1. Dicky Dermawan www.dickydermawan.net78.net dickydermawan@gmail.com
ITK-234 Termodinamika Teknik Kimia II
Nonideal Behavior
Dicky Dermawan

2. Nonideal Behavior, Outline
Introduction: Effect of Nonideality
Partial Molar Properties
Residual Properties
Fugacity & Fugacity Coefficient
Excess Properties
Activity & Activity Coefficient

3. Intorduction: Effect of Nonideality: Tetrahydrofuran(1)/Carbon-tetrachloride(2)
30oC
1 atm
P-x-y diagram
t-x-y diagram

4. Effect of Nonideality: Chloroform(1)/Tetrahydrofuran(2)
30oC
1 atm
P-x-y diagram
t-x-y diagram

5. Effect of Nonideality: Furan(1)/Carbontetrachloride(2)
30oC
1 atm
P-x-y diagram
t-x-y diagram

6. Effect of Nonideality: Ethanol(1)/Toluene(2)
65oC
1 atm
P-x-y diagram
t-x-y diagram

7. Effect of Nonideality: x – y Diagram at Constant P = 1 atm
a. Tetrahydrofuran(1)/Carbon-tetrachloride(2)
b Chloroform(1)/Tetrahydrofuran(2)
c. Furan(1)/Carbontetrachloride(2)
d. Ethanol(1)/Toluene(2)

8. Partial Molar Properties
Pure-species Properties:
Solution Properties:
NOT:
Partial Properties:
….are properties of component i in the state of mixtures, which, in general different from that in the state of pure species
What physical interpretation can be given for, viz. partial molar volume ?

9. Methanol – Water Mixture, An Example
For pure species at 25oC:
Methanol (1) : V1 = cm3/mol
Water (2) : V2 = cm3/mol
What is the volume of 10 moles of methanol/water solution containing 30% mol of methanol?
Most people would think, logically:
Mol of methanol : x 10 moles = 3 moles
Mol of water : (1-0.3) x 10 moles = 7 moles
Volume of methanol : 3 moles x = cm3
Volume of water : 7 moles x = cm3
Thus, the total volume : = cm3
Wrong answer!
The correct answer is cm3
Thus there is – = cm3 deviation from expected value

10. More on Partial Molar Properties
NOT:

11. Chemical Potential as Partial Molar Property Criteria for Vapor - Liquid Equilibria
The chemical potential of i-th component is defined as:

12. Chemical Potential as Partial Molar Property
If we set M = G:
The definition of chemical potential:
Thus:

13. Evaluation of Partial Molar Properties Methanol – Water Mixture Example

14. Exercise
A group of students came across an unsuspected supply of laboratory alcohol, containing 96 mass-percent ethanol and 4 mass-percent water.
As an experiment they decided to convert 2 L of this material into vodka, having a composition of 56 mass-percent ethanol and 44 mass-percent water. Wishing to perform the experiment carefully, they search the literature and found the following partial-specific volume data for ethanol – water mixtures at 25oC and kPa.
The specific volume of water at 25oC is L/kg. How many L of water should be added to the 2 L of laboratory alcohol, and how many L of vodka result?

15. Fugacity, f At constant T Ideal gas : Real gas :
Residual Gibbs energy :
Residual Property
Fugacity coefficient :

16. Evaluation of Pure Component Fugacity, fi
At constant T:
Real gas :
Pure Component Fugacity Coefficient:
The fugacity :

17. Evaluation of Pure Component Fugacity, fi
From the following compressibility data for hydrogen at 0oC, determine the fugacity of hydrogen at 950 atm

18. Evaluation of Pure Component Fugacity, fi
From the following compressibility data for isobutane,
determine the fugacity of butane at various temperature and pressure

19. Evaluation of Pure Component Fugacity, fi from Equation of State
Virial :

20. Critical Constants & Accentric Factors: Paraffins

21. Critical Constants & Accentric Factors: Olefin & Miscellaneous Organics

22. Critical Constants & Accentric Factors: Miscellaneous Organic Compounds

23. Critical Constants & Accentric Factors: Elementary Gases

24. Critical Constants & Accentric Factors: Miscellaneous Inorganic Compounds

25. Evaluation of Pure Component Fugacity, fi from Virial Equation of State, Example
Using virial equation of state,
calculate the fugacity and fugacity coefficient of:
Pure methyl-ethyl-ketone
Pure toluene
at 50oC and 25 kPa.
The required data:

26. Evaluation of Pure Component Fugacity, fi from Equation of State
Redlich-Kwong:
}to be solved simultaneously

27. Evaluation of Pure Component Fugacity, fi from Redlich-Kwong Equation of State
Using Redlich - Kwong equation of state,
calculate the fugacity and fugacity coefficient of:
Pure methyl-ethyl-ketone
Pure toluene
at 50oC and 25 kPa.
The required data:

28. Evaluation of Pure Component Fugacity, fi : Pitzer’s Generalized Correlation

29. Evaluation of Pure Component Fugacity, fi : Pitzer’s Generalized Correlation

30. Evaluation of Pure Component Fugacity, fi : Pitzer’s Generalized Correlation

31. Evaluation of Pure Component Fugacity, fi : Pitzer’s Generalized Correlation

32. Evaluation of Pure Component Fugacity, fi : Pitzer’s Generalized Correlation

33. Evaluation of Pure Component Fugacity, fi : Pitzer Correlation
Using Pitzer Correlation,
calculate the fugacity and fugacity coefficient of:
Pure methyl-ethyl-ketone
Pure toluene
at 50oC and 25 kPa.
The required data:

34. Evaluation of Liquid Pure Component Fugacity, fi
Since Vl is a weak function of P at temperatures well below Tc:
Poynting factor
Fugasity of saturated vapor,
calculated exactly as calculating gas phase fugacity

35. Estimation of Liquid Density Rackett Equation:

36. Examples of Evaluation of Liquid Pure Component Fugacity, fi
11.5
Estimate the fugacity of liquid acetone at 110oC and 275 bar.
At 110oC the vapor pressure of acetone is 4.36 bar and the molar volume of saturated-liquid acetone is 73 cm3.mol-1
11.6
Estimate the fugacity of liquid n-butane at 120oC and 34 bar.
At 120oC the vapor pressure of n-butane is bar and the molar volume of saturated-liquid n-butane is 137 cm3.mol-1

37. Examples of Evaluation of Liquid Pure Component Fugacity, fi
11.10
The normal boiling point of n-butane is 0.5oC.
Estimate the fugacity of liquid n-butane at this temperature and 200 bar.
11.11
The normal boiling point of 1-pentene is 30.0oC.
Estimate the fugacity of liquid 1-pentene at this temperature and 350 bar.
11.12
The normal boiling point of isobutane is -11.8oC.
Estimate the fugacity of liquid isobutane at this temperature and 150 bar.

38. Examples of Evaluation of Gas & Liquid Pure Component Fugacity, fi
11.13
Prepare plots of f vs P and f vs P for isopropanol at 200oC for the pressure range from 0 to 50 bar. For the vapor phase, values of Z are given by:
Where P is in bars. The vapor pressures of isopropanol at 200oC is bar, and the liquid-phase isothermal compressibility k at 200oC is bar-1, independent of P.
Hint:
Critical constants:
Vc = 219 cm3/mol Tc 508,8 K
Pc = 53,7 bar Zc = 0,278

39. Examples of Evaluation of Gas & Liquid Pure Component Fugacity, fi
11.14
Prepare plots of f vs P and f vs P for 1,3-butadiene at 40oC for the pressure range from 0 to 10 bar. At 40oC The vapor pressures of 1,3-butadiene is bar.
Assume virial model to be valid for the vapor phase.
The molar volume of saturated liquid 1,3-butadiene at 40oC is cm3.mol-1

40. Fugacity of Steam and Water, Using Steam Table
Up to Pisat, i.e. gas phase water (steam):
P* : lowest value of P in steam table
At P >= Pisat, i.e. liquid phase water:

41. Example of Steam and Water Fugacity Calculation Using Steam Table
11.7
From data in the steam tables, determine a good estimate for f/fsat of liquid water at 100oC and 100 bar, where fsat is the fugacity of saturated liquid at 100oC.
11.8
Steam at kPa and 380oC undergoes an isothermal change of state to a pressure of 275 kPa. Determine the ratio of the fugacity in the final state to that in the initial state
11.9
Steam at 1850 psia and 700oF undergoes an isothermal change of state to a pressure of 40 psia. Determine the ratio of the fugacity in the final state to that in the initial state

42. Fugacity of Mixtures Virial :
Are formulated exactly as calculation for pure component, but we use Mixing Rules to obtain the parameters
For binary mixtures, i = 1,2 and j = 1,2

43. Example of Calculation for Fugacity of Mixtures Using Virial Equation
Estimate the fugacity and fugacity coefficient of an equimolar mixture of methyl-ethyl-ketone (1) and toluene (2) at 50oC and 25 kPa
The required data are as follows:

44. Fugacity of Components in Mixture
is partial molar property of
Thus:
Virial, binary mixtures:

45. Fugacity of Components in Binary Mixtures, Example using Virial Eqn.
Estimate the fugacity and fugacity coefficient of methyl-ethyl-ketone (1) and toluene (2) for an equimolar mixture at 50oC and 25 kPa.
Set all kij = 0
The required data are as follows:
11.18
Estimate the fugacity and fugacity coefficient of ethylene (1) and propylene (2) for a binary mixture of 25% ethylene as a gas at 200oC and 20 bar.
Set all kij = 0

46. More on Virial Eqn: Fugacity of Ternary and Multicomponent Mixtures
Mixing Rules :
For ternary mixtures, i = 1,2,3 and j = 1,2,3

47. More on Virial: Fugacity of Ternary & Multicomponent Mixtures Example
11.19
Estimate the fugacity and fugacity coefficient of each component in a ternary mixture of methane (1) / ethane (2) / propane (3) at 40oC and 20 bar with the composition of 17% methane and 35% ethane
Set all kij = 0

48. Evaluation of Mixture Fugacity, f, from Equation of State
Redlich-Kwong:
}to be solved simultaneously

49. Evaluation of Mixture Fugacity, f , using Redlich-Kwong Equation of State
calculate the fugacity and fugacity coefficient of an equimolar mixture of methyl-ethyl-ketone (1) and toluene (2) at 50oC and 25 kPa
The required data:

50. Evaluation of Component Fugacity in Mixture Fugacity, f, from Equation of State
Redlich-Kwong:

51. Evaluation of Mixture Fugacity, f , using Redlich-Kwong Equation of State
calculate the fugacity and fugacity coefficient of MEK and toluene in equimolar mixture of methyl-ethyl-ketone (1) and toluene (2) at 50oC and 25 kPa
The required data:

52. UTS 1

53. Excess Gibbs Energy Pure-species Properties: Solution Properties:
Partial Properties:
Residual Property
Partial Property of the Excess Property
Excess Property
Partial Property of the Excess Property

54. Excess Gibbs Energy Pure-species Properties: Solution Properties:
Partial Properties:
Residual Property
Partial Property of the Excess Property
Excess Property
Partial Property of the Excess Property

55. Activity Coefficient Definition of fugacity: Integration
(Ideal solution)
The definition of activity coefficient gi

56. Models for Binary Mixtures Activity Coefficient: Margules(1856 – 1920)

57. Models for Binary Mixtures Activity Coefficient: van Laar

58. Models for Binary Mixtures Activity Coefficient: Wilson

59. Models for Binary Mixtures Activity Coefficient: Renon: NonRandom Two-Liquid (NRTL)

60. Models for Multicomponent Mixtures Activity Coefficient: Wilson

61. Models for Multicomponent Mixtures Activity Coefficient: UNIversal QUAsi Chemical (UNIQUAC) (Abrams & Prausnitz)

62. Models for Multicomponent Mixtures Activity Coefficient:
UNIquac Functional- group Activity Coefficient (UNIFAC) (Aa Fredenslund, Rl Jones & JM Prausnitz)

63. Models for Multicomponent Mixtures Activity Coefficient:
UNIFAC: Rk & Qk

64. Models for Multicomponent Mixtures Activity Coefficient:
UNIFAC: Rk & Qk Example

65. Models for Multicomponent Mixtures Activity Coefficient:
UNIFAC: amk