States of Matter - Result Question 3
####3. 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 ?
[2016]
(a) $1 / 8$
(b) $1 / 4$
(c) $3 / 8$
(d) $1 / 2$
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Solution:
- (a) Given, $n _{H_2}=n _{O_2}$ and $t _{H_2}=t _{O_2}$
According to Graham’s law of diffusion for two different gases. $\frac{r _{H_2}}{r _{O_2}}=\frac{v_1 / t_1}{v_2 / t_2} \Rightarrow \sqrt{\frac{M _{O_2}}{M _{H_2}}}=\sqrt{\frac{32}{2}}$
$\frac{1 / 2}{1 / x}=\sqrt{16}=4$
$\frac{x}{2}=4$
$\therefore x=8$
$\therefore$ Fraction of $O_2=1 / 8$
