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:

  1. Let $x$ grams of each hydrogen and methane are mixed,

$$ \begin{aligned} \text { Moles of } H _2 & =\frac{x}{2} \ \text { Moles of } CH _4 & =\frac{x}{16} \ \Rightarrow \quad \text { Mole fraction of } H _2 & =\frac{\frac{x}{2}}{\frac{x}{2}+\frac{x}{16}}=\frac{8}{9} \ \Rightarrow \quad \frac{\text { Partial pressure of } H _2}{\text { Total pressure }} & =\text { Mole fraction of } H _2=\frac{8}{9} \end{aligned} $$



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