Question

A gaseous mixture containing $He,C{H}_4$ and $S{O}_2$ was allowed to effuse through a fine hole. Find what molar ratio of gases comes out initially, if the mixture contains $He,C{H}_4$ and $S{O}_2$ in $1:2:3$ mole ratio.

• A. $2:2:3$
• B. $6:6:1$
• C. $\sqrt{2}:\sqrt{2}:3$
• D. $4:4:3$

Answer 1

The correct option is D $4:4:3$

$\text{Rate of effusion}\propto p\sqrt{\frac{1}{molarmass}}$
Where $p$ is the partial pressure of the gas in the container which is directly proportional to the number of moles present.
Hence,
$\text{Rate of effusion}\propto \text{number of moles present initially}\times \sqrt{\frac{1}{molarmass}}$
Hence, ratio of effusion rate of $He$ , $C{H}_4$ and $S{O}_2$ = $1\times \sqrt{\frac{1}{4}}:2\times \sqrt{\frac{1}{16}}:3\times \sqrt{\frac{1}{64}}$
= $\frac{1}{2}:\frac{2}{4}:\frac{3}{8}=4:4:3$