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A2 Daily A Level Physics question

2025-11-01 OCR A Kinetic theory model 5.1.4(h)

Two identical rigid 1.0 L steel flasks are stored side by side in a lab. One contains pure helium and the other contains pure oxygen. Both are at the same pressure and the same room temperature. Ignore non-ideal effects. Which statement must be true?

  1. A Both gases have the same typical molecular speed because their pressure and temperature are equal.
  2. B Helium atoms have about eight times the rms speed of oxygen molecules because speed is inversely proportional to molar mass at fixed temperature.
  3. C Helium atoms have about 2.8 times the rms speed of oxygen molecules because lighter particles must move faster to have the same average kinetic energy at the same temperature. (correct)
  4. D Oxygen molecules collide with the walls more often than helium atoms at the same pressure because the heavier molecules deliver larger impulses.

Answer

The correct answer is C.

Correct: C — Helium atoms have about 2.8 times the rms speed of oxygen molecules because lighter particles must move faster to have the same average kinetic energy at the same temperature. A confuses equal temperature with equal speed; at the same temperature the average kinetic energy is the same, so lighter particles must move faster. B assumes speed varies inversely with molar mass (linear) rather than with the square root, giving an incorrect factor (it should be √(32/4) = √8 ≈ 2.8). C is correct because with molar masses 4 (He) and 32 (O2), the speed ratio is √(32/4) ≈ 2.8. D is wrong because at equal T and p in equal volumes the number density is the same, but oxygen moves more slowly, so it does not hit the walls more often; the same pressure arises from slower, heavier hits occurring less frequently.

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