The ideal gas equation
The ideal gas equation links the pressure, volume and temperature of a gas to the number of moles it contains. Nearly every mistake with it is a unit, so the conversions come first.
Part 1 of 3: Learn it
In short
- pV = nRT, with R = 8.31 J K⁻¹ mol⁻¹.
- p in Pa, V in m³, T in K: kPa × 1000, cm³ × 10⁻⁶, dm³ × 10⁻³, °C + 273.
- Rearranged for Mᵣ: Mᵣ = mRT ÷ pV.
Where this is in your specification
Spec points: AQA 7405 3.1.2.3, OCR A H432 2.1.3, Edexcel 9CH0 Topic 5
| Board | Topic: Atomic structure and amount of substance |
|---|---|
| AQA 7405 | 3.1.1 and 3.1.2 |
| Edexcel 9CH0 | Topics 1 and 5 |
| OCR H432 | 2.1.1 to 2.1.3, 2.2.1 and 3.1.1 |
| Higher C813 76 | 1(a) Periodicity; 3(a) Getting the most from reactants |
The equation and its units
| Quantity | SI unit | Conversion |
|---|---|---|
| Pressure p | Pa | 1 kPa = 1000 Pa |
| Volume V | m³ | 1 dm³ = 10⁻³ m³; 1 cm³ = 10⁻⁶ m³ |
| Temperature T | K | T(K) = T(°C) + 273 |
| Amount n | mol |
Why kelvin
The equation says volume is proportional to absolute temperature at constant pressure. On the Celsius scale zero is arbitrary, so doubling 20 °C to 40 °C does not double the volume; doubling 293 K to 586 K does.
Finding Mᵣ
Use pV = nRT to find n from the measured pressure, volume and temperature, then Mᵣ = mass ÷ n. This is how the relative molecular mass of a volatile liquid is found: evaporate a known mass and measure the gas volume.
Convert 25 °C to kelvin.
Show the answer
298 K.
Part 2 of 3: See it worked
Worked examples
Example 1
How many moles of gas are in 2.00 dm³ at 100 kPa and 300 K?
- p = 1.00 × 10⁵ Pa, V = 2.00 × 10⁻³ m³
- n = pV ÷ RT = (1.00 × 10⁵ × 2.00 × 10⁻³) ÷ (8.31 × 300)
- = 200 ÷ 2493
Answer: 0.0802 mol.
Example 2
0.40 g of a gas occupies 250 cm³ at 101 kPa and 298 K. Find its Mᵣ.
- V = 2.50 × 10⁻⁴ m³, p = 1.01 × 10⁵ Pa
- n = (1.01 × 10⁵ × 2.50 × 10⁻⁴) ÷ (8.31 × 298) = 0.01020 mol
- Mᵣ = 0.40 ÷ 0.01020
Answer: 39 (2 s.f.), which fits argon.
Common mistakes
- Using temperature in °C.
- Converting cm³ to m³ by dividing by 1000 instead of 10⁶.
- Leaving pressure in kPa.
- Forgetting to convert an answer in m³ back to the units the question asks for.
Convert 500 cm³ to m³.
Show the answer
5.00 × 10⁻⁴ m³.
Part 3 of 3: Test yourself
Check yourself
Answer each one in your head or on paper first, then open it to check.
Convert 25 °C to kelvin.
298 K.
Convert 500 cm³ to m³.
5.00 × 10⁻⁴ m³.
What happens to the volume of a fixed amount of gas at constant pressure when its kelvin temperature doubles?
It doubles.
Jobs that use this
Each link opens the job profile on the National Careers Service (England). In the rest of the UK: My World of Work (Scotland), Careers Wales, nidirect careers (Northern Ireland).
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