Question

A gas "A", molecular weight 4 diffuses thrice as fast as the gas B. The molecular weight of B is :

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

Answer 1

The correct option is C $36$

The rate of diffusion (r) is inversely proportional to the molecular weight (M).

$r\propto \frac{1}{\sqrt{M}}$

$\therefore \frac{r_A}{r_B}=\sqrt{\frac{M_B}{M_A}}$

Here, $r_A$ and $r_B$ are the rates of diffusion of the gas A and the gas B and $M_A$ and $M_B$ are the molecular weight of gas A and gas B respectively.

Let the rate of diffusion of the gas B be r, i.e., $r_B=r$.

As the gas A diffuses thrice as fast as the gas B.

$\therefore$ rate of diffusion of the gas A $\left(r_A\right)=3r$

Given that molecular weight of A $\left(M_A\right)=4$

$\therefore \frac{3r}{r}=\sqrt{\frac{M_B}{4}}$

$\Rightarrow M_B=36$

Hence, the molecular weight of B is 36.