28. Gas Calculations: Volume & Moles

1. The Gas Volume Formula

At room temperature and pressure, one mole of any gas occupies a volume of 24 decimeters cubed (dm3).

Volume (dm3) = Number of Moles × 24

  • Calculating Volume: If you have 3.5 moles of a gas (like chlorine), multiply by 24:

    • 3.5 × 24 = 84 dm3.

  • Calculating Moles: If you have 60 dm3 of a gas (like oxygen), rearrange the formula:

    • Moles = Volume / 24

    • 60 / 24 = 2.5 moles.

2. Converting Mass to Gas Volume

If you are given the mass of a gas instead of moles, you must first convert mass to moles using the Mr (relative formula mass).

  • Step 1: Find Moles (Moles = Mass / Mr).

  • Step 2: Find Volume (Volume = Moles × 24).

  • Example: Find the volume of 27g of water vapor (H2O, Mr = 18).

    • Moles = 27 / 18 = 1.5 moles.

    • Volume = 1.5 × 24 = 36 dm3.

3. Using Molar Ratios for Gas Volumes

When reacting gases, the molar ratio in a balanced equation is directly proportional to the volume ratio.

  • The Quick Method: If you are only converting between volumes of gases, you don't need to calculate moles. Just use the ratio from the balanced equation.

  • Example Equation: N2 + 3H2 → 2NH3 (Ratio of N2 : NH3 is 1:2).

    • If you start with 18 dm3 of Nitrogen, it will produce 36 dm3 of Ammonia (18 × 2).

    • If you start with 4 dm3 of Nitrogen, it will react with 12 dm3 of Hydrogen (4 × 3).

4. Important Conditions

  • This specific calculation (using the number 24) only applies to gases at room temperature and pressure.

  • If temperature or pressure changes, the volume occupied by one mole of gas would change, but for GCSE exams, 24 is the standard number to use.