The molar volume of a binary mixture is given by: = V = 0.45x, +0.55x2 - 0.12x,xz [cm/mol] a. (10 pts) Derive expressions for the partial molar volumes of both components. b. (5 pts) Calculate the total volume of mixing in [cm3] of a mixture of 3 moles of component (1) and 2 moles of component (2). C. (10 pts) Write an expression for the molar enthalpy H [J/mol] for this mixture, given U [J/mol] = 100+0.5*T[K] and P [bar] = 1000. d. (10 pts) How much heat in [ku] is required to raise the temperature of the mixture from 20 to 100C? (Assume the mixture is heated in an adiabatic vessel and the molar proportions are the same as in part b). = =