Question

A closed vessel contains $8\, g$ of oxygen and $7\,g$ of nitrogen. The total pressure is $10$ atm at a given temperature. If now oxygen is absorbed by introducing a suitable absorbent the pressure of the remaining gas (in atm) will be

• A. 2
• B. 10
• C. 4
• D. 5

Answer 1

Answer: (D)

From Dalton's law, final pressure of the mixture of nitrogen and oxygen
$p_{\text{mix}}=p_{1}+p_{2} $
$=\frac{\mu_{1} \,R \,T}{V}+\frac{\mu_{2} \,R \,T}{V}$
$=\frac{m_{1}}{M_{1}} \frac{R\, T}{V}+\frac{m_{2}}{M_{2}} \frac{R \,T}{V} $
$=\frac{8}{32} \frac{R\, T}{V}+\frac{7}{28} \frac{R \,T}{V}=\frac{R \,T}{2 V} $
$10=\frac{R\, T}{2\, V}\,\,\,... (i) $
When oxygen is absorbed then for nitrogen by pressure
$p=\frac{7}{28} \frac{R T}{V} $
$p=\frac{R\, T}{4\, V}\,\,\,\,...(ii)$
From Eqs. (i) and (ii), we get
Pressure of the nitrogen
$p=5 \, atm $