5 G in a mixture of k components at T and P How is this equation reduced if n =1?
6 2 phases (each at T and P) in a closed system Apply this equation to each phaseSum the equations of both phases, take into account thatIn a closed system:
7 We end up withHow are dnia and dnib related at constant n?
8 For 2 phases, k components at equilibrium Thermal equilibriumMechanical equilibriumChemical equilibriumFor all i = 1, 2,…k
9 In order to solve the VLE problem Need models for mi in each phaseExamples of models of mi in the vapor phaseExamples of models of mi in the liquid phase
10 Now we are going to learn: Partial molar propertiesBecause the chemical potential is a partial molar propertyAt the end of this section think about thisWhat is the chemical potential in physical termsWhat are the units of the chemical potentialHow do we use the chemical potential to solve a VLE (vapor-liquid equilibrium) problem
18 Example 11.3We need 2,000 cm3 of antifreeze solution: 30 mol% methanol in water.What volumes of methanol and water (at 25oC) need to be mixed to obtain 2,000 cm3 of antifreeze solution at 25oCData:
19 solution Calculate total molar volume of the 30% mixture We know the total volume, calculate the number of moles required, nCalculate n1 and n2Calculate the total volume of each pure species needed to make that mixture
21 From Gibbs-Duhem:Divide by dx1, what do you conclude respect to the slopes?
22 Example 11.4Given H=400x1+600x2+x1x2(40x1+20x2) determine partial molar enthalpies as functions of x1, numerical values for pure-species enthalpies, and numerical values for partial enthalpies at infinite dilutionAlso show that the expressions for the partial molar enthalpies satisfy Gibbs-Duhem equation, and they result in the same expression given for total H.