Question

X mL of $H_2$ gas effuses through a hole in a container in 5 sec. The time taken for the effusion of the same volume of the gas specified below under identical conditions is:
(atomic mass of C = 12 u, O =16 u and He = 4 u)

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

Answer 1

The correct option is B 20 sec, $O_2$

$\text{rate of diffusion}\propto \frac{1}{\text{time}}$
$\text{rate of diffusion}\propto \frac{1}{\sqrt{\text{molar mass}}}$
Hence,
$\text{time}\propto \sqrt{\text{molar mass}}$

$\Rightarrow \frac{t_{H_2}}{t_{O_2}}=\sqrt{\frac{0.002}{0.032}}$

$\Rightarrow \frac{5}{t_{O_2}}=\sqrt{\frac{0.002}{0.032}}$

$\Rightarrow t_{O_2}=20\text{sec}$