Correlation of Liquid Phase Data
SVNA 12.1
Purpose of this lecture:
To show how activity coefficients can be calculated by means of
(published) tabulated data of GE vs. mixture composition for binary
mixtures
Highlights
• In binary systems, excess Gibbs energy data, plotted in the form
GE/RTx1x2, often follows a linear relationship with respect to mixture
composition for a wide range of mole fraction values
•Simple models for GE , such as the Redlich/Kister and Symmetric
Equation, can be used satisfactorily for binary mixtures
Reading assignment: Section 12.1 and 11.9 (refresher)
CHEE 311
Lecture 16
1
7. Correlation of Liquid Phase Data
SVNA 12.1
The complexity of molecular interactions in non-ideal systems
makes prediction of liquid phase properties difficult.
 Experimentation on the system of interest at the conditions
(P,T,composition) of interest is needed.
 Previously, we discussed the use of low-pressure VLE data
for the calculation of liquid phase activity coefficients.
As practicing engineers, you will rarely have the time to conduct
your own experiments.
 You must rely on correlations of data developed by other
researchers.
 These correlations are empirical models (with limited
fundamental basis) that reduce experimental data to
mathematical equations.
CHEE 311
Lecture 16
2
Correlation of Liquid Phase Data
Recall our development of activity coefficients on the basis of the
partial excess Gibbs energy :
E
id
Gi  Gi  Gi
where the partial molar Gibbs energy of the non-ideal model is
provided by equation 10.42:
G  l  i (T )  RT ln fˆl
i
i
i
and the ideal solution chemical potential is:
id
Gi
l
 id


(
T
)

RT
ln
x
f
i
i i
i
Leaving us with the partial excess Gibbs energy:
E
Gi  RT ln fˆil  RT ln x i fil
fˆil
 RT ln l
x i fi
 RT ln  i
CHEE 311
Lecture 16
(11.91)
3
Correlation of Liquid Phase Data
The partial excess Gibbs energy is defined by:
E
Gi
(nGE )

ni T,P,nj
In terms of the activity coefficient,
 (nG E / RT )
ln  i 

ni
T , P , nj
(11.96)
ln(i) is a partial molar property
GE/RT and activity coefficients are related using the summability
relationship for partial properties.
GE
  xi ln  i
RT i
(11.99)
This information leads to useful correlations for activity coefficients.
CHEE 311
Lecture 16
4
Correlation of Liquid Phase Data
We can now process our MEK/toluene data one step further to give
the excess Gibbs energy,
GE/RT = x1ln1 + x2ln2
CHEE 311
Lecture 16
5
Correlation of Liquid Phase Data
Note that GE/(RTx1x2) is reasonably represented by a linear
function of x1 for this system. This is the foundation for the simplest
correlations for experimental activity coefficient data
 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 16
6
Correlation of Liquid Phase Data
The chloroform/1,4-dioxane system
exhibits a negative deviation from
Raoult’s Law.
This low pressure VLE data can be
processed in the same manner as the
MEK/toluene system to yield both
activity coefficients and the excess
Gibbs energy of the overall system.
CHEE 311
Lecture 16
7
Correlation of Liquid Phase Data
Note that in this example, the activity
coefficients are less than one, and
the excess Gibbs energy is negative.
In spite of the this difference from
the MEK/toluene system behaviour,
the plot of GE/x1x2RT is well
approximated by a line.
CHEE 311
Lecture 16
8
Models for the Excess Gibbs Energy
Models that represent the excess Gibbs energy have several
purposes:
 they reduce experimental data down to a few parameters
 they facilitate computerized calculation of liquid phase
properties by providing equations from tabulated data
 In some cases, we can use binary data (A-B, A-C, B-C) to
calculate the properties of multi-component mixtures (A,B,C)
A series of GE equations for activity coefficients are derived from
the Redlich/Kister expansion:
GE
 B  C( x1  x 2 )  D( x1  x 2 )2
RTx 1x 2
(cons tan t T )
Equations of this form “fit” excess Gibbs energy data quite well.
However, they are empirical and cannot be generalized for multicomponent (3+) mixtures or multiple temperatures.
CHEE 311
Lecture 16
9
Symmetric Equation for Binary Mixtures
The simplest Redlich/Kister expansion results from C=D=…=0
GE
B
RTx 1x 2
To calculate activity coefficients, we express GE in terms of moles:
n1 and n2.
E
nG
Bnn

RT (n  n )
1
1
2
2
And through differentiation,
(nGE / RT )
ln 1 
n1
T,P,n2
we find:
CHEE 311
ln 1  Bx 22
and
Lecture 16
ln  2  Bx12
10