Question #44520

Two volatile liquids, \ce{A} and \ce{B}, form a non-ideal solution exhibiting a positive deviation from Raoult's law. At $300\text{ K}$, the vapor pressures of pure \ce{A} and pure \ce{B} are $300\text{ Torr}$ and $100\text{ Torr}$, respectively. A student incorrectly assumes that the mixture behaves ideally and that the vapor pressures of both pure liquids follow a temperature coefficient $Q_{10} = 2$ (i.e., vapor pressure doubles for every $10\text{ K}$ rise in temperature). Experimentally, the mixture forms a minimum-boiling azeotrope at $330\text{ K}$ with a liquid mole fraction of \ce{A}, $x_A = 0.5$. Calculate the magnitude of the difference between the true mole fraction of \ce{A} in the vapor phase ($y_{A, \text{true}}$) at the azeotropic point and the vapor mole fraction of \ce{A} ($y_{A, \text{calc}}$) calculated by the student at $330\text{ K}$ for the same liquid composition.