Liquids P and Q form an ideal solution. The vapour pressures of pure liquids P and Q at are 300 mm a — Solutions and Colligative Properties Chemistry Question
Question
Liquids P and Q form an ideal solution. The vapour pressures of pure liquids P and Q at $80^\circ\text{C}$ are 300 mm and 100 mm of Hg, respectively. Suppose that the vapour above a solution composed of 1.0 mole of P and 1.0 mole of Q at $80^\circ\text{C}$ is collected and condensed. This condensate is then heated to $80^\circ\text{C}$ and vapour is again condensed to form a liquid R. What is the mole fraction of P in R?
💡 Solution & Explanation
Initial liquid: $X_P = 0.5, X_Q = 0.5$. First vapour (condensate 1): $P_{total} = 300(0.5) + 100(0.5) = 200$. $Y_{P1} = 150/200 = 0.75$. Condensate 1 is heated, so its liquid mole fraction $X_{P2} = 0.75$ and $X_{Q2} = 0.25$. Second vapour (condensate 2, liquid R): $P_{total} = 300(0.75) + 100(0.25) = 225 + 25 = 250$. Mole fraction $Y_{P2} = 225 / 250 = 0.90$. Therefore, correct answer is C.