Question

Equal moles of hydrogen and oxygen gases are placed in a container with a pin-hole through which both can escape. What fraction of the oxygen escape in the time required for one-half of the hydrogen to escape?

• A. $\frac{1}{8}$
• B. $\frac{1}{4}$
• C. $\frac{3}{8}$
• D. $\frac{1}{2}$

Answer 1

The correct option is A $\frac{1}{8}$

By Graham's law of diffusion,

$\frac{r_{H_2}}{r_{O_2}}=\sqrt{\frac{M_{O_2}}{M_{H_2}}}+\sqrt{\frac{32}{2}}=\frac{4}{1}$

$\therefore r_{H_2}=4r_{O_2}$

$\therefore 1$ molecule of $H_2$ escapes in the same time in which $\frac{1}{4}$ molecule of $O_2$ escapes.

$\therefore \frac{1}{2}$ molecule of $H_2$ escapes in the same time in which $(\frac{1}{4}\times \frac{1}{2})$ molecules of $O_2$ escapes

$i.e.\frac{1}{8}$ molecules