States of Matter 1 Question 37
37. Equal weights of methane and hydrogen are mixed in an empty container at $25^{\circ} \mathrm{C}$. The fraction of the total pressure exerted by hydrogen is
$(1984,1 \mathrm{M})$
(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,
$$ \begin{aligned} \text { Moles of } \mathrm{H}{2} & =\frac{x}{2} \ \text { Moles of } \mathrm{CH}{4} & =\frac{x}{16} \ \Rightarrow \quad \text { Mole fraction of } \mathrm{H}{2} & =\frac{\frac{x}{2}}{\frac{x}{2}+\frac{x}{16}}=\frac{8}{9} \ \Rightarrow \quad \frac{\text { Partial pressure of } \mathrm{H}{2}}{\text { Total pressure }} & =\text { Mole fraction of } \mathrm{H}_{2}=\frac{8}{9} \end{aligned} $$
