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 dnia and dnib related at constant n?

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

9. In order to solve the VLE problem
Need models for mi in each phase
Examples of models of mi in the vapor phase
Examples of models of mi 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, Dnw
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 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 25oC
Data:

19. solution Calculate total molar volume of the 30% mixture
We know the total volume, calculate the number of moles required, n
Calculate n1 and n2
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=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 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.