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 :
Answer & explanation
Correct answer: option 4
From Dalton's Law, final pressure of the mixture of nitrogen and oxygen : \(P = P_1 + P_2\)
\(P = \frac{\mu_1 RT}{V} + \frac{\mu_2 RT}{V}\)
\(P = \frac{m_1}{M_1} \frac{RT}{V} + \frac{m_2}{M_2} \frac{RT}{V}\)
\(\frac{8}{32}\frac{RT}{V} + \frac{7}{28}\frac{RT}{V} = \frac{RT}{2V}\)
\(\Rightarrow 10 = \frac{RT}{2V}\) ... (i)
When oxygen is absorbed then for nitrogen let pressure : \(P = \frac{7}{28} \frac{RT}{V}\)
\(\Rightarrow P = \frac{RT}{4V}\) ... (ii)
From (i) and (ii), we get :
Pressure of the nitrogen : P = 5 atm