A sealed container of volume 2.4 x 10−3 m3 holds 0.15 mol of an ideal gas at 320 K. Calculate the gas pressure. Use R = 8.31 J/(mol K).
[3 marks]
Total for this question: 3
All equation deep-dives
Ideal gases and kinetic theory
Thermal physics
AQA 7408
In the data booklet
ORIGINAL
p V = n R T and 1/2 m <c2> = 3/2 k T
Temperature must be absolute, and the speed relationship uses mean square speed before you take the square root.
Board and spec code confirmed against AQA 7408 · registry checked 2026-07-11How this checking works
Know the equation
| Symbol | Quantity | Unit |
|---|---|---|
| p | gas pressure | Pa |
| V | gas volume | m3 |
| n | amount of gas | mol |
| R | molar gas constant | J/(mol K) |
| T | absolute temperature | K |
| m | mass of one molecule | kg |
| <c2> | mean square molecular speed | m2/s2 |
| k | Boltzmann constant | J/K |
Rearrangements
- p = n R T / V
- n = p V / (R T)
- T = p V / (n R)
- c(rms) = sqrt(3 k T / m)
Apply it — mark your own working
Work each one out on paper first, then reveal the mark scheme and tick the marks you actually earned. That is exactly how you should mark past papers.
Q1
Do the calculation on paper first — then mark it.
Q2
A nitrogen molecule has mass 4.65 x 10−26 kg. Calculate the root mean square speed of nitrogen molecules at 300 K. Use k = 1.38 x 10−23 J/K.
[3 marks]
Total for this question: 3
Do the calculation on paper first — then mark it.
Where the marks get lost
- Using temperature in degrees Celsius instead of kelvin; T/K = theta/C + 273.15.
- Leaving volume in dm3 or cm3 instead of converting to m3.
- Stopping at <c2>; root mean square speed is sqrt(<c2>), so take the square root at the end.
Exam tip: Check dimensions: R T has units J/mol, so n R T is energy in joules; p V also has units Pa m3 = J.
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