1. Solution thermodynamics theory—Part IV
Chapter 11

2. When we deal with mixtures of liquids or solids
We define the ideal solution model
Compare it to the ideal gas mixture, analyze its similarities and differences

3. Component i in a mixture of ideal gases
This eqn. is obtained by combining
Now we define
Ideal solution model

4. Other thermodynamic properties for the ideal solution: partial molar volume

5. partial molar entropy in the ideal solution

6. partial molar enthalpy in the ideal solution

7. Chemical potential ideal solution
Chemical potential component i
in a Real solution
Chemical potential
Pure component i
Subtracting:
For the ideal solution

8. Lewis-Randall rule Lewis-Randall rule
(Dividing by Pxi each side of the equation)

12. When is the ideal solution valid?
Mixtures of molecules of similar size and similar chemical nature
Mixtures of isomers
Adjacent members of homologous series

13. Virial EOS applied to mixtures

14. How to obtain the cross coefficients Bij
Mixing rules for Pcij, Tcij, wij, to 11.73

15. Fugacity coefficient from virial EOS
For a multicomponent mixture, see eqn

16. problem
For the system methane (1)/ethane (2)/propane (3) as a gas, estimate
at T = 100oC, P = 35 bar, y1 =0.21, and y2 =0.43
Assume that the mixture is an ideal solution
Obtain reduced pressures, reduced temperatures, and calculate

17. Results: methane (1) ethane (2) propane (3)
Virial model
Ideal solution

18. Now we want to define a new type of residual properties
Instead of using the ideal gas as the reference, we use the ideal solution

19. Excess properties The most important excess function is
the excess Gibbs free energy GE
Excess entropy can be calculated
from the derivative of GE wrt T
Excess volume can be calculated
from the derivative of GE wrt P
And we also define partial molar excess properties

21. Definition of activity coefficient

22. Summary

23. Summary

24. Note that:

25. problem a) Find expressions for ln g1 and ln g2 at T and P
The excess Gibbs energy of a binary liquid mixture at T and P is given by
a) Find expressions for ln g1 and ln g2 at T and P
Using x2 =1 – x1
GE/RT= x x x13

26. Since gi comes from
We can use eqns and 11.16

27. then
And we obtain

28. If we apply the additivity rule and the Gibbs-Duhem equation
At T and P
(b and c) Show that the ln gi expressions satisfy
these equations
Note: to apply Gibbs-Duhem, divide the equation by dx1 first

29. Plot the functions and show their values
GE/RT
ln g1
ln g2