States of Matter - Result Question 89
####89. A $4: 1$ molar mixture of $He$ and $CH _4$ 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 $A=1.0 atm$ partial pressure of $B=0.5 atm$
$$ \begin{aligned} & \text { Also } \quad n _A=\frac{p _A V}{R T}=\frac{V}{R T} \ & n _B=\frac{p _B V}{R T}=\frac{0.5 V}{R T} \ & \Rightarrow \quad \frac{n _B}{n _A}=\frac{1}{2}=\frac{w _B}{M _B} \times \frac{M _A}{w _A}=\frac{3}{2} \times\left(\frac{M _A}{M _B}\right) \ & \Rightarrow \quad M _A: M _B=1: 3 \end{aligned} $$
