How to find the volume of gas in a reaction

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Avogadro’s law is the basis for calculating the volume of gas produced in a reaction:  equal volumes of gases at constant temperature and constant pressure contain the same number of molecules.

The volume occupied by 1 mole of a gas at a particular temperature and pressure is known as its molar volume.

  • At standard temperature and pressure (273K, 101kPa) the molar volume is 22.4 dm3
  • At room temperature and pressure (298K, 101kPa) the molar volume is 24.0 dm3

The key is to remember that when we are working with gases, it’s all about molar ratios, which makes calculations simple and logical 😊.

E.g. Determine the volume of carbon dioxide produced when 8.0g of barium carbonate decomposes at room temperature and pressure.

BaCO3(s) ⇾ BaO(s) + CO2(g)

There are four steps to tackling this calculation …

  1. How many moles of BaCO3 do we have?
  1. What is the molar ratio of BaCO3 : CO2 from the balanced equation?
  1. How many moles of CO2 did we produce?
  1. What is the volume of this number of moles at RTP?

If the reaction only involves gases, then we can essentially substitute the molar ratio for a volume ratio because we know that one mole of any gas occupies the same volume (24.0dm3 at RTP). We are of course assuming that all gas measurements are made at the same temperature and pressure.

E.g. N2(g) + 3H2(g) ⇾ 2NH3(g)

Ratio is 1 mole of N2 : 3 moles of H2 : 2 moles of NH3 which is the same as saying the ratio is 1 volume of N2 : 3 volumes of H2 : 2 volumes of NH3.

If we started the reaction with 20cm3 of N2, then it would react with 60cm3 of H2 and the reaction would produce 40cm3 of NH3.

Practice questions

  1. What volume of carbon dioxide if produced when 6.0g of calcium carbonate react with excess hydrochloric acid at room temperature and pressure?

CaCO3(s) + 2HCl(aq) ⇾ CaCl2(aq) + CO2(g) + H2O(g)

  1. What volume of oxygen is needed to completely react with 10.0 cm3 of hydrogen at room temperature and pressure?

½O2(g) + H2(g) ⇾ H2O(g)

  1. Calculate the volume of hydrogen produced when 1.4g of magnesium reacts with excess sulphuric acid.

Mg(s) + H2SO4(aq) ⇾ MgSO4(aq) + H2(g)

  1. Determine the formula of a gaseous hydrocarbon if 100cm3 produces 300cm3 of carbon dioxide when it reacts completely with 500cm3 oxygen.

Answers