Question

Gas A four times denser than gas B. Find the ratio between their rates of diffusion.

Answer 1

Let density and rate of diffusion of gas ${}^{\prime }{A}^{\prime }$ is $d_A$ and $r_A$ and let density and rate of diffusion of gas ${}^{\prime }{A}^{\prime }$ is $d_B$ and $r_B$
$\therefore d_A=4d_B\therefore r_A\propto \frac{1}{\sqrt{d_A}},r_B\propto \frac{1}{\sqrt{d_B}}$
$\therefore \frac{r_A}{r_B}=\frac{\frac{1}{\sqrt{d_A}}}{\frac{1}{\sqrt{d_B}}}$ i.e., $\frac{r_A}{r_B}=\frac{\sqrt{d_A}}{\sqrt{d_B}}=\sqrt{\frac{d_B}{d_A}}$
i.e., $\frac{r_A}{r_B}=\sqrt{\frac{1}{4}}=\frac{1}{2}$
$r_A:r_B=1:2$