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

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

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

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

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

Example 1 CHEE 311 Lecture 17