Question

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

• A. $\frac{RT}{V}$
  
• B. $\frac{3RT}{2V}$
  
• C. $\frac{5RT}{4V}$
  
• D. $\frac{7RT}{5V}$

Answer 1

The correct option is C

$\frac{5RT}{4V}$

The pressure exerted by a gas is given by
$P=\frac{nRT}{V}=\frac{mass}{molecularweight}\times \frac{RT}{V}$
Pressure exerted by oxygen $P_1=\frac{8}{32}\frac{RT}{V}=\frac{1}{4}\frac{RT}{V}$
Pressure exerted by oxygen $P_2=\frac{14}{28}\frac{RT}{V}=\frac{1}{2}\frac{RT}{V}$
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 pressures, the total pressure exerted by the mixture is given by
$P=P_1+P_2+P_3=\frac{1}{4}\frac{RT}{V}+\frac{1}{2}\frac{RT}{V}+\frac{1}{2}\frac{RT}{V}=\frac{5RT}{V}whichischoice\left(c\right)$