Question

The rates of diffusion of two gases $A$ and $B$ are in the ratio $1:4.$ If the ratio of their masses present in the mixture is $2:3$. Calculate the ratio of their mole fraction.

Answer 1

Ratio of rate of diffusion $=1:4$

As rate of diffusion $\propto \frac{1}{\sqrt{M}}$

$\frac{r_1}{r_2}=\sqrt{\frac{M_2}{M_1}}=\frac{1}{4}$

$⟹\frac{M_2}{M_1}=\frac{1}{16}$

$⟹M_1=16M_2$

$X_1=\frac{n_1}{n_1+n_2}=\frac{\frac{2x}{M_1}}{\frac{2x}{M_1}+\frac{3x}{M_2}}$

$X_2=\frac{n_2}{n_1+n_2}=\frac{\frac{3x}{M_2}}{\frac{2x}{M_1}+\frac{3x}{M_2}}$

$⟹\frac{X_1}{X_2}=\frac{n_1}{n_2}=\frac{2M_2}{3M_1}=\frac{2M_2}{48M_2}=\frac{1}{24}$