Chapter 39 of 2363 min read

Ideal gas equation and kinetic interpretation of pressure

Why this is asked: At a fixed temperature, rms speed depends only on molar mass — lighter molecules move faster, not slower, which is why hydrogen effuses faster than oxygen at the same temperature.

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Test yourself

•A container has two chambers of volumes $V_{1} = 2$ litres and $V_{2} = 3$ litres separated by a partition made of a thermal insulator. The chambers contain $n_{1} = 5$ and $n_{2} = 4$ moles of ideal gas at pressures $p_{1} = 1$ atm and $p_{2} = 2$ atm, respectively. When the partition is removed, the mixture attains an equilibrium pressure of:
•An oxygen cylinder of volume 30 litre has 18.20 moles of oxygen. After some oxygen is withdrawn from the cylinder, its gauge pressure drops to 11 atmospheres at a temperature of $2 7^{\circ}$ C. The mass of the oxygen withdrawn from the cylinder is nearly equal to: [Given $R = \frac{100}{12} J mo l^{- 1} K^{- 1}$ , molecular mass of $O_{2}$ = 32, 1 atm pressure $= 1.01 \times 1 0^{5} N/ m^{2}$ ]
•The following graph represents the $T$ – $V$ curves of an ideal gas (where $T$ is the temperature and $V$ the volume) at three pressures $P_{1}$ , $P_{2}$ and $P_{3}$ , compared with those of Charles's law represented as dotted lines. Then the correct relation is:

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