A liquid mixture of ‘A’ and ‘B’ (assume ideal solution) is placed in a cylinder and piston arrangeme — Solutions and Colligative Properties Chemistry Question
Question
A liquid mixture of ‘A’ and ‘B’ (assume ideal solution) is placed in a cylinder and piston arrangement. The piston is slowly pulled out isothermally so that the volume of liquid decreases and that of the vapour increases. At the instant when the quantity of the liquid still remaining is negligibly small, the mole fraction of ‘A’ in the vapour is 0.4. If $P_A^\circ = 0.4 \text{ atm}, P_B^\circ = 1.2 \text{ atm}$ at this temperature, the total pressure at which the liquid has almost evaporated, is
💡 Solution & Explanation
When the last drop of liquid remains, the composition of the entire vapour phase equals the overall initial composition. So $Y_A = 0.4, Y_B = 0.6$. The total pressure $P$ relates to vapour composition by $1/P = Y_A / P_A^\circ + Y_B / P_B^\circ = 0.4 / 0.4 + 0.6 / 1.2 = 1 + 0.5 = 1.5$. Therefore, $P = 1 / 1.5 = 0.667 \text{ atm}$. Therefore, correct answer is A.