1. CHEE 311Lecture 161 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 G E vs. mixture composition for binary mixtures Highlights In binary systems, excess Gibbs energy data, plotted in the form G E /RTx 1 x 2, often follows a linear relationship with respect to mixture composition for a wide range of mole fraction values Simple models for G E, such as the Redlich/Kister and Symmetric Equation, can be used satisfactorily for binary mixtures Reading assignment: Section 12.1 and 11.9 (refresher)

2. CHEE 311Lecture 162 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.

3. CHEE 311Lecture 163 Correlation of Liquid Phase Data Recall our development of activity coefficients on the basis of the partial excess Gibbs energy : where the partial molar Gibbs energy of the non-ideal model is provided by equation 10.42: and the ideal solution chemical potential is: Leaving us with the partial excess Gibbs energy: (11.91)

4. CHEE 311Lecture 164 Correlation of Liquid Phase Data The partial excess Gibbs energy is defined by: In terms of the activity coefficient, (11.96) ln(  i ) is a partial molar property G E /RT and activity coefficients are related using the summability relationship for partial properties. (11.99) This information leads to useful correlations for activity coefficients.

5. CHEE 311Lecture 165 Correlation of Liquid Phase Data We can now process our MEK/toluene data one step further to give the excess Gibbs energy, G E /RT = x 1 ln  1 + x 2 ln  2

6. CHEE 311Lecture 166 Correlation of Liquid Phase Data Note that G E /(RTx 1 x 2 ) is reasonably represented by a linear function of x 1 for this system. This is the foundation for the simplest correlations for experimental activity coefficient data

7. CHEE 311Lecture 167 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.

8. CHEE 311Lecture 168 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 G E /x 1 x 2 RT is well approximated by a line.

9. CHEE 311Lecture 169 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 G E equations for activity coefficients are derived from the Redlich/Kister expansion: Equations of this form “fit” excess Gibbs energy data quite well. However, they are empirical and cannot be generalized for multi- component (3 + ) mixtures or multiple temperatures.

10. CHEE 311Lecture 1610 Symmetric Equation for Binary Mixtures The simplest Redlich/Kister expansion results from C=D=…=0 To calculate activity coefficients, we express G E in terms of moles: n 1 and n 2. And through differentiation, we find: