1. CHAPTER 9 Fugacity of a component in a mixture
Solution theories and applications

2. Important Notation

3. Learning objectives Be able to:
Understand the difference between ideal and non-ideal mixtures;
Understand the concepts of excess properties and activity coefficients;
Compute fugacity coefficients in vapor and liquid mixtures;
Compute correlative and predictive activity coefficients.

4. Ideal gas mixtures
Ideal gas mixtures are characterized by:

5. Partial molar properties in ideal gas mixtures
Partial molar volume and partial molar internal energy:

6. Partial pressure
In ideal and non-ideal gas mixtures, the partial pressure is defined as:
Note: the partial pressure is NOT a partial molar property.

7. Partial molar properties in ideal gas mixtures
Forming a binary ideal gas mixture at selected conditions:
T, P, N1
T, P, N2
T, P, (N1 + N2)

8. Partial molar properties in ideal gas mixtures
There are not heat effects (constant temperature and non-interacting molecules in an ideal gas). The difference in entropy when forming the ideal gas mixtures comes from that the molecules of each gas can now occupy the whole volume:

9. Partial molar properties in ideal gas mixtures
For mixtures with any number of components:
Then:

10. Partial molar properties in ideal gas mixtures
Summary:

11. Partial molar Gibbs energy and fugacity
The fugacity of a pure substance was defined in Chapter 7 as:
The fugacity of a component in a mixture is now defined as:

12. Partial molar Gibbs energy and fugacity
The fugacity coefficient of a component in a mixture is:
In practice, to compute the fugacity coefficient, you need an equation of state. From the EOS you can have an expression for the departure (residual) Gibbs energy.

13. Partial molar Gibbs energy and fugacity
It then follows that:
But:
And:

14. Partial molar Gibbs energy and fugacity
The overall result is:

15. Phase equilibrium criterion
From chapter 8, the phase equilibrium criterion for mixtures in a two-phase system is:
Isofugacity criterion

16. Phase equilibrium criterion
Equivalent forms of writing this criterion are:

17. Raoult’s law Model the vapor phase as a mixture of ideal gases:
Model the liquid phase as an ideal solution

18. VLE according to Raoult’s law:

19. Acetonitrile (1)/nitromethane (2)
Antoine equations for saturation pressures:
Calculate P vs. x1 and P vs. y1 at 75 oC

20. Diagram is at constant T
Bubble line
66.72
Dew line
0.75

21. Calculate the P-x-y diagram
Knowing T and x1, calculate P and y1
Bubble pressure calculations

22. Diagram is at constant T
59.74
0.43

23. Knowing T and y1, get P and x1
Dew point calculation

24. In this diagram, the pressure
is constant
78oC
0.51
0.67

25. Calculate a T-x1-y1 diagram
(1)
Given P and y1 solve
for T and x1
(2)
Why is this temperature
a reasonable guess?
get the two saturation temperatures
Then select a temperature from the range between
T1sat and T2sat
At the selected T,
summing (1) and (2) solve for x1

26. Given P and x1, get T and y1

27. Iterate to find T, then calculate y1
(II)
(III)
Estimate P1sat/P2sat using a guess T
Then calculate P2sat from (III)
Then get T from (I)
Compare calculated T with guessed T
Finally, y1 = P1sat x1/P and y2 = 1-y2

28. In this diagram, the pressure
is constant
Dew points
Bubble
points
78oC
76.4
0.51
0.75

29. Knowing P and y, get T and x
Start from point c last slide (70 kPa and y1= 0.6)

30. Iterate to find T, and then calculate x
Estimate P1sat/P2sat using a guess T
Then calculate P1sat from (III)
And then get T from (I)
(II)
(III)
x1= Py1/P1sat

31. 79.6
0.44

32. Ki = yi/xi
Ki = Pisat/P

33. Read
Examples
10.4, 10.5, 10.6

34. Flash Problem mass balance: L + V =1 V, {yi} T and P
mass balance component i
zi = xi L + yi V for i = 1, 2, …n
zi = xi (1-V) + yi V
1 mol of
L-V mixture
overall
composition {zi}
Using Ki values, Ki = yi/xi
xi= yi /Ki;
yi = zi Ki/[1 + V(Ki -1)]
L, {xi}
read and work examples 10.5 and 10.6
SUM {yi } =SUM{ zi Ki/[1 + V(Ki -1)]}

35. F=2-p+N
For a binary
F=4-p
For one phase:
P, T, x (or y)
Subcooled-liquid
above the upper
surface
Superheated-vapor
below the under surface
L is a bubble point
W is a dew point
LV is a tie-line
Line of critical points

37. Each interior loop represents the PT
behavior of a mixture of fixed composition
In a pure component, the bubble and dew
lines coincide
What happens at points A and B?
Critical point of a mixture is the point where
the nose of a loop is tangent to the envelope
curve
Tc and Pc are functions of
composition, and do not necessarily
coincide with the highest T and P

38. At the left of C, reduction
of P leads to vaporization
At F, reduction in P leads to
condensation and then
vaporization (retrograde
condensation)
Important in the operation of
deep natural-gas wells
At constant pressure,
retrograde vaporization
may occur
Fraction of the
overall system
that is liquid

40. Minimum and maximum of
the more volatile species
obtainable by distillation
at this pressure
(these are mixture CPs)

42. azeotrope
This is a mixture of very dissimilar
components

43. The P-x curve in (a) lies below
Raoult’s law; in this case there are stronger
intermolecular attractions between unlike
than between like molecular pairs
This behavior may result in a minimum
point as in (b), where x1=y1
Is called an azeotrope
The P-x curve in (c) lies above Raoult’s
law; in this case there are weaker
than between like molecular pairs; it could
end as L-L immiscibility
This behavior may result in a maximum
point as in (d), where x1=y1, it is also
an azeotrope

44. Usually distillation is carried
out at constant P
Minimum-P azeotrope is a
maximum-T (maximum boiling)
Point (case b)
Maximum-P azeotrope is a
minimum-T (minimum boiling)
Point (case d)

46. Limitations of Raoult’s law
When a component critical temperature is < T,
the saturation pressure is not defined.
Example: air + liquid water; what is in the vapor phase?
And in the liquid?
Calculate the mole fraction of air in water at 25oC and 1 atm
Tc air << 25oC

47. Henry’s law
For a species present at infinite dilution in the liquid phase,
The partial pressure of that species in the vapor phase is
directly proportional to the liquid mole fraction
Henry’s constant

48. Calculate the mole fraction of air in water at 25oC and 1 atm.
First calculate y2 (for water, assuming that air does not dissolve in water)
Then calculate x1 (for air, applying Henry’s law)

49. Modified Raoult’s law Fugacity vapor Fugacity liquid
g is the activity coefficient, a function of composition and
temperature
It corrects for non-idealities in the Liquid phase

50. Ideal mixtures
the more energetic molecules have enough energy to overcome the intermolecular attractions and escape from the surface to form a vapor.
The smaller the intermolecular forces, the more molecules will be able to escape at any particular temperature.
The same happens for another liquid

51. Ideal mixture The trend to escape is the same for both liquids.
That means that the intermolecular forces between two red (or two blue) molecules must be exactly the same as the intermolecular forces between a red and a blue molecule.

52. Ideal mixtures
This is why mixtures like heptane and iso-heptane get close to ideal behavior. They are similarly sized molecules and similar chemical structure and so have similar van der Waals attractions between them. However, they obviously aren't identical - and so although they get close to being ideal, they aren't actually ideal.

53. Ideal mixtures
The concept of ideal mixture, as the name implies, is an idealization that approximates the behavior of mixtures formed by components whose molecules are similar in size, shape, and intermolecular interactions.
Example: mixtures of n-heptane and iso-heptane
Beyond this physical interpretation, there is a mathematical definition and several consequences that derive from it.

54. Heat of mixing ideal mixtures
When you make any mixture of liquids, you have to break the existing intermolecular attractions (which needs energy), and then remake new ones (which releases energy).
If all these attractions are the same, there won't be any heat either evolved or absorbed.
That means that an ideal mixture of two liquids will have zero enthalpy change of mixing. If the temperature rises or falls when you mix the two liquids, then the mixture isn't ideal.

55. Ideal mixtures
Ideal mixtures can be liquids or gaseous. Mathematically, the following properties define an ideal mixture:
From this definition, it follows that:

56. Ideal mixtures
Consider the fugacity of a component in an ideal mixture and of a pure component at the same temperature and pressure:
Solving for P from each equation, it results:

57. Ideal mixtures
Using the definition of fugacity coefficients from previous slides:

58. Ideal mixtures

59. Ideal mixtures
But, for an ideal mixture:
It follows that: 1

60. Ideal mixtures
Then, in an ideal mixture:

61. Vapor-liquid equilibrium between ideal phases
With these assumptions:
For an ideal gas mixture:
For an ideal liquid mixture:

62. Vapor-liquid equilibrium between ideal phases
From Chapter 7, the fugacity of a pure liquid is:
Neglecting the fugacity coefficient at saturation and the Poynting correction:

63. Vapor-liquid equilibrium between ideal phases
For an ideal gas mixture:
For an ideal liquid mixture:

64. Vapor-liquid equilibrium between ideal phases
VLE:
Known as Raoult’s law

65. Ideal mixtures
Summary of the relationships for ideal mixtures (please refer to the book for the proofs):

66. Ideal mixtures
Summary of the relationships for ideal mixtures (please refer to the book for the proofs):

67. Excess mixing properties
An excess mixing property is the difference between the property of the real mixture and that of the ideal mixture, both of same temperature, pressure, and composition.

68. Excess mixing properties
An excess mixing property is the difference between the property of the real mixture and that of the ideal mixture, both of same temperature, pressure, and composition.

69. Excess mixing properties
An excess mixing property is the difference between the property of the real mixture and that of the ideal mixture, both of same temperature, pressure, and composition.

70. Excess mixing properties and activity coefficients
Define the activity coefficient of component i as:
Then:
But:

71. Excess mixing properties and activity coefficients
Then, collecting all the terms:

72. Excess mixing properties and activity coefficients
The fugacity of component i in the mixture is:
Note: the activity coefficient accounts from deviations from ideal mixture behavior.

73. Excess mixing properties and activity coefficients
To obtain an expression for the activity coefficient of a certain species, you need an expression for the excess mixing Gibbs energy:
Several expressions (models) exist.

74. Example
In a binary mixture, the excess Gibbs energy of mixing is given by Find the corresponding expression for the activity coefficients of components 1 and 2.

75. Example 7
In a binary mixture, the excess Gibbs energy of mixing is given by Find the corresponding expression for the activity coefficients of components 1 and 2.
Solution:

76. Example 7
Note that:

77. For component 2, the procedure is analogous, leading to:
These are the simplest formulas for activity coefficients, but generally give poor description of liquid phase behavior.

78. f9_5_4
f9_5_4.jpg
Benzene (1) +2,2,4-trimethyl pentane at 55oC.

79. Activity Coefficient Models
Expressions for activity coefficients are obtained from expressions for the molar excess Gibbs energy of mixing using the steps outlined in the previous example.
The molar excess Gibbs of energy of mixing can show very diverse behavior depending on the liquid mixture and its conditions of temperature and composition.

80. Activity Coefficient Models
Trimethyl methane (1) + benzene (2) at 100 oC
Trimethyl methane (1) + carbon tetrachloride (2) at 0 oC
methane (1) + propane (2) at 100 K
Water (1) + hydrogen peroxide (2) at 75 oC

81. Activity Coefficient Models
Redlich-Kister expansion:
For A and B different from zero with C, D, and other parameters equal to zero:

82. Activity Coefficient Models
Van Laar equations:

83. Activity Coefficient Models
Flory-Huggins model (for molecules very different in size, as in solvent+polymer solutions):

84. 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”

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

86. 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

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

88. 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?

89. Intermolecular pair potential
Uij
eij

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

91. NRTL (non-random, two-liquid)
Actual parameters: a, b12 and b21
See Table 12.5, next slide
Renon and Prausnitz, 1968

93. 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

94. 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-

95. Activity coefficients from UNIQUAC

98. 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

100. 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 !!

102. Activity Coefficient Models
Wilson model (local composition; expandable to any number of components):

103. Activity Coefficient Models
NRTL model (non-random two-liquid) (local composition; expandable to any number of components):

104. Activity Coefficient Models
UNIQUAC model (universal quasi-chemical) (local composition; expandable to any number of components):

105. Activity Coefficient Models
UNIQUAC model (universal quasi-chemical) (local composition; expandable to any number of components):

106. Activity Coefficient Models
A common feature of the models presented in the previous slides is the need for experimental data to fit the model parameters to represent a system of interest. They are correlation-based models.
A few models are predictive, i.e., they predict activity coefficients in the absence of experimental data for the system of interest.

107. Van Laar Model

108. Assumptions Van Laar
Species have similar sizes and interaction energies
How to calculate the excess Gibbs free energy: assume a thermodynamic cycle and Van der Waals equation is valid for both phases

109. Thermodynamic cycle Very low P Ideal gas Mix ideal gases (step II)
Pure liquid at P
Isothermal
Vaporization
Step I
Compression
(liquefaction)
Step III
Ideal gas mixture
Liquid mixture
Formation of a liquid mixture from the pure liquids at constant T

110. DU mixing
And using the Van der Waals EOS for both phases we can evaluate DU at each step

111. Excess Gibbs free energy for Van Laar model
Because of liquid incompressibility:

112. Using mixing rules for b and a
We get the Van Laar activity coefficients

113. Scatchard-Hildebrand model
Hildebrand (1929) found that the properties of iodine solutions in various nonpolar solvents in agreement with Van Laar model. Hildebrand called these REGULAR solutions (no excess entropy and no change of volume due to mixing)
Both Hildebrand and Scatchard working independently improved over the Van Laar model

114. Activity Coefficient Models
Regular solution model (Scatchard-Hildebrand)
Goes beyond the limitations of the use of the Van der Waals EOS

115. Cohesive energy density
experimental
For the mixture,
Using the concept of dispersion forces where c12 =(c11 c22)1/2

116. Activity Coefficient Models
Regular solution model (practical formulas for a binary mixture)

117. Consequences of assumptions of the regular solution model
Can give activity coefficients only > 1
That is positive deviations of Raoult’s law
Can be applied to certain nonpolar mixtures
Improvements:
The Flory-Huggins theory of polymer solutions
Gonsalves and Leland (1978) modified the equations for mixtures with appreciable differences in size and shape
HW: Discuss Gonsalves and Leland theory and more recent applications of regular solution theory

118. Lattice model Liquid state intermediate between gas and solid
In a quasicrystalline picture of a liquid, the molecules are arranged in a lattice
Typical statistical mechanical models
Nonidealities may arise from:
attractive forces between unlike molecules(enthalpy of mixing),
differences in size and shape between unlike molecules (entropy of mixing)
Differences in attractive forces between the three different pair of interactions

119. Molecules distributed on a lattice (no vacancies)
After mixing, there will be some interchange energy, w
Excess volume is zero
Concept of coordination number (z)
Total number of nearest neighbors = z/2(N1+N2)=N11+N22+N12
Picture of interchange energy

120. Total energy of the lattice
Interchange energy

121. Partition function of the lattice

122. What is N12?
Random distribution

123. Change of Helmholtz free energy of mixing

124. Change of entropy due to mixing

125. Regular solution limit

126. Ideal solution limit

127. Calculation of w from molecular properties

128. Non-random mixtures Quasichemical approximation

129. Obtaining N12 for the non random case

130. N12 for the non random case

131. Limit of very large w
At x1=x2=0.5

132. Excess Internal Energy for the lattice model (non random mixture)

133. Excess Helmholtz free energy for the lattice model (non random mixture)

134. Limit of moderate values of w/zkT

135. Conclusions
The random approximation becomes satisfactory as the exchange energy w between pair of molecules becomes small relative to the thermal energy (kT)
For a given mixture, randomness increases with temperature.
At fixed T, randomness increases as the interchange energy w falls.
The excess entropy is never > 0, thus the entropy of mixing is maximum for the random mixture

136. Conclusions
The excess G and excess H can be either positive or negative, depending on the sign of w
When w/zkT is not very large (totally miscible mixtures), Gex calculated by the random or nonrandom approximations do not differ much.
However when w/zkT is large enough to induce limited miscibility of the two components, deviations from random mixing can be significant.

141. The m-liquid theory Corresponding states theory applied to a mixture:
One fluid theory: mixture is assumed to be a hypothetical fluid with molecular size and potential energy comparable with the average of the mixture components.
m-fluid theory: (example NRTL, non-random two liquid) local composition ideas

142. 2-liquid theory Liquid 1 (molecule 1 at the center)
Fluid 1 has “cells” of type 1; fluid 2 has “cells” of type 2
Mmix = x1 M(1) + x2 M(2)
M is an extensive configurational property
Using these assumptions we can get to UNIQUAC derivation, see Maurer and Prausnitz,
Fluid Phase Equilibria, 2, 91 (1978)

143. Generalized Van der Waals partition function Q(N, V, T)
For a simple pure fluid, Vera and Prausnitz (1972) proposed:

144. Van der Waals “partition functions”

145. Van der Waals “partition functions”

146. molecular partition function
It could be assumed that
q(rot, vib) = qext (V) qint(T)
density dependent
T-dependent
how to include the effect of density
a large rigid molecule with r segments, bond lengths, bond angles and torsional
angles are fixed– 3 translational DOF; 2 (linear) or 3 (nonlinear) rotational DOF;
total= 5or 6
2. a large flexible molecule with r segments (no restrictions in bond lengths and angles)
3r DOF (each segment has 3)
real molecule will be intermediate between these limits

147. real large molecule case
introduce a parameter c, such that 1 < c < r
for a small molecule, c =1
for more complex molecules, c >1
for example, for n-decane c=2.7
therefore for isomers of decane, c < 2.7 (branched paraffin less flexible)

148. generalized PF for V der Waals fluid
Donohue (1978)

149. Free volume expression
Van der Waals assumption Vf = V- Nb/NA
has serious problems.
Percus Yevick theory (1958) developed an “integral equation” theory based on molecular structure and pair (and higher order) correlation functions. This theory and the development of molecular simulations improved the description of the free volume.
Carnahan and Starling (1969)

150. EOS for pure fluids and mixtures beyond the lattice theory
perturbation theory
z = PV/RT = zref + zpert
Reference fluid:
hard spheres (each sphere moves independent from each other)
hard spheres chains (each segment is connected to at least one sphere; chain connectivity)

151. Statistical Associated-Fluid Theory (SAFT)
Chapman and Gubbins (1989, 1990)
ARes(T, V, N) = A (T, V, N) – AIG(T, V, N) = AHS + Adispersion + Achain + Aassociation/solvation
AHS short-range repulsions
Adispersion long-range dispersions
Achain chemically stable chains
Aassociation/solvation example H-bonding

152. SAFT terms
Arepulsion
(Huang and Radosz, 1990)
Achain

153. SAFT terms Adispersion Aassociation (Wertheim’s association theory)
# association sites unlimited, but needs to be specified
Location of association sites not specified
There could be steric hindrance

154. VLE for propanol-n-heptane at 323 K (Fu and Sandler, 1995)

155. VLE for CO2/2-propanol at two temperatures

156. Flory-Huggins Theory solutions of polymers in liquid solvents
regular solutions Sex = 0, Hex is described
for mixtures of components of very different sizes, Sex needs to be described.
DHmix = 0 athermal solutions, similar energetic interactions, different sizes. example polystyrene and toluene
DSmix = DScomb + DSres

157. Flory-Huggins theory N1 molecules of type 1: spheres (solvent)
N2 molecules of type 2: flexible chains (polymers)
each segment (r) has the same size as the solvent molecule
# lattice sites = N1 + r N2
fractions of occupied sites:

158. Flory Huggins, athermal solutions

159. dependence on
molecular shape
q/r = 1 for Flory-Huggins

160. Flory-Huggins, athermal solutions

161. Dependence of the activity coefficient of the polymer on the number of segments, r

162. Flory Huggins model including the interaction energy parameter c

165. Activity Coefficient Models
UNIFAC (UNIQUAC functional activity coefficient)

166. Summary: equilibrium criterion
Fugacities are essential for phase and chemical equilibrium calculations. When a component is present in phases I, II, III, IV, etc…, it is valid that:
These phases I, II, III, IV, etc, can vapor, liquid, or solid.

167. Summary: vapor phase fugacities
Expressions for the fugacity coefficient of component i in the mixture can be derived from equations of state (usually long and cumbersome derivations).
Many EOS exist: the next slide has some recommendations.

168. Summary: vapor phase fugacities

169. Summary: liquid phase fugacities
There are two major paths, using equations of state or excess Gibbs energy of mixing models.
Path 1: equations of state
Expressions for the fugacity coefficient of component i in the mixture can be derived from equations of state (usually long and cumbersome derivations).
Many EOS exist: the next slide has some recommendations.

170. Summary: liquid phase fugacities

171. Summary: liquid phase fugacities
There are two major paths, using equations of state or excess Gibbs energy of mixing models.
Path 2: excess Gibbs energy of mixing models
Fugacity of pure liquid OR
Henry’s constant
Expressions for the activity coefficient of component i in the mixture can be derived from models for the excess Gibbs energy of mixing (usually long and cumbersome derivations).

172. Summary: liquid phase fugacities
There are two major paths, using equations of state or excess Gibbs energy of mixing models.
Path 2: excess Gibbs energy of mixing models
Fugacity of pure liquid OR
Henry’s constant
Fugacity of pure liquid

173. Summary: liquid phase fugacities

174. Summary: liquid phase fugacities

175. Recommendation
Read chapter 9 and review the corresponding examples.

176. Example 1
Use the XSEOS package to evaluate the fugacity of ethane and n-butane in an equimolar mixture at K at 1, 10, and 15 bar with the Peng-Robinson equation of state.

177. Example 2
Use the XSEOS package to compute vapor-liquid equilibrium for various compositions of the mixture of propane and n-butane at an K with the Peng-Robinson equation of state. Plot the Pxy diagram and identify the bubble and dew point curves.

178. Example 3
Use the XSEOS package to compute vapor-liquid equilibrium for various compositions of the mixture of propane and n-butane at 10 bar with the Peng-Robinson equation of state. Plot the Txy diagram and identify the bubble and dew point curves.

179. Example 4
A methane(1) + ethane(2) mixture is to be continuously separated by reverse osmosis at 320 K using a rigid membrane only permeable to methane. On the mixture side of the membrane, the mole fractions are kept constant (x1=0.3). The pressure on the pure methane side of the membrane is 2 bar. Find the minimum pressure to be imposed on the mixture side of the membrane for operating this reverse osmosis setup. Make your calculations using the with the Peng-Robinson equation of state.

180. Example 5
Assuming Raoult’s law is valid, compute the bubble point pressure of an-hexane(1) + n-heptane(2) mixture with x1=0.6 at K and the mole fractions in the vapor phase. Compute the vapor pressure of each component using the Antoine equation with parameters from NIST Chemistry Webbook.

181. Example 6
Assuming Raoult’s law is valid, compute the dew point temperature of an-hexane(1) + n-heptane(2) mixture with y1=0.6 at 3 bar and the mole fractions in the liquid phase. Compute the vapor pressure of each component using the Antoine equation with parameters from NIST Chemistry Webbook.

182. Example 8
Plot the values of the activity coefficients methyl ethyl ketone and toluene in their liquid binary mixture at K as function of composition, as predicted by the Margules 3-suffix formula. Use the XSEOS package.

183. Example 9
Knowing the vapor pressures of methyl ethyl ketone and toluene at K are respectively equal to kPa and kPa, plot the Pxy diagram of the vapor-liquid equilibrium of this mixture as function of composition assuming the vapor phase is an ideal gas mixture and the liquid phase can be described using the Margules 3-suffix formula. Use the XSEOS package.

184. Example 10
Use the Flory-Huggins model in the XSEOS package and vary the size of component 2 to have a sense of its effect on non-ideal solution behavior.

185. Example 11
Fit the binary interaction parameters of the NRTL for the best possible representation of the vapor-liquid equilibrium of a methanol (1) + water (2) mixture at K. Data and additional details are available in the “NRTL” Excel file.

186. Example 11
Use the UNIFAC model to compute the activity coefficients of the components of the binary mixture acetone (1) + n-pentane (2) at 307 K, with a mole fraction of acetone equal to Data and additional details are available in the “UNIFAC” Excel file.