Question

An enclosure of volume $4litres$ contains a mixture of $8g$ of oxygen, $14g$ of nitrogen and $22g$ of carbon dioxide. If the temperature of the mixture is ${27}^{\circ }C$ find the pressure of the mixture of gases. Given $R=8.315K{J}^{-1}mo{l}^{-1}$.

Answer 1

The pressure exerted by a gas is
$P=\frac{nRT}{V}=\frac{mass}{molecularweight}\times \frac{RT}{V}$
Pressure exerted by oxygen $P_1=\frac{8}{32}\frac{RT}{V}=\frac{1}{4}\frac{RT}{V}$
Pressure exerted by nitrogen $P_2=\frac{14}{28}\frac{RT}{V}=\frac{1}{2}\frac{RT}{V}$
Pressure exerted by carbon dioxide $P_3=\frac{22}{44}\frac{RT}{V}=\frac{1}{2}\frac{RT}{V}$
From Dalton's law of partial pressure, the total pressure exerted by the mixture is given by
$P=P_1+P_2+P_3=\frac{1}{4}\frac{RT}{V}+\frac{1}{2}\frac{RT}{V}+\frac{1}{2}\frac{RT}{V}$
$=\frac{5}{4}\frac{RT}{V}=\frac{5}{4}\times \frac{8.315\times 300}{4\times {10}^{-3}}=7.79\times {10}^{5}N/m^2$.