Question

The ratio of rates of diffusion of gases A and B is 1 : 4. If the ratio of their masses present in the initial mixture is 2 : 3. The ratio of their mole fractions will be

• A. 0.25
• B. 0.35
• C. 0.5
• D. 1.5

Answer 1

The correct option is B 0.35

The rate of diffusion is inversely proportional to the square root of molar mass.

$\frac{R_A}{R_B}=\sqrt{\frac{M_B}{M_A}}$

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

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

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

$\frac{W_A}{W_B}=\frac{2}{3}$

$\frac{n_A}{n_B}=\frac{W_A}{W_B}\times \frac{M_B}{M_A}$ = $\frac{2}{3}\times \frac{1}{16}=\frac{1}{24}$

The ratio of the mole fractions is equal to the ratio of the number of moles. It is equal to 1/24.