Explain, using the kinetic molecular model, why a fixed mass of ideal gas at constant temperature obeys Boyle's law.

IB DP Physics Standard Level (2023 syllabus) — B.3 Gas laws · Explain · 4 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

Boyle's law states that for a fixed mass of gas at constant temperature, pressure is inversely proportional to volume.

Model answer (4 marks)

Temperature is constant, so the average kinetic energy (and therefore average speed) of the molecules is unchanged.
When the volume decreases, the molecules are confined to a smaller space, so they travel shorter distances between collisions with the walls.
The increased frequency of collisions per unit area of the walls means the force per unit area (pressure) increases.
Since the increase in pressure is proportional to the decrease in volume (with no change in molecular speed), pressure and volume are inversely proportional, consistent with Boyle's law.

Examiner tips

  • Use the kinetic molecular model terms (molecules, collisions, average speed).
  • Show the logical chain: constant T → constant speed → smaller V → more collisions per area → higher pressure.
  • Mention that the proportionality comes from the inverse relationship between V and collision frequency.

Common mistakes

  • Failing to state that temperature is constant and speed is unchanged.
  • Confusing pressure with force instead of force per unit area.

Mark scheme (4 marks)

  1. Temperature is constant, so the average kinetic energy (and therefore average speed) of the molecules is unchanged.
  2. When volume decreases, the molecules are confined to a smaller space, so they travel shorter distances between collisions with the walls.
  3. The increased frequency of collisions per unit area of the walls means the force per unit area (pressure) increases.
  4. Since the increase in pressure is proportional to the decrease in volume (with no change in molecular speed), pressure and volume are inversely proportional, consistent with Boyle's law.

Key terms in this question

kinetic molecular model · Boyle's law

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