4.3.5Volumes of gasesHigher tier
Chemistry only, Higher tier — not assessed in Combined Science: Trilogy.
Equal amounts in moles of gases occupy the same volume under the same conditions of temperature and pressure.
That is a stronger statement than it looks. It does not matter which gas it is: one mole of hydrogen and one mole of carbon dioxide take up the same volume, even though one weighs 2 g and the other 44 g. In a gas the particles are so far apart that the size of the particle makes almost no difference to the space the gas fills.
The volume of one mole of any gas at room temperature and pressure — 20 °C and 1 atmosphere pressure — is 24 dm³.
That gives one relationship to learn, and two rearrangements of it:
volume in dm³ = moles × 24 moles = volume in dm³ ÷ 24
You should be able to change the subject of a mathematical equation, and to substitute numerical values into algebraic equations using appropriate units for physical quantities — so be ready to use it either way round.
Worked example
Calculate the volume of 8.0 g of oxygen gas at room temperature and pressure. (Ar of O = 16.)
- Oxygen gas is O₂, so its Mr = 2 × 16 = 32.
- moles = mass ÷ Mr = 8.0 ÷ 32 = 0.25 mol.
- volume = moles × 24 = 0.25 × 24.
- Give the unit: the molar volume is in dm³, so the answer is in dm³.
Answer: 6.0 dm³
Common mistake
Use the formula of the gas as it exists. Oxygen, hydrogen, nitrogen and chlorine are all diatomic — O₂, H₂, N₂, Cl₂ — so dividing by the atomic mass instead of the molecular mass doubles the number of moles and doubles the volume.
- Molar gas volume
- the volume occupied by one mole of any gas; equal amounts in moles of gases occupy the same volume under the same conditions of temperature and pressure
4.3.5Gas volumes from equationsHigher tier
Chemistry only, Higher tier — not assessed in Combined Science: Trilogy.
The volumes of gaseous reactants and products can be calculated from the balanced equation for the reaction.
You should be able to:
• calculate the volume of a gas at room temperature and pressure from its mass and relative formula mass • calculate volumes of gaseous reactants and products from a balanced equation and a given volume of a gaseous reactant or product.
The second is quicker than it looks. Because equal moles of any gas occupy equal volumes, the mole ratio in the equation is also the volume ratio — as long as every substance being compared is a gas at the same temperature and pressure. There is no need to convert to moles and back.
Worked example
N₂ + 3H₂ → 2NH₃. What volume of ammonia is made from 60 cm³ of nitrogen, with hydrogen in excess, at the same temperature and pressure?
- All three substances are gases at the same conditions, so the mole ratio is also the volume ratio.
- The ratio of nitrogen to ammonia in the equation is 1 : 2.
- So the volume of ammonia is twice the volume of nitrogen.
- 2 × 60 cm³ = 120 cm³. No conversion to moles is needed.
Answer: 120 cm³ of ammonia
Worked example
CaCO₃ → CaO + CO₂. Calculate the volume of carbon dioxide produced at room temperature and pressure when 5.0 g of calcium carbonate decomposes completely. (Mr of CaCO₃ = 100.)
- Here the reactant is a solid, so the volume shortcut does not apply — go through moles.
- moles of CaCO₃ = 5.0 ÷ 100 = 0.050 mol.
- The ratio in the equation is 1 : 1, so moles of CO₂ = 0.050 mol.
- volume = moles × 24 = 0.050 × 24 = 1.2 dm³.
- If cm³ are wanted, multiply by 1000: 1200 cm³.
Answer: 1.2 dm³, or 1200 cm³, of carbon dioxide
Common mistake
The volume ratio shortcut only works between gases. If a solid or a solution appears in the comparison, as in the second example, you must convert to moles first.
Before you practise
- This sub-topic is chemistry only and Higher tier only.
- Equal amounts in moles of gases occupy the same volume under the same conditions of temperature and pressure.
- One mole of any gas occupies 24 dm³ at room temperature and pressure — 20 °C and 1 atmosphere.
- volume in dm³ = moles × 24, and moles = volume in dm³ ÷ 24.
- 1 dm³ = 1000 cm³.
- Between gases at the same conditions, the mole ratio in the equation is also the volume ratio, so no conversion is needed.
- Remember that oxygen, hydrogen, nitrogen and chlorine are diatomic when calculating their moles from a mass.