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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 ?

$\begin{array}{1 1} (a)\;\frac{1}{4} \\(b)\;\frac{3}{8} \\ (c)\;\frac{1}{2} \\ (d)\;\frac{1}{8} \end{array} $

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A)
Solution :
We have given ,
a number of moles of hydrogen and $n_{H})$ that oxygen are $(n_0)$ not equal
$\therefore $ We have , the relation between radio number moles escaped and ratio of molecular mass.
$\large\frac{n0_2}{nH_2}=\sqrt{\large\frac{Mh_2}{Mo_2}}$
M= Molecular mass of the molecules
$\large\frac{n0_2}{nH_2}=\sqrt{\large\frac{2}{32}}$
$\large\frac{n0_2}{nH_2}=\sqrt{\large\frac{1}{16}}$
$\large\frac{n0_2}{0.5}=\sqrt{\large\frac{1}{4}}$
$no_2=\large\frac{0.5}{4}=\frac{1}{8}$
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