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  4. 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 ?

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Q. 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 ?

NEETNEET 2016States of Matter

Solution:

$\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} $