Question

The rates of diffusion of two gases $A$ and $B$ are in the ratio 1:4. A mixture contains these gases $A$ and $B$ in the weight ratio 2:3. The ratio of mole fraction of the gases $A$ and $B$ in the mixture is: (Assume $P_A=P_B)$

• A. 1:6
• B. 1:12
• C. 1:18
• D. 1:24

Answer 1

The correct option is D 1:24

$\frac{r_A}{r_B}=\sqrt{\frac{M_B}{M_A}}=\frac{1}{4}$
$\frac{m_B}{m_A}=\frac{1}{16}$
Now, $\frac{x_A}{x_B}=\frac{n_A}{(n_A+n_B)}\times \frac{(n_A+n_B)}{n_B}=\frac{w_A}{M_A}\times \frac{M_B}{w_A}=\frac{2}{3}\times \frac{1}{16}=\frac{1}{24}$