Question

$Xml$ of $H_2$ gas effuse through a hole in a container in $5$ seconds. The time taken for the effusion of the same volume of the gas specified below under identical conditions is:

• A. $10$ seconds : He
• B. $20$ seconds : $O_2$
• C. $25$ seconds : CO
• D. $55$ seconds : $C{O}_2$

Answer 1

The correct option is B $20$ seconds : $O_2$

Rate of effusion of gases is inversely proportional to square root of molecular mass of gases.

$Rate\propto \sqrt{\frac{1}{M}}$.

The smaller the value of $M$, more is the rate of effusion.

For effusion of same volume,

$\frac{t_1}{t_2}=\sqrt{\frac{M_1}{M_2}}\Rightarrow \frac{t_1}{\sqrt{M_1}}=\frac{t_2}{\sqrt{M_2}}$

This is clearly seen from the options that the ratio of $\frac{t}{\sqrt{M}}$ is same for $H_2$ and $O_2$.
$(\frac{5}{\sqrt{2}}=\frac{20}{\sqrt{32}}=\frac{5}{\sqrt{2}})$

So B is correct.