An enclosure of volume $V$ contains a mixture of $8 g$ of oxygen, $14 g$ of nitrogen and $22 g$ of carbon- dioxide at absolute temperature $T$ . The pressure of the mixture of gases is ( $R$ is universal gas constant)

$\frac{R T}{V}$

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$\frac{3 R T}{2 V}$

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$\frac{5 R T}{4 V}$

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$\frac{7 R T}{5 V}$

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Solution

The correct option is C
$\frac{5 R T}{4 V}$

The pressure exerted by a gas is given by

$P = \frac{n R T}{V}$

= $\frac{m a s s}{m o l e c u l a r w e i g h t} \times \frac{R T}{V}$

Pressure exerted by oxygen $P_{1} = \frac{8}{32} \frac{R T}{V} = \frac{1}{4} \frac{R T}{V}$

Pressure exerted by oxygen $P_{2} = \frac{14}{28} \frac{R T}{V} = \frac{1}{2} \frac{R T}{V}$

Pressure exerted by carbon dioxide

$P_{3} = \frac{22}{44} \frac{R T}{V} = \frac{1}{2} \frac{R T}{V}$

From Dalton's law of partial pressures, the total pressure exerted by the mixture is given by

$P = P_{1} + P_{2} + P_{3}$

= $\frac{1}{4} \frac{R T}{V} + \frac{1}{2} \frac{R T}{V} + \frac{1}{2} \frac{R T}{V}$

= $\frac{5 R T}{4 V}$ ,

which is choice (c)

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An enclosure of volume V contains a mixture of 8 g of oxygen, 14 g of nitrogen and 22 g of carbon- dioxide at absolute temperature T. The pressure of the mixture of gases is (R is universal gas constant)

An enclosure of volume $V$ contains a mixture of $8 g$ of oxygen, $14 g$ of nitrogen and $22 g$ of carbon- dioxide at absolute temperature $T$ . The pressure of the mixture of gases is ( $R$ is universal gas constant)