At a given constant temperature, the total vapour pressure (in Torr) of a binary mixture of volatile — Solutions and Colligative Properties Chemistry Question

💡 Solution & Explanation

According to Raoult's law, $P_{total} = P_A^0 X_A + P_B^0 X_B$. Because $X_A = 1 - X_B$, we substitute to get $P_{total} = P_A^0(1 - X_B) + P_B^0 X_B = P_A^0 + (P_B^0 - P_A^0) X_B$. By comparing this theoretical equation with the given empirical equation $P_{total} = 120 - 75 X_B$, we can match the terms: $P_A^0 = 120\text{ Torr}$ and $(P_B^0 - P_A^0) = -75$. Solving for $P_B^0$ yields $120 - 75 = 45\text{ Torr}$.