A-LevelPhysicsIdeal gases9702/42 · Oct/Nov 2018 · Q210 Marks

State what is meant by an ideal gas.

(a)State what is meant by an ideal gas.[2]
(b)(i)An ideal gas comprised of single atoms is contained in a cylinder and has a volume of 1.84×10-2 m³ at a pressure of 2.12×107 Pa. The mass of gas in the cylinder is 3.20 kg. Determine, to three significant figures, the root-mean-square (r.m.s.) speed of the atoms of the gas.[3]
(b)(ii) 1.The temperature of the gas in the cylinder is 22°C. Determine, to three significant figures, the amount, in mol, of the gas,[2]
(b)(ii) 2.The temperature of the gas in the cylinder is 22°C. Determine, to three significant figures, the mass of one atom of the gas.[2]
(c)Use your answer in (b)(ii) part 2 to determine the nucleon number A of an atom of the gas.[1]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

[M1] gas that obeys equation pV = constant × T
[A1] symbols p, V and T explained
[C1] pV = 1/3 Nm<c²> and M = Nm (and so) p = 1/3ρ<c²>
[C1] 2.12 × 10^7 = 1/3 x [3.20/(1.84 × 10⁻²)] × <c²>
[A1] c r.m.s. = 605 ms⁻¹
[C1] pV = nRT and T = (22 + 273) K
[A1] n = (2.12 × 10^7 × 1.84 × 10⁻²)/(8.31 × 295) = 159 mol
[C1] mass = 3.20/(159 × 6.02 × 10^23) or mass = [2 × (3/2) × 1.38 × 10⁻²³ × 295]/605²
[A1] mass = 3.34 × 10⁻²⁶ kg
[A1] A = (3.34 × 10⁻²⁶)/(1.66 × 10⁻²⁷) = 20

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