JAMB Chemistry 2019 Paper

Concept:The velocity of a gas is inversely proportional to the square root of its molecular mass.Explanation:The kinetic theory of gases gives the average molecular velocity as $V = \sqrt{\frac{3RT}{M}}$.In this expression, $R$ is the gas constant, $T$ is the absolute temperature, and $M$ is the molecular mass.If temperature, $T$, is kept constant, then $3RT$ becomes a fixed value.Therefore, $V$ depends only on $M$.So, $V \propto \frac{1}{\sqrt{M}}$.Introducing the proportionality constant $k$ gives:$$V = \frac{k}{\sqrt{M}}$$Since $\sqrt{M} = M^{\frac{1}{2}}$, we can write:$$V = \frac{k}{M^{\frac{1}{2}}}$$This relationship makes sense because a heavier gas moves more slowly than a lighter gas at the same temperature.Answer:$$V = \frac{k}{M^{\frac{1}{2}}}$$Therefore, option B is correct.