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Dalton's Law of Partial Pressures

A gaseous mix...

Question

A gaseous mixture containing equal masses of $H e$ and $C H_{4}$ is a total pressure of $2 a t m$ . Calculate partial pressure of $H e$ .

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Solution

Let $x g m$ of $H e$ and $C H_{4}$ be present.

Given, $P_{t o t a l} = 2 a t m$

Number of moles of $H e = \frac{x}{4}$

Number of moles of $C H_{4} = \frac{x}{16}$

According to Dalton’s law of partial pressure,

$P_{A} = χ_{A} P_{t o t a l}$

$χ_{A}$ is mole fraction of $A$

$χ_{C H_{4}} = \frac{\frac{x}{4}}{\frac{x}{4} + \frac{x}{16}} = \frac{0.25}{0.3125} = 0.8$

$P_{C H_{4}} = 0.8 \times 2 = 1.6 a t m$
$∴ P_{H e} = 0.4 a t m$

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