Question

$X$ $ml$ of $H_2$ gas effuse through a hole in a container in $5sec$. The time taken for the effusion of the same volume of the gas specified below under ideal conditions is:

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

Answer 1

The correct option is B $20$ second, $O_2$

According to Graham's law of diffusion

Rate of Diffusion$\left(r_1\right)=\frac{Volumeeffused}{TimeTaken}$

$\Rightarrow$ Rate of diffusion $\propto \frac{1}{\sqrt{M}}$

$\Rightarrow \frac{r_1}{r_2}=\sqrt{\frac{M_2}{M_1}};$ As the volume effused is same in both cases.

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

For Oxygen, $\Rightarrow \frac{t_2}{5}=\sqrt{\frac{32}{2}}\Rightarrow t_2=5\times 4=20Sec$

$\Rightarrow 20$ Seconds is time taken for oxygen to effuse.