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 $49\, u$ . 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} $
$M_{B} \,=\frac{49}{4}=12.25 \,u$