Question

Calculate relative rate of effusion of $O_2$ to $C{H}_4$ through a container containing $O_2$ and $C{H}_4$ in $3:2$ mass ratio.

• A. $\frac{3\sqrt{2}}{4}$
• B. $\frac{3}{4\sqrt{2}}$
• C. $\frac{3}{2\sqrt{2}}$
• D. None of these

Answer 1

The correct option is B $\frac{3}{4\sqrt{2}}$

We know
$r\propto nr\propto \sqrt{\frac{1}{M}}$
The ratio of given mass of $O_2$ and $C{H}_4$ is $3:2$
$\text{Number of moles (n)}=\frac{\text{Weight}}{\text{Molecular mass}}$
So,
$\frac{r_{O_2}}{r_{C{H}_4}}=\frac{n_{O_2}}{n_{C{H}_4}}\times \sqrt{\frac{M_{C{H}_4}}{M_{O_2}}}$
$=\frac{3}{2}\times \frac{16}{32}\times \sqrt{\frac{16}{32}}=\frac{3}{4\sqrt{2}}$