Excess Gibbs Energy Models
Purpose of this lecture:
To introduce some popular empirical models (Margules, van Laar) that
can be used for activity coefficients in binary mixtures
Highlights
• Margules and van Laar equations (Lecture 18) are simple correlations
to obtain activity coefficients.
• They are derived by assuming GE/RT x1 x2 follows a polynomial
• They only work for binary mixtures
Reading assignment: Sections 12.1 and 12.2
CHEE 311
Lecture 17
1
Excess Gibbs Energy Models
Practicing engineers usually get information about activity
coefficients from correlations obtained by making assumptions
about excess Gibbs Energy. These correlations:
 reduce vast quantities of experimental data into a few
empirical parameters,
 provide information an equation format that can be used in
thermodynamic simulation packages (Provision, Unisym,
Aspen)
Simple empirical correlations
 Symmetric, Margules, van Laar
 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
 Wilson, NRTL, Uniquac
 Some fundamental basis
 Parameters are temperature dependent, and multicomponent behaviour can be predicted from binary data.
CHEE 311
Lecture 17
2
Excess Gibbs Energy Models
Our objectives are to learn how to fit Excess Gibbs Energy models
to experimental data, and to learn how to use these models to
calculate activity coefficients.
 yP 
ln  1  ln 1 sat 
 x1P1 
 y P 
ln  2  ln 2 sat 
 x 2P2 
GE / RT  x1 ln 1  x 2 ln  2
CHEE 311
Lecture 17
3
Margules’ Equations
While the simplest Redlich/Kister-type correlation is the Symmetric
Equation, but a more accurate equation is the Margules correlation:
GE
 A 21x1  A12 x 2
(12.9a)
RTx 1x 2
Note that as x1 goes to zero,
GE
RTx1x 2
 A 12
x1 0
Also,
E
G


ln

lim
1
RTx
x
x10
1 2
so that
A12  ln 1
CHEE 311
and similarly
Lecture 17
A 21  ln  2
4
Margules’ Equations
If you have Margules parameters, the activity coefficients can be
derived from the excess Gibbs energy expression:
GE
 A 21x1  A12 x 2
(12.9a)
RTx 1x 2
to yield:
ln 1  x 22 [ A12  2( A 21  A12 )x1]
(12.10ab)
ln  2  x12 [ A 21  2( A12  A 21)x 2 ]
These empirical equations are widely used to describe binary
solutions. A knowledge of A12 and A21 at the given T is all we
require to calculate activity coefficients for a given solution
composition.
CHEE 311
Lecture 17
5
Example 1
You desire to separate an equimolar binary mixture of n-pentane (1) and acetone (2) by feeding it
You desire to separate an equimolar binary mixture of n-pentane (1) and acetone
into a flash drum that operates at T=24 oC and
kPa.thatUsing
provided
below,
into aP=50
flash drum
operatesinformation
at T=24 oC and P=50
kPa. Using
information prov
determine whether
not separation of theunder
mixturethese
can be operating
accomplished under th
determine whether or not separation of the mixture
can beoraccomplished
conditions.
conditions.
- DewP = 45 kPa (at T= 24 oC)
sat
o
sat
o
- P1 (24 C )=65.0 kPa; P2 (24 C )=31.0 kPa
- DewP = 45 kPa (at T= 24 oC)
- Reduced experimental P-x-y data for this mixture (GE/RTx1x2 vs. x1) are given
- The activity coefficients can be calculated from the Margules model
- P1sat(24 oC )=65.0 kPa; P2sat(24 oC )=31.0 kPa
- Due to low pressures
involved, you can assume here that all fugacity coefficien
E
- Reduced experimental P-x-y data for this mixture
(G
/RTx
factors are equal to one.
1x2 vs. x1) are given in Figure 1.
- The activity coefficients can be calculated from the Margules model
- Due to low pressures involved, you can assume here that all fugacity coefficients and Poynting
factors are equal to one.
CHEE 311
Lecture
17
6 (1)/acetone (2)
Figure
1: Reduced
P-x-y data for the mixture n-pentane