A-LevelPhysicsIdeal gases9702/43 · Oct/Nov 2019 · Q29 Marks

(a) The kinetic theory of gases is based on a number of assumptions about the molecules of a gas. State the assumption that is related to the volume of the molecules of the gas. (b) An ideal gas occupies a volume of 2.40 × 10⁻² m³ at a pressure of 4.60 × 10⁵ Pa and a temperature of 23 °C.

(a)State the assumption that is related to the volume of the molecules of the gas.[2]
(b)(i)Calculate the number of molecules in the gas.[3]
(b)(ii)Each molecule has a diameter of approximately 3 × 10⁻¹⁰ m. Estimate the total volume of the gas molecules.[3]
(c)By reference to your answer in (b)(ii), suggest why the assumption in (a) is justified.[1]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

[M1] (a) (total volume of molecules is) negligible
[A1] (a) compared with volume occupied by the gas
[C1] (b)(i) pV = NkT
[C1] (b)(i) 4.60 × 10⁵ × 2.40 × 10⁻² = N × 1.38 × 10⁻²³ × (273 + 23)
[A1] (b)(i) N = 2.7 x 10²⁴
[C1] (b)(ii) volume of one atom = d³ (= 2.7 × 10⁻²⁹ m³)
[C1] (b)(ii) volume of all atoms = 2.7 × 10⁻²⁹ x 2.7 x 10²⁴
[A1] (b)(ii) = 7 x 10⁻⁵ m³
[B1] (c) numerical comparison between answer to (b)(ii) and 2.4 × 10⁻² (m³) showing (b)(ii) is much less than 2.4 × 10⁻² (m³)

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