Question

4: 1 molar mixture of $He$ and $N_2$ gases is contained in a vessel at 10 bar pressure. Due to a hole in the vessel, the gas mixture leaks out. The ratio of number of moles of $He$ to $N_2$ in the mixture effusing out initially will be:

• A. $\sqrt{28}:1$
• B. $\sqrt{7}:1$
• C. $4\sqrt{7}:1$
• D. $1:\sqrt{28}$

Answer 1

The correct option is C $4\sqrt{7}:1$

Molar ratio of $He$ and $N_2=4:1$
$\therefore$ Partial pressure of hydrogen, $P_{He}=\frac{4}{5}\times 10=8$ bar
Partial pressure of methane, $P_{N_2}=\frac{1}{5}\times 10=2$
$\therefore P_{He}:P_{N_2}=8:2$
$\because$ Time of diffusion is same hence,
$\frac{r_{He}}{r_{N_2}}=\frac{n_{He}}{n_{N_2}}=\frac{P_{He}}{P_{N_2}}\times \sqrt{\frac{M_{N_2}}{M_{He}}}=\frac{8}{2}\times \sqrt{\frac{28}{4}}=4\sqrt{7}:1$