3.5 Use of amount of substance in relation to volumes of gases

- Avogadro's law states that equal amounts in moles of gases occupy the same volume under the same conditions of temperature and pressure.
- The volume of one mole of any gas at room temperature and pressure (20°C and 1 atmosphere pressure) is 24 dm³.
- This means, for example, 2 moles of oxygen will occupy 48 dm³, and 3 moles of hydrogen will occupy 72 dm³.
- The volumes of gaseous reactants and products can be calculated from the balanced equation for the reaction.

Calculating Volumes

Calculate the volume of a gas at room temperature and pressure from its mass and relative formula mass using:
Volume (dm³) = (mass (g) / relative formula mass) × 24
Calculate volumes of gaseous reactants and products from a balanced equation and a given volume of a gaseous reactant or product by:
- Finding the mole ratio from the equation.
- Using the ratio to determine the volume of other gases (since 1 mole = 24 dm³ at RTP).
You may need to rearrange the equation. For example, to make mass the subject in the equation above:
mass (g) = (Volume (dm³) × relative formula mass) / 24

Worked example

Suppose you have 48 g of oxygen gas (O₂) at room temperature and pressure. Calculate the volume it will occupy.
1. Find the relative formula mass (Mr) of O₂:
    - O₂: 16 × 2 = 32

2. Calculate the number of moles:
    - Moles = mass / Mr = 48 g / 32 = 1.5 mol

3. Calculate the volume using the molar volume at RTP (24 dm³ per mole):
    - Volume = moles × 24 = 1.5 × 24 = 36 dm³

Answer:
48 g of oxygen gas will occupy 36 dm³ at room temperature and pressure.