Question

$X\text{ml}$ of $H_2$ gas effuses 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 condition is:

• A. 10 seconds: $He$
• B. 20 seconds: $O_2$
• C. 25 seconds: $CO$
• D. 35 seconds: $C{O}_2$

Answer 1

The correct option is B 20 seconds: $O_2$

$\text{Rate of diffusion}=\frac{\text{Volume of gas diffused}}{\text{time taken}}$
$r_{H_2}=\frac{X}{5}$
$r_g=\frac{X}{t}$
$\frac{r_{H_2}}{r_g}=\frac{t}{5}$
Option (a)
$\frac{r_{H_2}}{r_{He}}=\frac{t}{5}=\frac{10}{5}=2$
$\frac{r_{H_2}}{r_{He}}=\sqrt{\frac{4}{2}}=\sqrt{2}$
$\therefore$ (a) is incorrect
Option (b)
$\frac{r_{H_2}}{r_{O_2}}=\frac{t}{5}=\frac{20}{5}=4$
$\frac{r_{H_2}}{r_{O_2}}=\sqrt{\frac{32}{2}}=4$
$\therefore$ (b) is correct.
Option (c)
$\frac{r_{H_2}}{r_{CO}}=\frac{t}{5}=\frac{25}{5}=5$
$\frac{r_{H_2}}{r_{CO}}=\sqrt{\frac{28}{2}}=\sqrt{1}4$
$\therefore$ (c) is incorrect
Option (d)
$\frac{r_{H_2}}{r_{C{O}_2}}=\frac{t}{5}=\frac{35}{5}=7$
$\frac{r_{H_2}}{r_{C{O}_2}}=\sqrt{\frac{44}{2}}=\sqrt{22}$
$\therefore$ (d) is incorrect.