Question

$20d{m}^{3}ofS{O}_2$ diffuse through a porous partition in 60s. What volume of $O_2$ will diffuse under similar condition in 30s?

• A. 20
• B. 45
• C. 14.1
• D. 10

Answer 1

The correct option is C 14.1

Let $r_1,M_1$ be the rate of diffusion and Molecular weight of $S{O}_2$ and $r_2,M_2$ be the rate of diffusion and Molecular weight of $O_2$.
Let V $d{m}^3$ of $O_2$ diffusion in 30 sec.
$\therefore r_1=\frac{20}{60},r_2=\frac{V}{30},M_1=64,M_2=32$
$\frac{r_1}{r_2}=\sqrt{\frac{M_2}{M_1}}\Rightarrow \frac{\frac{1}{3}}{\frac{V}{30}}=\sqrt{\frac{32}{64}}$
$\Rightarrow \frac{10}{V}=\sqrt{\frac{1}{2}}$ $\Rightarrow \frac{10\times 10}{V^2}=\frac{1}{2}$
$\Rightarrow V^2=200$ or, $V=\sqrt{200}=14.1d{m}^3$