Ideal gases and kinetic theory

Sample questions

Original practice questions written in the style of the exam.

1. Question 13 marks

   A gas cylinder of volume $0.050\,\text{m}^3$ contains an ideal gas at a pressure of $2.0 \times 10^{5}\,\text{Pa}$ and a temperature of $20\,^\circ\text{C}$.

   Calculate the number of molecules in the cylinder.

   Mark scheme

   • Converts temperature: $T = 293\,\text{K}$ (1)
   • $n = \dfrac{pV}{RT} = \dfrac{2.0 \times 10^{5} \times 0.050}{8.31 \times 293} = 4.1\,\text{mol}$ (1)
2. Question 23 marks

   Calculate the root-mean-square speed of nitrogen molecules at $300\,\text{K}$. The mass of a nitrogen molecule is $28\,\text{u}$.

   Mark scheme

   • $m = 28 \times 1.66 \times 10^{-27} = 4.65 \times 10^{-26}\,\text{kg}$ (1)
3. Question 36 marks

   A sealed rigid container holds a fixed mass of gas. The gas is heated.

   Use the kinetic theory of gases to explain why the pressure of the gas increases.

   Mark scheme

   Indicative content:

   • Molecules collide with the container walls and rebound, undergoing a change in momentum (1)
   • By Newton's second law, a force is exerted on the molecules, equal to the rate of change of momentum; by Newton's third law, the molecules exert an equal and opposite force on the wall (1)
   • Pressure is the total force per unit area on the walls (1)
   • Heating increases the temperature, so the mean kinetic energy and mean speed of the molecules increase (1)
   • The change in momentum per collision is greater (1)
   • Collisions with the walls are more frequent, as the volume is constant; so the rate of change of momentum, and hence the pressure, increases (1)

   Award 1 mark per relevant point, max 6.