Question

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

• A. $1:4$
• B. $1:24$
• C. $4:1$
• D. $24:3$

Answer 1

The correct option is B

$1:24$

$\frac{r_A}{r_B}=\sqrt{\frac{M_B}{M_A}}=\frac{1}{4}$ or $\frac{M_B}{M_A}=\frac{1}{16}$
Let $W_A$ and $W_B$ be the masses of $A$ and $B$ respectively,
Mole fraction of $A=\frac{\frac{W_A}{M_A}}{\frac{W_A}{M_A}+\frac{W_B}{M_B}}$
Mole fraction of $B=\frac{\frac{W_B}{M_B}}{\frac{W_A}{M_A}+\frac{W_B}{M_B}}$
ratio of mole fractions of $A$ and $B$
$=\frac{W_A}{M_A}\times \frac{M_B}{W_B}=\frac{2}{3}\times \frac{1}{16}=\frac{1}{24}$