Explain, using the kinetic model of an ideal gas, why two different gases that occupy the same volume at the same temperature and pressure contain the same number of molecules.

IB DP Physics Higher 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).

This relationship is known as Avogadro's law and applies to all ideal gases regardless of the nature of the gas molecules.

Model answer (4 marks)

Pressure is produced by the rate of change of momentum of gas molecules striking the walls. At the same temperature, the mean kinetic energy of the molecules in both gases is equal, so each molecule has the same average speed. For a given volume and pressure, the total force (or total momentum transfer per unit time) on the walls must be the same for both gases. Because the mean kinetic energy per molecule is the same, the only way to give the same total momentum transfer is for the number of molecules to be equal in the two gases.

Examiner tips

  • Use the kinetic theory to link pressure to momentum transfer; state that equal temperature gives equal mean kinetic energy; show that equal pressure/volume requires equal total momentum transfer; conclude equal number of molecules.
  • Include the key terms: kinetic energy, momentum transfer, pressure, volume, Avogadro's law.
  • Keep the answer to 4 points – one sentence per point.

Mark scheme (4 marks)

  1. Pressure depends on the rate of change of momentum of molecules colliding with the container walls.
  2. At the same temperature, molecules of both gases have the same mean kinetic energy.
  3. For the same pressure and volume, the total force (or total rate of momentum transfer) on the walls must be identical for both gases.
  4. Because the mean kinetic energy per molecule is the same, the number of molecules must be equal in both gases.

Key terms in this question

kinetic model · pressure

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