Question

$4:1$ molar mixture of $He$ and $C{H}_4$ is contained in a vessel at $20$ bar pressure. Due to the hole in the vessel, the gas mixture leaks out.

What is the composition of the mixture effusing out initially?

Answer 1

The molar ratio of He and CH4 is 4:1

The partial pressure ratio of He and CH4 is 16:4

$\frac{n_{He}}{n_{C{H}_4}}=$$\sqrt{\frac{M_{C{H}_4}}{M_{He}}}$$\times \frac{P_{He}}{P_{C{H}_4}}$

Since total pressure = 20 bar

$=\sqrt{\frac{16}{4}}\times \frac{16}{4}$

Since the time of diffusion for both is same

$=8:1$

The composition of mixture initially gone out for He and CH${}_4$ is $8:1$