Effect of Activity Coefficients on Excess Functions and Phase Equilbria©
Baudilio Coto
Department of Chemical and Environmental Technology
ESCET, Rey Juan Carlos University
C/ Tulipan
Móstoles ( Madrid ) 28933
mail to: baudilio.coto@urjc.es

Immaculada Suárez
Department of Chemical and Environmental Technology
ESCET, Rey Juan Carlos University
Móstoles ( Madrid ) 28933


The comparison between ideal and non ideal behavior in liquid mixtures in terms of experimental properties as vapor pressures or boiling temperatures is easy to show. However, it is quite complex for students to understand such behavior in terms of activity coefficients, activities or excess functions. In adition, a numerical problem arises because, althlough the expressions for the activity coefficients, even in quite simple models are not difficult to manage, they are very cumbersome. The application of such models to calculate vapor liquid equilibrium conditions in some cases introduces a numerical problem which has to be solved iteratively. As consequence, from the academic point of view, two possibilities are to have the students carry out the calculations by hand using very simple models or even ideal solution behavior, or, alternativley, they carry out very complex calculations with the help of commercial simulation software used as a black box where the thermodynamic equations are far away from the view of the student.

In this work we reverse the point of view. We start from the activity coefficient as a known property. We examine how from activity coefficients some functions change from the "ideal solution" value, the excess functions differ from zero and vapor liquid equilibrium diagrams can show very complex behavior. The use of Maple to evaluate such functions, to solve the equilibrium equations, and to display calculated values allows the students both to obtain numerical values and to plot the functions in order to understand the meaning of the calculations.

The model used is a simple one in order to avoid the use of a very complex iterative procedure to solve equilibrium equations. Activity and fugacity are calculated from activity coefficient values, and some theoretical aspects of the Henry and Raoult limit laws are shown. Excess and mixing Gibbs energies are calculated and plotted. Finally, vapor liquid equilibrium equations are solved to compute both isobaric and isothermal binary diagrams; calculations for given mixtures are carried out and clearly shown in diagrams.

Editor's Commentary
Audiences: Upper-Division Undergraduate
Pedagogies: Computer-Based Learning
Domains: Physical Chemistry
Topics: Equilibrium, Mathematics / Symbolic Mathematics, Thermodynamics
File NameDescriptionSoftware TypeSoftware Version
ExcessFunctions12.mw JCE Maple 12 Computational Document Maple 12
ExcessFunctions12.pdf Read-Only Document
JCE JCE Subscribers only: name and password or institutional IP number access required.
Suárez, I.; Coto, B. J. Chem. Educ. 2009, 86, 1468
Comments to: Baudilio Coto at baudilio.coto@urjc.es
©Copyright 2009 Division of Chemical Education, Inc., American Chemical Society.