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Sigma Bond and Pi Bond

A vessel cont...

Question

A vessel contains equal weights of He and $C H_{4}$ gases at 20 bar pressure.Due to the leakage, the gases in the vessel started effusing out.What is the volume ratio of He and $C H_{4}$ gases coming out initially.

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Solution

Molar ratio of $H e$ and $C H_{4}$ is $4 : 1$

Partial pressure ratio of $H e$ and $C H_{4}$ is $16 : 4$

$\frac{n_{H e}}{n_{C H_{4}}} = \sqrt{\frac{M_{C H_{4}}}{M_{H e}}} \times \frac{P_{H e}}{P_{C H_{4}}}$

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 $H e$ and $C H_{4}$ is 8:1

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