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A level: Kinetic Theory Questions

Q3.

(a) State two quantities which increase when the temperature of a given mass of gas is increased at constant volume.

The pressure of the gas and the (average) kinetic energy [or rms speed] of the molecules.

(2 marks)

(b) A car tyre of volume 1.0 × 10–2 m3 contains air at a pressure of 300 kPa and a temperature of 290 K. The mass of one mole of air is 2.9 × 10–2 kg. Assuming that the air behaves as an ideal gas, calculate

(i) n, the amount, in mol, of air,

pV = nRT

n = pV/RT

= 300 x 1.0 × 10–2/(8.31 x 290)

= 1.24

= 1.2 mol

You need to quote the answer to 2 significant figures but should calculate to one more for use in later calculations. This avoids compounding rounding errors in future calculations, but does not entail you indicating more precision than measurements indicate in quoting answers..

(ii) the mass of the air,

mass of air = 1.24 × 29 × 10–3 = 0.036 kg

(iii) the density of the air.

= m/V

= 0.036/1.0 x 10-2

= 3.6 kg m–3 

(5 marks)

(c) Air contains oxygen and nitrogen molecules. State, with a reason, whether the following are the same for oxygen and nitrogen molecules in air at a given temperature.

(i) The average kinetic energy per molecule

The average kinetic energy per molecule is the same because the temperature is the same

(ii) The r.m.s. speed

The r.m.s. speed is different because the mass of the molecules are different

(4 marks)

(Total 11 marks)