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Mixture

The density o...

Question

The density of a mixture of $N_{2}$ and $O_{2}$ at NTP is $1.3 g L^{- 1}$ . Calculate partial pressure of $O_{2}$ .

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Solution

Let $n_{1}$ and $n_{2}$ moles of $N_{2}$ and $O_{2}$ be present in the mixture respectively.
Average molecular mass of the mixture $= \frac{28 n_{1} + 32 n_{2}}{n_{1} + n_{2}} . . (i)$
Average molecular mass from general gas equation,
$M = \frac{D}{P} \times R T = \frac{1.3}{1} \times 0.0821 \times 273 = 29.137 . . (i i)$
So, $\frac{28 n_{1} + 32 n_{2}}{n_{1} + n_{2}} = 29.137$ or $\frac{4 n_{2}}{n_{1} + n_{2}} = 1.137$
or $\frac{n_{2}}{n_{1} + n_{2}} = 0.28 =$ mole fraction of oxygen
Partial pressure of $O_{2} = 0.28 \times 1 = 0.28 a t m$ .

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