Explain why the volume of an ideal gas doubles when its pressure is halved at constant temperature.

IB DP Chemistry Standard Level (2023 syllabus) — S1.5 Ideal gases · Explain · 4 marks · View as Markdown

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

Model answer (4 marks)

In an ideal gas the particles move randomly and exert pressure by colliding with the walls. At constant temperature the average kinetic energy and speed of the particles are unchanged, so the force delivered in each collision is the same. If the pressure is halved, the number of collisions per unit area per unit time must also halve. This can only happen if the gas occupies twice the volume, because the same number of particles is now spread over a larger space and collides with any given wall area only half as often. Thus, at constant temperature, halving the pressure doubles the volume, in agreement with Boyle’s law (P∝1/V).

Examiner tips

  • Use the definition of pressure as force per area from particle collisions; link constant temperature to unchanged kinetic energy; explain how halving pressure requires halving collision frequency; conclude with Boyle’s law.

Mark scheme (4 marks)

  1. In an ideal gas, particles are in constant random motion and exert pressure through collisions with the container walls.
  2. At constant temperature, the average kinetic energy (and speed) of the particles remains unchanged, so the force per collision stays the same.
  3. Halving the pressure means the frequency of collisions per unit area of wall must halve.
  4. Doubling the volume spreads the same number of particles over a greater space, so collisions with any given area of wall occur half as often, which halves the pressure — consistent with Boyle's law (P ∝ 1/V at constant T).

Key terms in this question

ideal gas · pressure · constant temperature

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