An enclosure of volume V contains a mixture of 8 g of oxygen, 14

Question

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)

Options:

A . RTV

B . 3RT2V

C . 5RT4V

D . 7RT5V

Answer: Option C
:
C
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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