12.22. Consider a binary mixture of two species 1 and 2 that is at vapor-liquid equilibrium. Both species are present in the liquid and gas phases. One might define a partition coefficient for each species between the two phases according to K1x1y1,K2x2y2 where the x and y terms denote mole fractions in the liquid and vapor phases, respectively. Assume that the temperature-independent enthalpies of vaporization and boiling temperatures for pure species 1 and 2, namely h1,h2,Tb1, and Tb2, are known. Further assume that both phases behave as ideal mixtures, although the vapor phase is not necessarily an ideal gas (only an ideal mixture). (a) Develop expressions for the partition coefficients as a function of temperature and the pure heats of vaporization and boiling temperatures. (b) Is this model capable of predicting an azeotrope, for which x1=y1 ? Why or why not? Justify your answer with an equation or two. (c) Express x1 and y1 in terms of the partition coefficients K1 and K2. (d) A single-phase liquid mixture is well below its boiling point and has an overall composition of species 1 of z1. It is then heated to a temperature in the twophase regime. Express the molar fraction of the solution that is in the vapor phase f as a function just of z1 and the partition coefficients K1 and K2. (e) Show that the temperature at which the entire solution in (d) vaporizes is given by an equation of the form 1=C1exp(kBTh1)+C2exp(kBTh2) Find C1 and C2