1. Solution Thermodynamics: Applications Chapter 12-Part IV

2. Other models for G E /RT

3. The Van-Laar equation

4. example Benzene(1)-ethanol(2) system exhibits an azeotrope at 760 mm Hg and 68.24 o C containing 44.8 mole% ethanol. Calculate the composition of the vapor in equilibrium with an equimolar liquid solution at 760 mm Hg given the Antoine constants. Use van Laar equation for the activity coefficients.

5. solution First, consider that these eqns. can be rearranged to give:

6. So, at the azeotrope Calculate  1 =P/P 1 sat,  2 =P/P 2 sat, since we know x 1 az and x 2 az, we can obtain A 12 ’=1.3421 and A 21 ’=1.8810 Now lets consider x 1 =x 2 =0.5. Using Van Laar we get  1 = 1.579;  2 = 1.386; and get the bubble T with the usual procedure. The solution is T=68.24 o C, y 1 = 0.54, y 2 =0.46

7. Important points The T-x diagram is fairly flat near an azeotrope. Important effect on temperature profiles in distillation columns. This system has a minimum boiling azeotrope. It has positive deviations from Raoult’s law (activity coefficients > 1). The components will have a greater fugacity (tendency to escape from the liquid) than they would have in an ideal solution.

8. Local composition theory There are cases were the cross-parameter may be a function of composition. A 12 = A 12 (x) So, there could be “local” compositions” different than the overall “bulk” compositions. For example AAAAAAA AABBAAAx AB = ; x BB = AAAAAAA “A around B” or “B around B”

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

10. Nomenclature x 21 = mole fraction of “2” around “1” x 11 = mole fraction of “1” around “1” x 11 + x 21 =1 x 12 = mole fraction of “1” around “2” x 22 = mole fraction of “2” around “2” x 22 + x 12 =1 Local compositions are related to overall compositions: If the weighting functions are =1 random solutions

11. Key are the weighting factors

12. Two-fluid theory Define a departure function: Functions of composition, represent local composition variations Using this equation, excess functions can be constructed

13. Wilson equation Wilson assumes that the weighting functions are functions of size and energetic interactions: even if  ij =  ji (this is not always the case) z is the coordination number for atom i

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

15. NRTL (non-random, two-liquid) Renon and Prausnitz, 1968 Actual parameters: a, b 12 and b 21

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

18. UNIQUAC cont. The coordination number, z = 10 q j accounts for sizes and shapes Energetic parameters Pure species molecular parameters (in tables): r 1, r 2, q 1, q 2  ji =exp-(  ji -  ii )/RT

19. Activity coefficients from UNIQUAC

20. UNIFAC (UNIversal Functional Activity Coefficient model) The solution is made of molecular fragments (subgroups) New variables (R k and Q k ) Combinatorial part is the same as UNIQUAC

21. Residual part of UNIFAC is different Calculated in a solution of groups for ALL molecules in the mixture Calculated in a solution of groups ONLY for molecule 1

22. UNIFAC Residual contribution is different

25. Mixing process at T and P

27. V E =  V and H E =  H But  G is not equal to G E and  S is not equal to S E (see equations 12.25 to 12.33)

30. HW # 7, due Monday, 10/15 12.18 for acetone-methanol; 12.19 for the same system; at the conditions of problem 12.14 for the system acetone-water: a) use UNIQUAC equation, b) use UNIFAC equation 12.25 12.26