States of Matter - Result Question 81
82. At $27^{\circ} C$, hydrogen is leaked through a tiny hole into a vessel for $20 min$. Another unknown gas at the same temperature and pressure as that of hydrogen is leaked through same hole for $20 \hspace {1mm} min$. After the effusion of the gases the mixture exerts a pressure of $6 atm$. The hydrogen content of the mixture is 0.7 mole. If the volume of the container is $3 L$. What is the molecular weight of the unknown gas?
(1992, 3M)
Show Answer
Answer:
Correct Answer: 82. $(1020 {~g}{~mol}^{-1})$
Solution:
Total moles of gas in final mixture $=\frac{p V}{R T}=\frac{6 \times 3}{0.082 \times 300}=0.731$
$\because$ Mole of $H _2$ in the mixture $=0.70$
$\therefore \quad$ Mole of unknown gas $(X)=0.031$
Because both gases have been diffused for same time
$ \frac{r\left(H _2\right)}{r(X)} =\frac{0.70}{0.031}=\sqrt{\frac{M}{2}} $
$\Rightarrow M =1020 g mol^{-1}$
BETA
