JAMB Chemistry 2023 Paper

Concept:Graham’s law states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass.Explanation:Let $r_A$ and $r_B$ be the diffusion rates of gas A and gas B.Then, $\frac{r_A}{r_B} = \sqrt{\frac{M_B}{M_A}}$.Given $M_A = 32\ \mathrm{g/mol}$ and $M_B = 64\ \mathrm{g/mol}$:$\frac{r_A}{r_B} = \sqrt{\frac{64}{32}} = \sqrt{2} \approx 1.41$.So gas A diffuses about $1.41$ times faster than gas B.Thus, the exact ratio is $r_A : r_B = \sqrt{2} : 1 \approx 1.41 : 1$.This is not exactly $2:1$, since $\sqrt{2} \approx 1.41$.Answer:$r_A : r_B = \sqrt{2} : 1 \approx 1.41 : 1$, so none of the given options is exactly correct.