A stainless steel chamber contains Ar gas at a temperature T and pressure P. The total number of Ar atoms in the chamber is n. Now Ar gas in the chamber is replaced by CO₂ gas and the total number of CO₂ molecules in the chamber is n/2 at the same temperature T. The pressure in the chamber now is P'. Which one of the following relations holds true? (Both the gases behave as ideal gases)

The correct answer is C, P' = P/2. For an ideal gas in a fixed volume at a fixed temperature, pressure is proportional to the number of molecules, so half the molecules give half the pressure.

The ideal gas law in molecular form is PV = NkT, where N is the number of particles and k is Boltzmann's constant. The chamber's volume V and the temperature T stay the same, so P ∝ N. Going from n argon atoms to n/2 carbon dioxide molecules halves N, so the pressure falls to P/2. What kind of gas it is does not matter: by Avogadro's law equal volumes of ideal gases at the same temperature and pressure hold equal numbers of molecules, whatever their mass.

A, P' = P, would need the same number of molecules.

B, P' = 2P, would need twice as many molecules, 2n.

D, P' = P/4, would need only n/4 molecules.

Exam tip: PV = NkT; at fixed V and T, pressure depends on how many molecules there are, not on which gas.