Question

At ${27}^{\circ }C$, hydrogen is leaked through a tiny hole into a vessel for $20$ minute. Another unknown gas at the same temperature and pressure as that of hydrogen leaked through the same hole for $20$ minute. After the effusion of the gases the mixture exerts a pressure of $6$ atmosphere. The hydrogen content of the mixture is $0.7$ mole. If the volume of the container is $3$ litre, what is the molecular mass of the unknown gas?

Answer 1

Let $p_{H_2}$ and $p_{un}$ be the partial pressures of hydrogen and unknown gas respectively and $w$ be the number of moles of unknown gas.
$p_{H_2}=\frac{0.7}{3}\times 0.0821\times 300$
$p_{un}=\frac{w}{3}\times 0.0821\times 300$
Adding both,
$p_{H_2}+p_{un}=6=\left(1/3\right)\times 0.0821\times 300(0.7+w)$
$w=0.0308mole$
Applying law of diffusion,
$\frac{0.7/20}{0.0308/20}=\sqrt{\frac{M}{2}}$ or $M=1033$