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AS · Practice questions · Ideal gases and pV = nRT

Convert, then substitute.

Six original Cambridge-style questions on the gaseous state: the kinetic model, deviations from ideal behaviour and calculations with pV = nRT.

Original questions All questions on this page are original work, written in the Cambridge AS & A Level style. They are not from past papers. They test the same concepts and skills the syllabus rewards.
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SI units every time.

01
Recall
[2 marks]

State two assumptions of the kinetic theory that apply to an ideal gas.

  • Any two of: the molecules have negligible volume; there are no intermolecular forces; collisions are perfectly elastic; the molecules move randomly and rapidly. ✓
02
Calculation
[2 marks]

Calculate the pressure, in kPa, of 0.0200 mol of gas in a 500 cm3 container at 350 K. (R = 8.31 J K−1 mol−1)

  • V = 500 × 10−6 = 5.00 × 10−4 m3. ✓
  • p = nRT ÷ V = 0.0200 × 8.31 × 350 ÷ 5.00 × 10−4 = 1.16 × 105 Pa = 116 kPa. ✓
03
Calculation
[2 marks]

1.00 g of a gaseous element occupies 0.600 dm3 at 20 °C and 100 kPa. Calculate its Mr and suggest its identity.

  • M = mRT ÷ pV = 1.00 × 8.31 × 293 ÷ (1.00 × 105 × 6.00 × 10−4) = 40.6. ✓
  • An element with Mr about 40 that is a gas: argon. ✓
04
Calculation
[2 marks]

A gas has a density of 1.25 g dm−3 at 273 K and 101 kPa. Calculate its Mr.

  • Density = 1250 g m−3; M = ρRT ÷ p (from M = mRT ÷ pV with m ÷ V = ρ). ✓
  • M = 1250 × 8.31 × 273 ÷ 101 000 = 28.1 (for example N2 or CO). ✓
05
Calculation
[2 marks]

0.400 mol of gas occupies 5.00 dm3 at 200 kPa. Calculate the temperature in K.

  • T = pV ÷ nR = 2.00 × 105 × 5.00 × 10−3 ÷ (0.400 × 8.31). ✓
  • T = 1000 ÷ 3.324 = 301 K. ✓
06
Explain
[3 marks]

Explain why real gases deviate from ideal behaviour at high pressure and at low temperature.

  • At high pressure the molecules are close together, so their own volume is not negligible compared with the container volume. ✓
  • At low temperature the molecules move slowly, so intermolecular attractions become significant. ✓
  • Both contradict assumptions of the ideal gas model, so pV = nRT no longer holds exactly. ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.