Question

The ratio of rate of diffusion of gases $A$ and $B$ is $1:4$. If the ratio of their masses present in the mixture is $2:3$, what is the ratio of their mole fraction?

• A. $\frac{1}{8}$
• B. $\frac{1}{12}$
• C. $\frac{1}{16}$
• D. $\frac{1}{24}$

Answer 1

Answer: (D)

$\frac{1}{24}$

The rate of diffusion is inversely proportional to the square root of molar mass.
$\frac{R_A}{R_B}=\sqrt{\frac{M_B}{M_A}}$

$\frac{1}{4}=\sqrt{\frac{M_B}{M_A}}$

$\frac{1}{16}=\frac{M_B}{M_A}$

$\frac{M_A}{M_B}=\frac{16}{1}$ .....(1)

$\frac{W_A}{W_B}=\frac{2}{3}$.....(2)

Divide (2) with (1)

$\frac{n_A}{n_B}=\frac{\frac{W_A}{W_B}}{\frac{M_A}{M_B}}=\frac{\frac{2}{3}}{\frac{16}{1}}$

$\frac{n_A}{n_B}=\frac{2}{3}\times \frac{1}{16}$

$\frac{n_A}{n_B}=\frac{1}{24}$

The ratio of the mole fractions is equal to the ratio of the number of moles. It is equal to $\frac{1}{24}$.

Hence the correct option is D.