Question

Two gases $A$ and $B$ having the same volume diffuse through a porous partition in $20$ and $10$ seconds respectively. The molecular mass of $A$ is $49u$ . Molecular mass of $B$ will be

• A. 12.25 u
• B. 6.50 u
• C. 25.00 u
• D. 50.00 u

Answer 1

Answer: (A)

According to Graham's law of diffusion,rate of diffusion
$r\propto \frac{1}{\sqrt{M}},r\propto \frac{V}{t}$
where, $V$ is the volume of the gas diffused in time $t$
$\frac{r_A}{I_B}=\sqrt{\frac{M_B}{M_A}}$
or $\frac{V_A}{t_A}\times \frac{t_B}{V_B}=\sqrt{\frac{M_B}{M_A}}$
Given, $V_A=V_B$
$\therefore \frac{10}{20}=\sqrt{\frac{M_B}{49}}$
$\Rightarrow \frac{1}{4}=\frac{M_B}{49}$
$M_B=\frac{49}{4}=12.25u$