States of Matter - Result Question 37
####37. Equal weights of methane and hydrogen are mixed in an empty container at $25^{\circ} C$. The fraction of the total pressure exerted by hydrogen is
$(1984,1 M)$
(a) $\frac{1}{2}$
(b) $\frac{8}{9}$
(c) $\frac{1}{9}$
(d) $\frac{16}{17}$
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Solution:
- Let $x$ grams of each hydrogen and methane are mixed,
$$ \begin{aligned} \text { Moles of } H _2 & =\frac{x}{2} \ \text { Moles of } CH _4 & =\frac{x}{16} \ \Rightarrow \quad \text { Mole fraction of } H _2 & =\frac{\frac{x}{2}}{\frac{x}{2}+\frac{x}{16}}=\frac{8}{9} \ \Rightarrow \quad \frac{\text { Partial pressure of } H _2}{\text { Total pressure }} & =\text { Mole fraction of } H _2=\frac{8}{9} \end{aligned} $$
