Mole ratios with gases and gas volumes (HT)
For gases, the volume at the same temperature and pressure is proportional to the number of moles (Avogadro's law). At room temperature and pressure (RTP, 20 °C and 1 atm), one mole of any gas occupies 24 dm³.
Avogadro's law
Equal volumes of any gas at the same T and P contain the same number of molecules.
So at RTP: 1 mole = 24 dm³ (or 24,000 cm³).
This is true for any gas — H₂, O₂, CO₂, He — regardless of its molecular size.
Working with gas volumes
moles of gas = volume (dm³) ÷ 24 (at RTP) volume (dm³) = moles × 24 (at RTP)
✦Worked example— Worked examples
Example 1
What volume does 0.25 mol of CO₂ occupy at RTP?
V = 0.25 × 24 = 6 dm³
Example 2
How many moles in 480 cm³ of O₂ at RTP?
V = 480/1000 = 0.48 dm³ moles = 0.48 / 24 = 0.02 mol
Example 3 — combined with stoichiometry
What volume of CO₂ is produced at RTP when 5.0 g of CaCO₃ is heated?
CaCO₃ → CaO + CO₂. M_r CaCO₃ = 100.
- moles CaCO₃ = 5.0/100 = 0.05 mol
- moles CO₂ = 0.05 mol (1:1)
- V CO₂ = 0.05 × 24 = 1.2 dm³ (or 1200 cm³)
Example 4 — gas + gas
What volume of O₂ reacts with 100 cm³ of CH₄ at RTP?
CH₄ + 2O₂ → CO₂ + 2H₂O.
Mole ratio CH₄ : O₂ = 1 : 2. So volumes are in 1 : 2 ratio at the same T and P.
V O₂ = 2 × 100 = 200 cm³.
(For gas + gas problems you don't even need to convert to moles — volumes scale directly.)
Why volumes scale by moles for gases
Avogadro's law: at the same temperature and pressure, equal volumes of gas contain equal numbers of particles. Particle size and mass don't matter — gas particles are far apart, so each molecule "uses" the same volume.
✦Worked example— Worked example — practical
In a school experiment, marble chips (CaCO₃) react with hydrochloric acid: CaCO₃ + 2HCl → CaCl₂ + H₂O + CO₂
A student uses 1.0 g of CaCO₃ in excess HCl. What volume of CO₂ is produced at RTP?
- moles CaCO₃ = 1.0/100 = 0.01 mol
- moles CO₂ = 0.01 mol
- V = 0.01 × 24 = 0.24 dm³ = 240 cm³
⚠Common mistakes
- Using 24 cm³ instead of 24 dm³. 1 mole = 24,000 cm³ if you're working in cm³.
- Forgetting the mole ratio. A 1 : 2 ratio means the gas volume of one is twice the other.
- Working at non-RTP without adjusting. The 24 dm³/mol value only applies at RTP. (Outside GCSE, use ideal gas equation pV = nRT.)
- Mixing units in a single calculation.
Links
Builds on C3.4 (moles), C3.5 (mole ratios). Useful in C5 (energy from gases), C6.1 (rates of gas-producing reactions) and C9.1–C9.5 (atmospheric chemistry).
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