 0.10 × 24 = 2.4 dm3

Avogadro's law

Equal volumes of different gases at the same temperature and pressure contain the same number of molecules.

So for reacting gases, the ratio of volumes is the same as the ratio of moles in the equation.

Example: N2 + 3H2 → 2NH3

30 cm3 of hydrogen reacts with 10 cm3 of nitrogen to make 20 cm3 of ammonia.

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