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LearnCambridge97022025–2027Paper 4 · A Level Structured QuestionsIdeal gases

Paper 4 · Module

Ideal gases

2 subtopics≈ 75 min in total

Start the module: The ideal gas equation Open graphing calculator

The ideal gas equation
One mole contains $N_A=6.02\times10^{23}$ particles. An ideal gas obeys $pV=nRT$ , where $n$ is the number of moles, $R=8.31$ J mol⁻¹ K⁻¹ and $T$ is in kelvin. Equivalently $pV=NkT$ , with $N$ molecules and the Boltzmann constant $k=\dfrac R{N_A}=1.38\times10^{-23}$ J K⁻¹. Boyle's law, Charles's law and the pressure law are special cases.
≈ 35 min
Kinetic theory of gases
Gas pressure comes from molecules colliding with the walls, each collision changing momentum. Under the kinetic theory assumptions, $pV=\tfrac13Nm\langle c^2\rangle$ . Comparing with $pV=NkT$ gives the mean translational kinetic energy of a molecule: $\tfrac12m\langle c^2\rangle=\tfrac32kT$ . Temperature is a direct measure of average molecular kinetic energy; the r.m.s. speed is $\sqrt{\langle c^2\rangle}$ .
≈ 40 min