The ideal gas equation — AQA A-Level Chemistry
Test yourself on The ideal gas equation with AQA A-Level practice questions.
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The ideal gas equation explained
The ideal gas equation is pV = nRT, and it only works when every quantity is in base SI units.
Read the full explanation
Pressure must be in pascals, so kilopascals are multiplied by 1000. Volume must be in cubic metres, so cubic centimetres are divided by 10⁶ and cubic decimetres by 1000. Temperature must be in kelvin, so add 273 to a Celsius value. The gas constant R is 8.31 J K⁻¹ mol⁻¹, and its units are the check: joules per kelvin per mole only cancel correctly when pressure is in pascals and volume in cubic metres. The equation applies to an ideal gas, in which the particles have negligible volume and no forces between them.
Students should be able to: use the equation in calculations.
A typical calculation chains the gas equation to a mole calculation. Given a mass of propanone, first find the amount using n = mass ÷ molar mass. Then convert the data: 95 °C becomes 368 K and 103 kPa becomes 103000 Pa. Rearranging gives V = nRT/p, which returns a volume in cubic metres; multiplying by 10⁶ converts to the cubic centimetres the question wanted, about 75 cm³. Working the other way, a measured volume of gas gives an amount, and combining that amount with a measured mass gives a molar mass. Each conversion and the rearrangement carry their own marks, so an arithmetic slip at the end still leaves most of them available.
Your focus
- Convert pressure, volume and temperature data into the SI units required before substituting into the gas equation.
- Rearrange pV = nRT to make any one of its variables the subject.
- Explain how the units of the gas constant determine the units in which the other quantities must be expressed.
Show all 6 objectives
- Calculate the volume occupied by a known mass of a gas at a stated temperature and pressure, giving the answer in cubic centimetres.
- Determine the relative molecular mass of a gas from its mass, volume, temperature and pressure.
- Identify which conversions are needed before substitution by inspecting the units given in the question.
The ideal gas equation exam tips
Marking Points
- one mark for converting a temperature in degrees Celsius into kelvin by adding 273
- one mark for converting a pressure in kilopascals into pascals
- one mark for converting a volume into cubic metres before substituting
- one mark for a correct rearrangement of pV = nRT for the quantity required
- one mark for the amount in moles obtained from mass divided by molar mass
- one mark for converting both the temperature and the pressure into SI units
- one mark for the correct rearrangement of the gas equation for the required quantity
- one mark for the final answer converted into the unit demanded by the question
Examiner Tips
- 💡List p, V, n, R and T down the page with their converted values before substituting anything.
- 💡Use the units of R printed in the question to confirm which units each other quantity needs.
- 💡Rearrange the equation symbolically first, then substitute; it is easier to spot an inverted fraction that way.
- 💡Show the substituted equation in full; substitution marks are awarded even when the final value is wrong.
- 💡Convert the answer to the requested unit as a separate final line so it is clearly visible.
- 💡Sense-check the result: roughly one mole of any gas occupies about 24 dm³ near room temperature and pressure.
Common Mistakes
- substituting a temperature in degrees Celsius
- using kilopascals with a gas constant expressed in joules
- dividing a volume in cubic centimetres by 1000 instead of by 10⁶
- reporting a volume in cubic metres when the question asked for cubic centimetres
- leaving the answer in cubic metres when cubic centimetres were requested
- rounding the amount in moles to one or two significant figures early and carrying the error through
- using the gas constant in joules alongside a pressure left in kilopascals
- using the molar mass of the wrong species, for example the product rather than the gas measured