Volume equations in chemistry

There are two main volume equations in GCSE Chemistry. For a gas at room temperature and pressure, volume (dm³) = moles × 24, because one mole of any gas takes up 24 dm³. For a solution, volume (dm³) = moles ÷ concentration (mol/dm³). So 0.25 mol of carbon dioxide gas fills 0.25 × 24 = 6.0 dm³, and 0.020 mol of acid at 0.50 mol/dm³ needs 0.020 ÷ 0.50 = 0.040 dm³, which is 40 cm³. At A-level, the ideal gas equation, pV = nRT, gives a gas's volume at any temperature and pressure.

Volume of a gas: V = n × 24

AQA's GCSE Chemistry specification states that the volume of one mole of any gas at room temperature and pressure (20 °C and 1 atmosphere pressure) is 24 dm³. This is the molar volume. It does not matter which gas: equal amounts in moles of gases take up the same volume under the same conditions of temperature and pressure.

Remember 1 dm³ = 1000 cm³. If the volume is in cm³, divide by 24 000 to get moles.

Volume of a solution: V = n ÷ c

This comes from the concentration equation, concentration = moles ÷ volume. AQA's specification asks students to explain how the concentration of a solution in mol/dm³ is related to the mass of solute and the volume of the solution. The same rearrangement gives the volume needed in a titration.

Volumes from burettes and pipettes are in cm³, so divide by 1000 to get dm³ before using these equations.

Volume equation worked examples

Example 1: moles to gas volume

What volume does 0.25 mol of carbon dioxide occupy at room temperature and pressure?

Example 2: mass to gas volume

What volume does 8.8 g of carbon dioxide (Mr = 44) occupy at room temperature and pressure?

First the moles: 8.8 ÷ 44 = 0.20 mol. Then:

Example 3: gas volume to moles

A reaction gives off 1800 cm³ of oxygen at room temperature and pressure. How many moles is that?

Example 4: gas volumes from an equation

Nitrogen and hydrogen react to make ammonia: N₂(g) + 3H₂(g) → 2NH₃(g). What volume of hydrogen reacts with 30 cm³ of nitrogen, and what volume of ammonia forms?

Because equal moles of gases have equal volumes, the volumes are in the same ratio as the moles in the equation, 1 : 3 : 2. So 30 cm³ of nitrogen reacts with 3 × 30 = 90 cm³ of hydrogen to make 2 × 30 = 60 cm³ of ammonia, all measured at the same temperature and pressure.

Example 5: volume of a solution

What volume of 0.50 mol/dm³ hydrochloric acid contains 0.020 mol of HCl?

Example 6: a titration volume

25.0 cm³ of 0.100 mol/dm³ sodium hydroxide is neutralised by hydrochloric acid of concentration 0.125 mol/dm³. NaOH + HCl → NaCl + H₂O. What volume of acid is needed?

Moles of NaOH = 0.100 × 25.0 ÷ 1000 = 0.00250 mol. The ratio is 1 : 1, so 0.00250 mol of HCl is needed.

The Molarity Calculator links concentration, moles, mass and volume, and the Stoichiometry Calculator works out reacting amounts from a balanced equation.

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The ideal gas equation: volume at any conditions (A-level)

The 24 dm³ figure only works at room temperature and pressure. At A-level, the ideal gas equation gives the volume at any temperature and pressure:

AQA's A-level specification uses pV = nRT with the variables in SI units: p in pascals, V in m³, n in moles, T in kelvin, and the gas constant R = 8.31 J K⁻¹ mol⁻¹, which is given, not recalled.

Example 7: volume from pV = nRT

Find the volume of 0.50 mol of gas at 300 K and 100 kPa.

That is 12.5 dm³: multiply m³ by 1000 to get dm³.

Common mistakes

• Mixing cm³ and dm³. Divide cm³ by 1000 to get dm³. Use 24 000 for gas volumes in cm³.
• Using 24 dm³ at other conditions. It only applies at room temperature and pressure.
• Using the molar volume for a solid or liquid. 24 dm³ per mole is for gases only.
• Forgetting the ratio from the balanced equation in reacting volume questions.
• Wrong units in pV = nRT. Pressure in Pa (not kPa), volume in m³ (not dm³), temperature in K (not °C).

Practise chemistry in a short timed paper

GCSE Chemistry Higher and A-level Chemistry: Year 1 each give you a short timed paper every day, with 8 questions worth 25 to 35 marks across the course, so moles, volumes and concentrations turn up regularly but not in every paper. Our guide to what a mole is covers the amount of substance these equations rely on.

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Chemistry · Moles and quantitiesConcentration calculator: molarity, mass and volumeFind the concentration of a solution in mol/dm³ (mol/L) or g/dm³, the moles or mass in it, or the mass to weigh out, with worked examples.