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:

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

Answer 1

The correct option is B 20 sec $O_2$

Rate of diffusion(R) $\propto \frac{1}{\sqrt{Molarmass}}$

$⟹\frac{R_2}{R_1}=\sqrt{\frac{M_1}{M_2}}⟹\frac{\frac{V_2}{t_2}}{\frac{V_1}{t_1}}=\sqrt{\frac{M_1}{M_2}}⟹\frac{\frac{X}{t_2}}{\frac{X}{5}}=\sqrt{\frac{2}{M_2}}⟹\frac{5}{t_2}=\sqrt{\frac{2}{M_2}}$

Using trial and error method:

For oxygen, M=32

$⟹\frac{5}{t_2}=\sqrt{\frac{2}{M_2}}⟹t_2=20sec$