Gas volumes

At the same temperature and pressure, one mole of any gas fills the same volume. At room temperature and pressure (about 20°C and 1 atmosphere) this molar volume is 24 dm³; at STP (0°C and 1 atmosphere) it is 22.4 dm³. So you can turn volumes of gases into moles, and use balanced equations to find the volumes of gases that react or form.

Key facts

  • One mole of any gas fills 24 dm³ (24,000 cm³) at room temperature and pressure (RTP).
  • At STP (0°C and 1 atmosphere) one mole of gas fills 22.4 dm³: CAPS and US courses use this value.
  • volume of gas = moles × molar volume, so moles = volume ÷ molar volume.
  • Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules (Avogadro’s law).
  • So for gases, the ratio of volumes is the same as the mole ratio in the balanced equation.
  • Change cm³ into dm³ by dividing by 1000.

Worked examples

Example 1

What volume does 8 g of oxygen, O2, fill at room temperature and pressure? (Aᵣ: O = 16; molar volume 24 dm³)

  1. Mᵣ of O2. 2 × 16 = 32
  2. Moles of oxygen. 8 ÷ 32 = 0.25 mol
  3. Multiply by the molar volume. 0.25 × 24 = 6 dm³

Answer: 6 dm³

Example 2

What volume of carbon dioxide forms at room temperature and pressure when 5 g of calcium carbonate reacts with excess acid? CaCO3 + 2HCl → CaCl2 + H2O + CO2 (Mᵣ of CaCO3 = 100)

  1. Moles of calcium carbonate. 5 ÷ 100 = 0.05 mol
  2. The ratio CaCO3 : CO2 is 1 : 1, so 0.05 mol of CO2 forms.
  3. Volume at room temperature and pressure. 0.05 × 24 = 1.2 dm³ = 1200 cm³

Answer: 1.2 dm³ (1200 cm³)

Example 3

What volume of oxygen is needed to burn 50 cm³ of methane? CH4 + 2O2 → CO2 + 2H2O (all volumes at the same temperature and pressure)

  1. For gases at the same temperature and pressure, volumes are in the same ratio as moles.
  2. The equation gives CH4 : O2 = 1 : 2.
  3. So double the volume of methane. 50 × 2 = 100 cm³

Answer: 100 cm³