Question

Two containers A and B have the same volume. Container 'A' contains 5 mole of oxygen gas. Container 'B' contains 3 moles of He gas and 2 mole of $C{H}_4$ gas. Both the containers are separately kept in vaccum at the same temperature. Both the containers have very small orifices of the same area through which the gases leak out. The rate of diffusion of $O_2$ is how many times the rate of diffusion of He and $C{H}_4$ mixture.

• A. $\sqrt{\frac{8.8}{32}}$
• B. $\sqrt{\frac{7}{32}}$
• C. $\frac{3}{2}\sqrt{\frac{8.8}{32}}$
• D. $\sqrt{\frac{32}{8.8}}$

Answer 1

The correct option is B

$\sqrt{\frac{7}{32}}$

$\frac{r_{He}}{r_{C{H}_4}}=\frac{P_{He}}{P_{C{H}_4}}\sqrt{\frac{M_{C{H}_4}}{M_{He}}}=\frac{3}{2}\sqrt{\frac{16}{4}}=\frac{3}{1}$

Molar ratio of He and $C{H}_4$ gases coming out from B is 3:1

M.W. of mix coming out from

B = $\frac{3}{4}\times 4+\frac{1}{4}\times 16=7$

$\frac{r_{O_2}}{r_{mix}}=\sqrt{\frac{M_{mix}}{M_{O_2}}}=\sqrt{\frac{7}{32}}\Rightarrow \frac{r_{O_2}}{r_{mix}}=\sqrt{\frac{7}{32}}$