FRQ — Behaviour of Perfect Gases and Kinetic Theory of Gases

Case study·Hard exam skill (4/5)·Calculator allowed

Difficulty guide

The label describes the problem, not your ability.

1/5 - Foundational

Warm-up setup; checks one basic idea.

2/5 - Routine exam skill

Normal syllabus skill; usually one main rule or interpretation.

3/5 - Standard multi-step

Exam-style problem with multiple steps or a common trap.

4/5 - Hard exam skill

High-end exam problem; combines methods carefully.

5/5 - Challenge

Stretch problem beyond normal exam pressure.

Question

Two chambers contain the same gas at the same temperature. Chamber A is at

2.0\text{ atm}

. Chamber B is at

0.50\text{ atm}

and has volume

2.0\text{ L}

300\text{ K}

. Take

1\text{ atm}=1.0\times10^5\text{ Pa}

R=8.3\text{ J mol}^{-1}\text{ K}^{-1}

and

N_A=6.0\times10^{23}\text{ mol}^{-1}

Total: 5 marks

(a) Find the ratio of number density in A to that in B. (1 mark)

(b) Find the ratio of mean free path in B to that in A. (1 mark)

(d) Find the approximate number of molecules in chamber B. (2 marks)

Your response (optional — you can also work on paper)

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