Q54 / 180 · NEET 2016 (Phase 1) · Chemistry

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?

Correct answer
A
$\frac{1}{8}$
B
$\frac{1}{4}$
C
$\frac{3}{8}$
D
$\frac{1}{2}$

Solution

\frac{\frac{n_{1}}{t_{1}}}{\frac{n_{2}}{t_{2}}} = \sqrt{\frac{M_{2}}{M_{1}}} \Rightarrow n_{2} = \frac{1}{2}, n_{1} = n^{'}

\Rightarrow \frac{2 t_{2} n^{'}}{t_{1} x_{1}} = \sqrt{\frac{M_{2}}{M_{1}}} = \sqrt{\frac{2}{32}} = \sqrt{\frac{1}{16}} = \frac{1}{4}

Assuming

t_{2} = t_{1}

\frac{2 n^{'} t_{2}}{t_{1}} = \frac{1}{4}

∴ n^{'} = \frac{1}{8}

Hence, the correct answer is option: 'A'.

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