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 escapes in the time required for one-half of the hydrogen to escape ?

• A. 1/4
• B. 3/8
• C. 1/2
• D. 1/8

Answer 1

Answer: (D)

$\frac{r_{O_2}}{r_{H_2}}=\sqrt{\frac{M_{H_2}}{M_{O_2}}}$
$\frac{\frac{n_{O_2}}{t}}{\frac{n_{H_2}}{t}}=\sqrt{\frac{2}{32}}=\sqrt{\frac{1}{16}}=\frac{1}{4}$
$\therefore \frac{n_{O_2}}{n_{H_2}}=\frac{1}{4}$
as $\frac{1}{2}$ moles of $H_2$ are diffused, moles of $O_2$ diffused in same time. $\frac{n_{O_2}}{1/2}=\frac{1}{4}\Rightarrow n_{O_2}=\frac{1}{8}$