A-LevelPhysicsIdeal gases9702/41 · Oct/Nov 2019 · Q29 Marks

The kinetic theory of gases is based on a number of assumptions about the molecules of a gas.

(a)State the assumption that is related to the volume of the molecules of the gas.[2]
(b)(i)An ideal gas occupies a volume of 2.40 × 10⁻²m³ at a pressure of 4.60 × 10⁵ Pa and a temperature of 23 °C. Calculate the number of molecules in the gas. number = ...........................................................[3]
(b)(ii)Each molecule has a diameter of approximately 3 × 10⁻¹⁰ m. Estimate the total volume of the gas molecules. volume = ........................................................... m³[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] (total volume of molecules is) negligible
[A1] compared with volume occupied by the gas
[C1] pV = NkT
[C1] 4.60 × 105 × 2.40 × 10-2 = N × 1.38 × 10-23 × (273 + 23)
[(C1)] or pV = nRT
[(C1)] 4.60 x 105 x 2.40 × 10-2 = n x 8.31 × (273 + 23)
[(C1)] n = 4.49 (mol)
[(C1)] N = nNA
[(C1)] = 4.49 × 6.02 × 1023
[A1] N = 2.7 x 1024
[C1] volume of one atom = d³ (= 2.7 × 10-29 m³)
[C1] volume of all atoms = 2.7 × 10-29 x 2.7 x 1024
[A1] = 7 x 10-5 m³
[(C1)] or volume of one atom = (4/3)πι³ (= 1.41 × 10−29 m³)
[(C1)] volume of all atoms = 2.7 x 1024 x 1.41 x 10-29
[(A1)] = 4 x 10-5 m³
[B1] 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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