Gas Volumes Triple Higher
The volume of any gas is directly proportional to the number of moles of gas, at constant temperature and pressure. So under the same conditions, equal numbers of moles of different gases occupy the same volume.
At room temperature and pressure (RTP) — 20 °C and 1 atmosphere — one mole of any gas occupies 24 dm³ (24,000 cm³). This is the molar gas volume and you need to learn this number.
number of moles of gas = volume of gas (dm³)24
If the volume is given in cm³ instead of dm³, divide by 24,000 instead of 24.
Because equal moles mean equal volumes, the big numbers in a balanced equation also give the ratio of gas volumes. For example, in the complete combustion of propane the volumes are in the same 1 : 5 : 3 ratio as the moles:
C3H8 + 5O2 → 3CO2 + 4H2O
so 150 cm³ of propane needs 5 × 150 = 750 cm³ of oxygen, and makes 3 × 150 = 450 cm³ of carbon dioxide.
Read the units the question asks for. If you are given a mass, convert it to moles first (mass ÷ Mr), then multiply by 24 to get a volume in dm³.
(a) Volume from mass. Calculate the volume of 154 g of nitrogen gas, N2, at RTP. (Mr N2 = 28.)
- Mass → moles: 154 ÷ 28 = 5.5 mol.
- Moles → volume (× 24): 5.5 × 24 = 132 dm³.
(b) Volumes from an equation. 50 cm³ of methane is burned completely. What volume of oxygen reacts, and what volume of carbon dioxide is produced?
CH4 + 2O2 → CO2 + 2H2O
Equal volumes contain equal moles, so the big numbers give the volume ratio directly: O2 = 2 × 50 = 100 cm³, and CO2 = 1 × 50 = 50 cm³. (The water is liquid at RTP, so it is not counted as a gas volume.)
🧪 Exam-style questions
Calculate the volume occupied by 8 g of oxygen gas, O2, at RTP.Mr(O2) = 32. Molar gas volume = 24 dm³/mol.
Show answer
- moles of O2 = mass ÷ Mr = 8 ÷ 32 = 0.25 mol 1 mark
- volume = moles × 24 = 0.25 × 24 = 6 dm³ 1 mark
100 cm³ of methane is burned completely. What volume of oxygen reacts with it? (All gas volumes measured at the same temperature and pressure.)
Show answer
- Equal volumes of gas contain equal moles, so the big numbers give the volume ratio directly: CH4 : O2 = 1 : 2.
- volume of O2 = 2 × 100 = 200 cm³ 1 mark