Question

A gas $A$ having molecular weight $4$ diffuses thrice as fast as the gas $B$ at a given $T$. The molecular weight of gas $B$ is :

• A. $36$
• B. $12$
• C. $18$
• D. $24$

Answer 1

The correct option is A $36$

A gas $A$ having molecular weight 4 diffuses thrice as fast as the gas $B$ at a given $T$. The molecular weight of gas $B$ is 36.
The rate of diffusion is inversely proportional to the molar mass.
$r=\frac{1}{\sqrt{M}}$

Here, $r$ and $r^{\prime }$ are the rates of diffusion of the gas $A$ and the gas $B$ and $M$ and $M^{\prime }$ are the molar masses of gas $A$ and gas $B$ respectively.
$\frac{r}{r^{\prime }}=\sqrt{\frac{M^{\prime }}{M}}$
$\frac{3r^{\prime }}{r^{\prime }}=\sqrt{\frac{M^{\prime }}{4}}$
$M^{\prime }=36$