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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?

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a

$\frac{3}{8}$

b

$\frac{1}{2}$

c

$\frac{1}{8}$

d

$\frac{1}{4}$

answer is C.

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Detailed Solution

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According to Graham’s Law
(1) $\frac{r_{H_{2}}}{r_{O_{2}}} = \sqrt{\frac{M_{O_{2}}}{M_{H_{2}}}} = \sqrt{\frac{32}{2}} = 4$
(2) $r_{H_{2}}^{2} = 4 r_{O_{2}^{2}}^{2}$
$r_{O_{2}} = \frac{1}{2} \times \frac{1}{4}$
(3) 1/8 th fraction of the oxygen escapes.

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