CHEE 311 Lecture 17 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.

sat11

11 Px

Pylnln

sat22

22 Px

Pylnln

2211E lnxlnxRT/G

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

21212121

E

xAxAxRTx

G

1

210xln

xRTxG

lim

E

1

12

0x21

E

AxRTx

G

1

112 lnA 221 lnA

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.

21212121

E

xAxAxRTx

G

]x)AA(2A[xln 1122112221

]x)AA(2A[xln 2211221212

CHEE 311 Lecture 17 6

Example 1