Question

A certain volume of $H_2$ effuses from an apparatus in 1 minute. The same volume of ozonised oxygen $(O_3+O_2\text{mix})$ took $246\text{s}$ to effuse from the apparatus under identical conditions. Find the $\%$ composition of the ozonised oxygen.

• A. 10.125
• B. 99.87
• C. 79.87
• D. 69.87

Answer 1

The correct option is A 10.125

Let the molecular wt. of the mixture $(O_3+O_2)$ be $M_2$ then from
$\frac{\frac{V}{t_1}}{\frac{V}{t_2}}=\sqrt{\frac{M_2}{M_1}}$
$\Rightarrow \frac{t_2}{t_1}=\sqrt{\frac{M_2}{M_1}}$
$\Rightarrow \frac{246}{60}=\sqrt{\frac{M_2}{2}}$
$\Rightarrow M_2=33.62$ (average mol. Wt. of $O_3+O_2$)
Let the mol $\%$ of $O_3$ be a then the mol $\%$ of $O_2=100-a$
then average mole wt. $=\frac{a\times 48+(100-a)32}{100}$
$\Rightarrow 33.62=\frac{a\times 48+(100-a)32}{100}$
$\Rightarrow O_2=189.75\partial \therefore O_3=10.125$