States of Matter 1 Question 89
89. A $4: 1$ molar mixture of $\mathrm{He}$ and $\mathrm{CH}_{4}$ is contained in a vessel at 20 bar pressure. Due to a hole in the vessel, the gas mixture leaks out. What is the composition of the mixture effusing out initially?
(1994, 2M)
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Solution:
- From the given information, it can be easily deduced that in the final mixture,
partial pressure of $A=1.0 \mathrm{~atm}$ partial pressure of $B=0.5 \mathrm{~atm}$
$$ \begin{aligned} & \text { Also } \quad n_{A}=\frac{p_{A} V}{R T}=\frac{V}{R T} \ & n_{B}=\frac{p_{B} V}{R T}=\frac{0.5 V}{R T} \ & \Rightarrow \quad \frac{n_{B}}{n_{A}}=\frac{1}{2}=\frac{w_{B}}{M_{B}} \times \frac{M_{A}}{w_{A}}=\frac{3}{2} \times\left(\frac{M_{A}}{M_{B}}\right) \ & \Rightarrow \quad M_{A}: M_{B}=1: 3 \end{aligned} $$
