1. Solution Thermodynamics: Applications
Chapter 12-Part IV

2. Other models for GE/RT

3. The Van-Laar equation

4. Local composition theory
There are cases where the cross-parameter may be a function of composition.
A12 = A12(x)
So, there could be “local” compositions different than the overall “bulk” compositions. For example (if coordination number is 8)
AAAAAAA
AABBAAA xAB = ; xBB =
“A around B” or “B around B”

5. examples
Specific interactions such as H-bonding and polarity

6. Nomenclature x21 = mole fraction of “2” around “1”
x11 + x21 =
111111
x12 = mole fraction of “1” around “2”
x22 = mole fraction of “2” around “2”
x22 + x12 =1
Local compositions are related to overall compositions:
If the weighting functions
are =1 random solutions

7. Key are the Wij weighting factors
If Wij =1 => random mixture

8. Wilson equation
Wilson assumes that the weighting functions are functions of size and energetic interactions:
z is the coordination number for atom i
even if eij =eji (this is not always the case), the Lij parameters
may be different, why?

9. Intermolecular pair potential
Uij
eij

10. Wilson’s equation for a binary
For infinite dilution:

11. NRTL (non-random, two-liquid)
Actual parameters: a, b12 and b21
See Table 12.5, page 474
Renon and Prausnitz, 1968

12. page 474

13. UNIQUAC equation
UNIversal QUAsi Chemical model (Abrams and Prausnitz, AIChE J. 21:116 (1975)
Uses surface areas (qi) to represent shapes
qi is proportional to the surface area of i
z is the coordination number

14. UNIQUAC cont. coordination number, z = 10
qj accounts for shape, rj accounts for size
Energetic parameters
tji=exp-(eji-eii)/RT= exp [(-aji)/RT]
Pure species
molecular parameters (in tables): r1, r2, q1, q2
ri are molecular size
parameters relative to –CH2-

15. Activity coefficients from UNIQUAC

18. UNIFAC (UNIQuac Functional Activity Coefficient model)
The solution is made of molecular fragments (subgroups)
New variables (Rk and Qk)
Combinatorial part is the same as UNIQUAC
where Fk and qk are the volume fractions and surface fractions

20. Residual part of UNIFAC is different
i identify species
# of subgroups k in molecule i
Be careful,
this q is different
than the
surface fraction !!

22. Property changes of mixing
We showed that for ideal solutions:
From these properties we can evaluate ME = M - Mid

23. Property changes of mixing
Let’s define:

24. Property changes of mixing
This means that the excess
properties and the properties change
of mixing can be calculated from
each other
What are the DM for ideal solutions?

25. Mixing process at T and P