Density of dry air (only $N_{2} & O_{2}$ ) is 1.146g litre at 740mm and 300K. Calculate composition of air by weight assuming ideal nature:

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Solution

$P M = d R T$
$\Rightarrow \frac{740}{760} \times M = 1.146 \times 0.082 \times 300$
$\Rightarrow M = \frac{1.146 \times 8.2 \times 3 \times 38}{37}$
$\Rightarrow x \times M_{1} = 28.59 + (1 - x) M_{2}$
$\Rightarrow x \times 28 + (1 - x) 32 = 28.59$
$\Rightarrow 32 - 4 x = 28.5 x$
$\Rightarrow x = + \frac{3.04}{4} \times 0.76$
$∴ O_{2} \to 1 - x = 0.24$ by mol in $1$ molcur
$∴$ by weight $N_{2} : O_{2} = \frac{0.76 \times 28}{0.24 \times 32}$
$= 133 : 48$

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