A-LevelPhysicsIdeal gases9702/42 · Feb/Mar 2019 · Q210 Marks

The pressure p of an ideal gas having density ρ is given by the expression p = ⅓ ρ⟨c²⟩.

(a)(i)State what is meant by: an ideal gas[2]
(a)(ii)the symbol ⟨c²⟩.[1]
(b)(i)A cylinder contains a fixed mass of a gas at a temperature of 120 °C. The gas has a volume of 6.8 x 10⁻³ m³ at a pressure 2.4 × 10⁵ Pa. Assuming the gas acts like an ideal gas, show that the number of atoms of gas in the cylinder is 3.0 × 10²³.[3]
(b)(ii)Each atom of the gas, assumed to be a sphere, has a radius of 3.2 × 10⁻¹¹ m. Use the answer in (i) to estimate the actual volume occupied by the gas atoms.[2]
(b)(iii)One of the assumptions of the kinetic theory of gases is related to the volume of the atoms. State this assumption. Explain whether your answer in (ii) is consistent with this assumption.[2]

Mark scheme

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

[M1] gas obeys formula pV/T = constant
[A1] symbols V and T explained
[B1] mean-square-speed (of atoms / molecules)
[C1] use of T = 393
[C1] pV = nRT OR pV = NkT
[A1] 2.4 x 10⁵ x 6.8 × 10⁻³ = n x 8.31 × 393 and N = n x 6.02 × 10²³ = 3.0 × 10²³ OR 2.4 x 10⁵ x 6.8 × 10⁻³ = N x 1.38 x 10⁻²³ x 393 hence N = 3.0 × 10²³
[C1] volume of one atom = 4 / 3πr³
[A1] volume occupied = 3.0 × 10²³ x 4 / 3 × π× (3.2 × 10⁻¹¹)³ = 4 x 10⁻⁸ m³
[B1] assumption: volume of atoms negligible compared to volume of container/cylinder
[B1] 4 × 10⁻⁸ (m³) << 6.8 × 10⁻³ (m³) so yes

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