Question

Calculate the relative rate of diffusion of $O_2$ to $C{H}_4$ from a container containing $O_2$ and $C{H}_4$ is 3 : 2 mass ratio.

• A. $\frac{3\sqrt{2}}{4}$
• B. $\frac{3}{4\sqrt{2}}$
• C. $\frac{3}{2\sqrt{2}}$
• D. none of these

Answer 1

The correct option is B $\frac{3}{4\sqrt{2}}$

$\frac{r_{O_2}}{r_{C{H}_4}}=\frac{P_{O_2}}{P_{C{H}_4}}=\sqrt{\frac{m_{C{H}_4}}{m_{O_2}}}=\frac{n_{O_2}}{n_{C{H}_4}}\times \sqrt{\frac{m_{C{H}_4}}{m_{O_2}}}$

$\Rightarrow \frac{r_{O_2}}{r_{C{H}_4}}=\frac{3}{32}\times \frac{16}{2}\sqrt{\frac{16}{32}}=\frac{3}{4\sqrt{2}}$

This is because we know $r\propto \frac{P}{\sqrt{m}}$ where $r$ is rate of diffusion. $P$ is pressure and $m$ is Molecular mass.

Hence, the correct answer is option $\text{B}$.