1. Faulty of engineering, technology & research
CHEMICAL ENGINEERINH DEPARTMENT
Sub.:- solution thermodynamic application
Prepared by:
Aal Vinod
Ahir Sanjay
Bhadaja Jiten
Dankhara Nikunj
Desai Rohan
Guided by:-
Mr. Kimshuk D. Desai

2. OUTLINES Liquid Phase Properties From VLE Data
Fugasity And Fugasity Co-efficent
Excess Gibb’s Energy

3. Liquid-phase properties from VLE data
Fugacity
For species i in the vapor mixture:
Vapor/liquid equilibrium:
The vapor phase is assumed an ideal gas:
Therefore:
The fugacity of species i (in both the liquid and vapor phases) is equal to the partial pressure of species i in the vapor phase.
Its value increases from zero to Pisat for pure species i

4. Fig. 12.1
Table 12.1
The first three columns are P-x1-y1 data.
Columns 4 and 5 are:
Column 6 is:

5. Fig 12.3
Fig 12.2
Henry’s constant, the limiting slope of the
curve at xi = 0.
Henry’s law expresses: , it is approximate valid for small values of xi

6. Henry’s law Lewis/Randall rule Gibbs/Duhem equation x1 → 0 x2 → 1
Gibbs/Duhem equation for binary mixture at const. T and P:
The Lewis/Randall rule,
Division by dx1
when x1 = 1,
limit

7. 11.5 Fugacity & Fugacity Coefficient: Pure Species
As evident from Eq. (11.6), the chemical potential μi provides the fundamental criterion for phase equilibria. This is true as well for chemical reaction equilibria. However, it exhibits characteristics which discourage its use. The Gibbs energy, and hence μi , is defined in relation to the internal energy and entropy. Because absolute values of internal energy are unknown, the same is true for μi .

8. 11.5 Fugacity & Fugacity Coefficient: Pure Species
Moreover, Eq. (11.20) shows that μiig approaches negative infinity when either P or yi approaches zero. This is true not just for an ideal gas but for any gas. Although these characteristics do not preclude the use of chemical potentials, the application of equilibrium criteria is facilitated by introduction of the fugacity, a property that takes the place of μi but which does not exhibit its less desirable characteristics.

9. 11.5 Fugacity & Fugacity Coefficient: Pure Species
The origin of the fugacity concept resides in Eq. (11.28), valid only for pure species i in the ideal gas state. For a real fluid, we write an analogous equation that defines fi, the fugacity of pure species i:

10. 11.5 Fugacity & Fugacity Coefficient: Pure Species
The origin of the fugacity concept resides in Eq. (11.28), valid only for pure species i in the ideal gas state. For a real fluid, we write an analogous equation that defines fi, the fugacity of pure species i:
(11.31)
This new property fi , with units of pressure, replaces P in Eq.(11.28). Clearly, if (11.28) is a special case of Eq. (11.31), then:

11. 11.5 Fugacity & Fugacity Coefficient: Pure Species
(11.32)
and the fugacity of pure species i as an ideal gas is necessarily equal to its pressure. Subtraction of Eq. (11.28) from Eq. (11.31), both written for the same T and P, gives:
By the definition of Eq. (6.41), Gi – Giig is the residual Gibbs Energy, GiR；thus，

12. 11.5 Fugacity & Fugacity Coefficient: Pure Species
(11.33)
where the dimensionless ratio fi /P has been defined as another new property, the fugacity coefficient, given by symbolΦi :
(11.34)
These equations apply to pure species i in any phase at any condition. However, as a special case they must be valid for ideal gases, for which GiR = 0, Φi = 1, and Eq. (11.28) is recovered from Eq. (11.31).

13. 11.5 Fugacity & Fugacity Coefficient: Pure Species
Moreover, we may write Eq. (11.33) for
P = 0, and combine it with Eq. (6.45):
As explained in connection with Eq. (6.48), the value of J is immaterial, and is set equal to zero. Whence,

14. 11.5 Fugacity & Fugacity Coefficient: Pure Species
And
The identification of lnΦi with GiR / RT by Eq. (11.33) permits its evaluation by the integral of Eq. (6.49):

15. 11.5 Fugacity & Fugacity Coefficient: Pure Species
Fugacity coefficients (and therefore fugacities) for pure gases are evaluated by this equation from P V T data or from a volume-explicit equation of state.
For example, when the compressibility factor is given by Eq. (3.38),

16. 11.5 Fugacity & Fugacity Coefficient: Pure Species
Because the second virial coefficient Bii is a function of temperature only for a pure speciues, substitution into Eq. (11.35) gives:

17. 11.5 Fugacity & Fugacity Coefficient: Pure Species
Vapor/Liquid Equilibrium for Pure Species

18. 11.5 Fugacity & Fugacity Coefficient: Pure Species
Vapor/Liquid Equilibrium for Pure Species
For a pure species coexisting liquid and vapor phases are in equilibrium when they have the same temperature, pressure, and fugacity.

19. 11.6 Fugacity & Fugacity Coefficient: Species in Solution
The definition of the fugacity of a species in solution is parallel to the definition of the pure species fugacity. For species I in a mixture of real gases or in a solution of liquids, the equilibrium analogous to Eq. (11.20), the ideal-gas expression, is:

20. 11.6 Fugacity & Fugacity Coefficient: Species in Solution
where is the fugacity of species i in solution, replacing the partial pressure yiP. This definition of does not make it a partial molar property, and it is therefore identified by a circumflex rather than by an overbar.
A direct application of this definition indicates its potential utility. Equation (11.6) is the fundamental criterion for phase equilibrium.

21. 11.6 Fugacity & Fugacity Coefficient: Species in Solution
At equilibrium
Thus, multiple phases at the same T and P are in equilibrium when the fugacity of each constituent species is the same in all phases.
This criterion of equilibrium is the one usually applied by chemical engineers in the solution of phase-equilibrium problems.

22. 11.6 Fugacity & Fugacity Coefficient: Species in Solution
For the specific case of multicomponent vapor/liquid equilibrium, Eq. (11.47) becomes:
Equation (11.39) results as a special case when this relation is applied to the vapor/liquid equilibrium of pure species i.

23. 11.6 Fugacity & Fugacity Coefficient: Species in Solution
The definition of a residual property is given in Sec. 6.2:
Where M is the molar (or unit mass) value of a thermodynamic property and M ig is the value that the property would have for an ideal gas of the same composition at same T and P. The defining equation for a partial residual property

24. 11.6 Fugacity & Fugacity Coefficient: Species in Solution

25. 11.6 Fugacity & Fugacity Coefficient: Species in Solution

26. 11.6 Fugacity & Fugacity Coefficient: Species in Solution

27. 11.6 Fugacity & Fugacity Coefficient: Species in Solution

28. 11.6 Fugacity & Fugacity Coefficient: Species in Solution

29. 11.5 Fugacity & Fugacity Coefficient: Pure Species
The Nature of Excess Properties
Consider the change in G to G* at very low pressure

30. Fugacity & Fugacity Coefficient: Pure Species

31. Fugacity & Fugacity Coefficient: Pure Species

32. Fugacity & Fugacity Coefficient: Pure Species

33. Generalized Correlations for the Fugacity Coefficient

34. Generalized Correlations for the Fugacity Coefficient
The average properties at the critical point and the 2nd Virial coefficient can be determined from Equation

35. Fugacity of a Pure Liquid
fi of a compressed liquid is calculated in 2 steps:
fi of saturated liquid and vapor
Compress liquid from Psat to P

36. Generalized Correlations for the Fugacity Coefficient
The average properties at the critical point and the 2nd Virial coefficient can be determined from Equation

37. Fugacity and Fugacity Coefficient: Species in solution
fi of a solution is parallel to the pure solution
The ideal solution (analogous to the ideal gas)
At equilibrium:
Thus, multiple phases at the same T and P are in equilibrium when the fugacity of each constituent species is the same in all phases.

38. Fugacity and Fugacity Coefficient: Species in solution
A partial residual property,

39. The Fundamental Residual-Property Relation

40. Fugacity Coefficient from the Virial EOS
For mixture
e.g. binary mixture
B = y1y1B11 + y1y2B12 + y2y1B21+ y2y2B22
B = y12B11 + 2y1y2B12 + y22B (11.58)

41. The Ideal Solution
Serves as a standard to which real-solution behavior can be compared.

42. The Ideal Solution: The Lewis/Randall Rule
Fugacity calculation of i in ideal solution.

43. Excess Properties
Fundamental of excess property relation

44. The Excess Gibbs Energy and the Activity Coefficient

45. The Excess Gibbs Energy and the Activity Coefficient

46. The Excess Gibbs Energy and the Activity Coefficient

47. Gibbs-Duhem Equation

48. The Nature of the Excess Properties
All MEs become 0 as either species approaches purity.
Plot between GE vs. x1 is approximately parabolic in shape,
Both HE and TSE exhibit individualistic composition
dependencies
When an excess property has a single sign (as does GE in
all six cases, the extreme value of ME (maximum or minimum)
Often occurs near the equimolar composition.