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Solution thermodynamics theory—Part I Chapter 11.

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Presentation on theme: "Solution thermodynamics theory—Part I Chapter 11."— Presentation transcript:

1 Solution thermodynamics theory—Part I Chapter 11

2 topics Fundamental equations for mixtures Chemical potential Properties of individual species in solution (partial properties) Mixtures of real gases Mixtures of real liquids

3 A few equations For a closed system Total differential form, what are (nV) and (nS) Which are the main variables for G?? What are the main variables for G in an open system of k components?

4 G in a mixture (open system)

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 phase Sum the equations of both phases, take into account that In a closed system:

7 We end up with How are dn i  and dn i  related at constant n?

8 For 2 phases, k components at equilibrium For all i = 1, 2,…k Thermal equilibrium Mechanical equilibrium Chemical equilibrium

9 In order to solve the VLE problem Need models for  i in each phase Examples of models of  i in the vapor phase Examples of models of  i in the liquid phase

10 Now we are going to learn: Partial molar properties Because the chemical potential is a partial molar property At the end of this section think about this – What is the chemical potential in physical terms – What are the units of the chemical potential – How do we use the chemical potential to solve a VLE (vapor-liquid equilibrium) problem

11 Partial molar property Solution property Partial property Pure-species property

12 example Open beaker: ethanol + water, equimolar Total volume nV T and P Add a drop of pure water,  n w Mix, allow for heat exchange, until temp T Change in volume ?

13 Total vs. partial properties See derivation page 384

14 Derivation of Gibbs-Duhem equation

15 Gibbs-Duhem at constant T&P Useful for thermodynamic consistency tests

16 Binary solutions See derivation page 386

17 Obtain dM/dx1 from (a)

18 Example 11.3 We need 2,000 cm 3 of antifreeze solution: 30 mol% methanol in water. What volumes of methanol and water (at 25 o C) need to be mixed to obtain 2,000 cm 3 of antifreeze solution at 25 o C Data:

19 solution Calculate total molar volume of the 30% mixture We know the total volume, calculate the number of moles required, n Calculate n 1 and n 2 Calculate the total volume of each pure species needed to make that mixture

20 Note curves for partial molar volumes

21 From Gibbs-Duhem: Divide by dx1, what do you conclude respect to the slopes?

22 Example 11.4 Given H=400x x 2 +x 1 x 2 (40x 1 +20x 2 ) determine partial molar enthalpies as functions of x 1, numerical values for pure-species enthalpies, and numerical values for partial enthalpies at infinite dilution Also show that the expressions for the partial molar enthalpies satisfy Gibbs-Duhem equation, and they result in the same expression given for total H.

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