1. 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

2. 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 multi-component behaviour can be predicted from binary data.
CHEE 311
Lecture 17

3. 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.
CHEE 311
Lecture 17

4. Margules’ Equations
While the simplest Redlich/Kister-type correlation is the Symmetric Equation, but a more accurate equation is the Margules correlation:
(12.9a)
Note that as x1 goes to zero,
Also,
so that
and similarly
CHEE 311
Lecture 17

5. Margules’ Equations
If you have Margules parameters, the activity coefficients can be derived from the excess Gibbs energy expression:
(12.9a)
to yield:
(12.10ab)
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

6. Example 1
CHEE 311
Lecture 17