For a binary ideal liquid mixture of volatile components A and B, which of the following mathematica — Solutions and Colligative Properties Chemistry Question
Question
For a binary ideal liquid mixture of volatile components A and B, which of the following mathematical plots will theoretically yield a perfect straight line? (Where $P_{total}$ is the total vapour pressure, $X_B$ is the mole fraction of B in the liquid phase, and $Y_A$ is the mole fraction of A in the vapour phase).
💡 Solution & Explanation
By Raoult's law, $P_{total} = P_A^0 X_A + P_B^0 X_B$. In the vapour phase, Dalton's law gives $Y_A = \frac{P_A^0 X_A}{P_{total}}$. We know $X_A + X_B = 1$. By substituting $X_A = \frac{Y_A P_{total}}{P_A^0}$ and $X_B = \frac{Y_B P_{total}}{P_B^0}$ into the sum, we get $\frac{Y_A P_{total}}{P_A^0} + \frac{Y_B P_{total}}{P_B^0} = 1$. Dividing by $P_{total}$ yields $\frac{1}{P_{total}} = \frac{Y_A}{P_A^0} + \frac{1 - Y_A}{P_B^0} = Y_A(\frac{1}{P_A^0} - \frac{1}{P_B^0}) + \frac{1}{P_B^0}$. This perfectly matches the linear equation $y = mx + c$ for plotting $\frac{1}{P_{total}}$ against $Y_A$.