(I re-posted it so a real expert can answer), these questions have long solutions.

consider two liquids A and B that form an ideal solution with ideal vapors. assume the normal freezing points of A and B are Ta= 250 K and Tb =300 K, respectively. Assume that the molar heats of fusion of A and B are equal and is! KJ/mole. If a solution of B containing a mole fraction of A,Xa, is cooled, eventua either A or B will freeze out of solution. If one desires to make the temperatures at which one of the two components freezes out solution as low as possible by adjustments of the Xa one can use the following expression: Xa = 1/(exp{-Hf(Tb-Ta)/RTaTb) + 1) The lowest freezing point temperature will be reached whenever the freezing points of A and B in the solution become equal. a) use the above equation to compute the Xa that gives the lowest freezing point. b) Make a careful plot of freezing point of the soluti versus Xa. If you were using a mixture of A and B as antifreeze in your car, what would be the optimum ratio? Hint: Look for where the component freezing points are the same: This problem will explain why adding more anti freeze to your car does not always produce a lower freezing point in radiator fluid