Question

4 : 1 molar mixture of $He$ and $C{H}_4$ gases is contained in a vessel at 20 bar pressure. Due to a hole in the vessel, the gas mixture leaks out. The ratio of number of moles of $He$ to $C{H}_4$ in the mixture effusing out initially will be:

• A. 8 : 1
• B. 1 : 8
• C. 1 : 4
• D. 4 : 1

Answer 1

The correct option is A 8 : 1

Molar ratio of $He$ and $C{H}_4=4:1$
$\therefore$ Partial pressure of hydrogen, $P_{He}=\frac{4}{5}\times 20=16$ bar
Partial pressure of methane, $P_{C{H}_4}=\frac{1}{5}\times 20=4$
$\therefore P_{He}:P_{C{H}_4}=16:4$
$\because$ Time of diffusion is same hence,
$\frac{r_{He}}{r_{C{H}_4}}=\frac{n_{He}}{n_{C{H}_4}}=\frac{P_{He}}{P_{C{H}_4}}\times \sqrt{\frac{M_{C{H}_4}}{M_{He}}}=\frac{16}{4}\times \sqrt{\frac{16}{4}}=4\times 2=8:1$