At what pressure, half of the total moles of liquid solution will vaporize? — Solutions and Colligative Properties Chemistry Question

💡 Solution & Explanation

If half vaporizes, $n_L = 10$ and $n_V = 10$. Mass balance for benzene: $10 X_B + 10 Y_B = 10 \Rightarrow X_B + Y_B = 1$. Since $Y_B = \frac{P_B^\circ X_B}{P}$, and from the other component $1 - X_B + 1 - Y_B = 1 \Rightarrow X_T + Y_T = 1$. Solving this system for an equimolar binary mixture yields $P = \sqrt{P_B^\circ P_T^\circ} = \sqrt{100 \times 40} = \sqrt{4000} \approx 63.245 \text{ mm Hg}$. Therefore, correct answer is B.