1. CHEMICAL ENGINEERING THERMODYANAMICS-II EVALUATION OF ACTIVITY COEFFICENT
Prepared By
Hitesh N. Panchal
Assistant Professor
D.D.University Nadiad.

2. Liquid Phase Properties from VLE Data
Calculate activity coefficient at infinite dilution or Margule’s constants or limiting activity coefficient

3. Infinite dilution
It is the particular behavior of a two substances mixture when the concentration of one component approaches the limit of zero and the other approaches 1(second component being the solvent).
Behavior when the mixture is sufficiently dilute that solute-solute interactions are negligeble.

4. Importance and use of infinite dilution activity coefficient data
Most difficult and costly stage of a separation process is the removal of the last traces of impurity.
Greatest departure from ideality occurs in the very dilute regions
Synthesis, design and optimization of separation processes
Predicting the existence of an azeotropes

5. VLE data for methyl ethyl ketone(1)/toluene(2) at 500C

7. Method to predict

9. Example

10. Positive deviation from Raoult’s Law
Plot of experimental P-x-y, activity coefficient and molar excess Gibbs free energy data

11. Negative deviation from Raoult’s Law
Plot of experimental P-x-y, activity coefficient and molar excess Gibbs free energy data

12. Azeotropes
Importance of boiling point diagram(T-x-y diagram) & P-x-y diagram.
An Azeotrope is a mixture of two or more liquids in such a way that its components cannot be altered by simple distillation. 
This happens because, when an azeotrope is boiled, the vapor has the same proportions of constituents as the unboiled mixture.
Because their composition is unchanged by distillation, azeotropes are also called constant boiling mixtures.

13. Azeotropes
In some real systems, the temperature / composition curve is far from ideal.
A maximum or minimum in the curve is possible; this is an azeotrope.
At the azeotrope, the liquid and vapor have the same composition.
Word azeotrope is derived from the Greek words, overall meaning, "no change on boiling".

14. Ethanol-water system
A example of a positive azeotrope is 89.44% ethanol and 11.56% water (by weight).
Ethanol boils at 78.4 °C, water boils at 100 °C, but the azeotrope boils at 78.2 °C, which is lower than either of its constituents.
78.2 °C is the minimum temperature at which any ethanol/water solution can boil at atmospheric pressure.

16. This limit is 0.8943 mole fraction of ethanol for an ethanol-water mixture at P = 1 atm.
To separate a mixture containing 0.9 ethanol liquid mole fraction at 1 atm
Azeotropes are dependent upon pressures and one way to avoid this problem is to vary the pressure.
For example, under a vacuum (P = 70 mmHg), no azeotrope exists for the ethanol-water mixture. This is one reason that vacuum distillation is often done for many separations.
Azetropes are often also component dependent.
For example, the addition of a 3rd component to a binary system, may change or “break” the azeotrope.

17. Example
Construct the P-x-y diagram for the cyclohexane(1)-benzene(2) system at 313 K given that at 313 K the vapour pressures are and
The liquid phase activity coefficients are given by

18. Answer X1
0.2
0.4
0.6
0.8
1.0
1.5809
1.3406
1.1793
1.0760
1.0185 P
24.41
26.49
27.37
27.41
26.61
24.62 Y1
0.2492
0.4243
0.5799
0.7540

19. Example
A mixture of benzene(1) and ethanol(2) for which the vapor pressures and activity coefficients given by the following equations.
ln γ1 = 1.25 x22 ln γ2 = 1.25 x12
Assuming the validity of Modified Raoult’s Law, show whether or not the system exhibits an azeotrope at temperature 70 oC.
What is the azeotropic pressure at 70oC?

20. VAPOR-LIQUID EQUILIBRIUM AT LOW TO MODERATE PRESSURE

21. Activity Models Wohl’s equations & Redlich Kister Expression
Margules model
Two suffix equation or one constant equation
Porter equations
Three suffix equation or two constant equation
Vanlaar equation
Wilson equation
NRTL model
UNIQUAC (Universal Quasi Chemical) model
Abrams and Prausnitz
UNIFAC (UNIQuac Functional Activity Coefficient model) model

22. Activity Models “Simple” empirical models
Symmetric, Margule’s, vanLaar
No fundamental basis but easy to use
Parameters apply to a given temperature, and the models usually cannot be extended beyond binary systems.
Local composition models
Wilsons, NRTL, Uniquac
Some fundamental basis
Parameters are temperature dependent, and multi-component behaviour can be predicted from binary data.

23. VAPOR-LIQUID EQUILIBRIUM AT LOW PRESSURE
Various activity coefficient models commonly used for VLE calculations.
Divided into two major groups depending upon their applicability to various types of solutions:
Margules/Van Laar models
Homogeneous Mixture models
Wilson/NRTL (Non-Random Two Liquid)/UNIQUAC (Universal Quasi Chemical) Models
Local Composition models

24. Non-ideal behavior of liquid solutions derives from two sources:
difference in molecular size/shape of constituent
difference between the molecular interaction energies.
Type 1 models generally apply to systems in which the inter-species and molecular interaction energies differ from each other.
Type 2 models are principally useful for describing systems where the constituent molecular species differ on account of both size/shape as well molecular interaction energies.

25. Models for Excess Gibbs free energy

26. Activity models
GE/RT is a function of T, P, and composition
For liquids at low to moderate pressure, it is very week function of P.
P dependence of the activity coefficients is usually neglected
Thus for data at constant T, GE/RT is a function of composition (x1, x2,..,xN)
For binary mixture, the function that are most often represented is GE/x1x2RT and it can be expressed as a power series in x1.
An equivalent power series with certain advantages known as Redlick/Kister expression

27. Derivation of Margules Equations

28. Margules equation
Max Margules introduced in 1895 a simple thermodynamic model for the excess Gibbs free energy of a liquid mixture.
He had introduced the concept of the activity coefficient, the model could be used to derive an expression for the activity coefficients of a compound i in a liquid.

29. Case I: Ideal Solution A = B = C = 0
Case II: One-Parameter Margules Euation
A ≠ 0, B =C = 0
For binary mixture:

30. Margules one parameter Equations
This model provide a good representation for many simple liquid mixtures, for mixtures of molecules which are similar in size, shape and chemical nature.
When lny1 and lny2 are plotted against x2(or x1), the two curves are mirror images.
Symmetrical nature of activity coefficients for this model

31. Case III- Two-Parameters Margules Equation

32. Margules Two parameter Equations
A12 → single molecule of 1 surrounded by 2 A21 → single molecule of 2 surrounded by 1

33. Margules Two parameter Equations

34. Margules Two parameter Equations

35. Margules Two parameter Equations
A12 → single molecule of 1 surrounded by 2 A21 → single molecule of 2 surrounded by 1

36. Vanlaar Equation

37. Van Laar Equations

38. Vanlaar Equation
Van Laar equation is an activity model, which was developed by Johannes van Laar in , to describe phase equilibria of liquid mixtures.
Where A and B are known as vanlaar constants, if the constants are known the activity coefficients can be estimated.

39. Estimation of Vanlaar constants
First method:
If the activity coefficients are known at any one composition, then vanlaar constants A and B can be estimated by rearranging the equation.

40. Estimation of Vanlaar constants
Second method:
For a systems forming azeotrope, if the temperature and pressure are known at azeotropic composition then activity coefficients can be calculated as,
At azeotrpic composition x1=y1

42. Example - 1
A mixture of two compounds, 2-propanol(1) and water(2),calculate excess Gibbs energy at x1= and fit one parameter Margules equation. Data provided
T=300C & P=66.9 mmHg
= mmHg
= mmHg
y1 =
X1 =
Also fit the two-parameter Margules equation(Determine the numerical values of A12 and A21 which describe this mixture)

43. Answers Activity coefficient of component 1=1.118
Excess Gibbs energy=0.328
A =1.42
A12 = 1.99
A21 = 1.09

44. Example - 2
A mixture of two compounds, A and B, has an azeotrope at T = K, P = kPa and xA = yA = The vapor pressures at this temperature are = kPa and = kPa. To describe the properties of this mixture, use the Margules equation in the form:
Determine the numerical values of A12 and A21 which describe this mixture.

45. Example - 3
An azeotrope consists of 42 mol per cent acetone(1) and 58 mol per cent methanol(2) at 760 mm Hg and 313 K. At 313 K, vapor pressure of acetone and methanol are 786 mm Hg and 551 mmHg respectively. Calculate the van Laar constants.

46. Estimation of Vanlaar constants

47. Answer
A =
B = 0.274

48. Example - 4
Liquids A and B form an azeotrope containing 46.1 mole per cent A at101.3 kPa and 345 k.At 345 K, the vapor pressure of A is 84.8 kPa and that of B is 78.2 kPa. Calculate the van Laar constants.

49. Answer
A=1.2955
B=0.6530

50. Example - 5
The azetrope of the benzene(1) & cyclohexane(2) system has a composition of 53.2 mol % benzene with a boiling point of K at kPa. At this temperature the vapor pressure of benzene(1) & cyclohexane(2) is kPa and kPa respectively. Determine the activity coefficient for the solution containing 10 mol % benzene.

51. Answer Activity coefficient of benzene = 1.062
Activity coefficient of cyclohexane = 1.002

52. Local composition models
Concept of LCMs is based on the hypothesis of that the local concentration around a molecule is different from the bulk concentration.
Local composition is incorporated to model to account for the nonrandom molecular orientations resulting from differences in molecular size and intermolecular forces.
This difference is due to a difference between the interaction energy of the central molecule with the molecules of its own kind  and that with the molecules of the other kind .
Energy difference also introduces a non-randomness at the local molecular level.

53. Local composition model

54. Wilson equation
Concept of local composition was introduced by G.M.Wilson in 1964 with the development of model in which he was proposed that the local composition is different from the overall mixture composition or bulk composition.
Local composition model is postulated to account for the non-random molecular orientations that result from differences in molecular size and intermolecular forces.

55. Wilson equation for binary solution
Wilson proposed the following expression for the excess Gibbs energy of a binary solution
Wilson equation have two adjustable parameters and known as Wilson parameter. These are related to pure component molar volume and characteristic energy difference and are given by,

56. Wilson equation for binary solution

57. Wilson equation for binary solution
V1 and V2 – molar volumes of pure liquids at temperature.
- Energies of interaction between molecule
a - constant for a given pair of components independent of temp & prssure.

58. Wilson equation
Strength of Wilson’s approach resides in its ability to describe multi-component (3+) mixtures using binary data.
Experimental data of the mixture of interest (ie. acetone, ethanol, benzene) is not required
We only need data (or parameters) for acetone-ethanol, acetone-benzene and ethanol-benzene mixtures

59. Wilson’s Equations for 3-Component Mixtures

60. Wilson equation-advantage
Provides a good representation of VLE of a variety of miscible mixtures.
Considered the temperature dependent of the parameter
Applicable to the completely miscible system
Suitable for solutions of polar or associating components like alcohols in non-polar solvents for which the Margules and van Laar equations are generally inadequate.

61. Wilson equation-Disadvantage
It is not suitable for systems showing maxima or minima on the lnY versus x curves.
It is not suitable for systems exhibiting limited miscibility
recommended only for liquid systems that are completely miscible, or for partially miscible systems in the region where only one phase exists.

62. Non-Random Two-Liquid(NRTL) equation
NRTL equation was developed by Renon & Prausnitz in 1968 & this equation is applicable to miscible or partially miscible systems.
NRTL equation for the excess Gibbs free energy is given by,

63. Non-Random Two-Liquid(NRTL) equation
Activity coefficients are

64. Non-Random Two-Liquid(NRTL) equation
Here are independent of composition & temperature & it is related to the non-randomness of the solution.
If = 0, the solution is completely random & NRTL equation reduces to the one parameter Margules model.
The value of varies from 0.20 to 0.57, in absence of the experimental data = 0.3.

65. NRTL equations
Applicable to partially miscible as well as totally miscible systems.
For moderately non-ideal systems, it offers no advantage over the van laar and margules equations. But for strongly non-ideal solutions and especially partially miscible systems, the NRTL equations provide a good representation
Disadvantage:
For moderately non-ideal systems, it offers no advantage over the Van Laar & Margules equation

66. Characteristics of Models
NRTL is especially suited for acid gas adsorption, which includes the removal of carbon dioxide and hydrogen sulfide from a gas stream. Refineries routinely use this process when making hydrogen.
UNIFAC model is a group contribution method that allows the model parameters to be estimated using the molecular structure of each chemical. When experimental data is not available, this is the only method that can be used.

67. Characteristics of Models
UNIQUAC model uses binary parameters, which must be determined from experimental data. Once found, however, the same parameters can be used in multicomponent mixtures of three or more chemicals.
Both UNIFAC and UNIQUAC can be used when two liquid phases or azeotropes are present.
Wilson equation is an option if there is only one liquid phase,and it does handle azeotroipes.

68. Applicability of Activity Coefficient Models

69. Models for the Excess Gibbs Energy and Activity Coefficients for Binary Systems

70. Models for the Excess Gibbs Energy and Activity Coefficients for Binary Systems

71. Relation between the model parameters and infinite dilute activity coefficients

73. THANK YOU