In short: In the ideal gas equation pV = nRT, use pressure in Pa, volume in m³, amount in mol and temperature in K. Then R = 8.31 J K⁻¹ mol⁻¹ works. The most common slip is leaving the volume in dm³ or cm³.
Gas questions are full of easy marks, and a wrong unit throws them away even when the method is perfect. The fix is one habit: convert every value before it goes into the equation.
Spot the mistake
In the clip, there are five quantities, each with its unit: pressure, volume, amount of substance, temperature and the gas constant. Four are right.
The mistake is the volume, given in dm³. The gas constant R = 8.31 J K⁻¹ mol⁻¹ only works with the volume in m³. Pressure must be in Pa, amount in mol and temperature in K.
Rich's tip: Make sure you convert every value before it goes into the equation. Simple as that.
The equation and its units
pV = nRT
- p: pressure, in Pa (pascals)
- V: volume, in m³
- n: amount of substance, in mol
- R: the gas constant, 8.31 J K⁻¹ mol⁻¹
- T: temperature, in K (kelvin)
Why the units have to match
The gas constant is in joules, and a joule is a pascal multiplied by a cubic metre. So if p is in Pa and V is in m³, then pV comes out in J, and it matches nRT. Use dm³ and the answer is out by a factor of 1000.
Unit conversions
- cm³ to m³: multiply by 10⁻⁶
- dm³ to m³: multiply by 10⁻³
- kPa to Pa: multiply by 10³
- °C to K: add 273
A quick check for volume: 1 dm³ is a litre, and 1 m³ is 1000 of them. So 1 dm³ is 0.001 m³.
Worked example
Question: What amount of gas, in mol, is in 250 cm³ at 100 kPa and 298 K?
- Convert the volume: 250 cm³ × 10⁻⁶ = 2.50 × 10⁻⁴ m³
- Convert the pressure: 100 kPa × 10³ = 1.00 × 10⁵ Pa
- Rearrange: n = pV ÷ RT
- Substitute: n = (1.00 × 10⁵ × 2.50 × 10⁻⁴) ÷ (8.31 × 298)
That gives n = 0.0101 mol (3 significant figures).
Rearranging
Rearrange before you substitute, then put the numbers in.
- Amount: n = pV ÷ RT
- Volume: V = nRT ÷ p
- Temperature: T = pV ÷ nR
If you work out V, the answer is in m³. Convert it back to cm³ or dm³ if the question asks for that.
Checking your answer
Ask whether the answer is sensible. One mole of an ideal gas is about 24 dm³ at room temperature and pressure, so a few hundred cm³ of gas should be a small fraction of a mole, as in the example above.
Common mistakes
- Leaving the volume in cm³ or dm³, or the pressure in kPa. This is the big one.
- Using the temperature in °C instead of K.
- Converting only some of the values.
- Rounding the answer in the middle of the calculation. Keep the full calculator value until the end.
- Quoting the final answer to the wrong number of significant figures. Match the data in the question.
If you want to practise gas calculations, Dexter, the A Level Chemistry tutor I built, can set you pV = nRT questions on the gas calculations in your course and show you where a unit went wrong.