Vapor-Liquid Equilibria Using the Gibbs Energy and the Common Tangent Plane Criterion


  • María del Mar Olaya University of Alicante
  • Juan A. Reyes-Labarta University of Alicante
  • María Dolores Serrano University of Alicante
  • Antonio Marcilla University of Alicante


Phase thermodynamics is often perceived as a difficult subject with which many students never become fully comfortable. The Gibbsian geometrical framework can help students to gain a better understanding of phase equilibria. An exercise to interpret the vapor-liquid equilibrium of a binary azeotropic mixture, using the equilibrium condition based on the common tangent plane criterion (the Gibbs stability test), is presented in this paper. From a T-composition phase diagram for the mixture, the temperature is set at different values: above, intermediate to, and below the boiling temperatures of the pure components, to intersect different regions of the system. Students prepare an Excel spreadsheet where the Gibbs energy of mixing of the vapor and liquid mixtures are calculated and represented over the whole range of compositions and then, apply the Gibbs stability test to ascertain the aggregation state of the system and to calculate the VL phase equilibrium compositions. Finally, Matlab is used to generate the 3-D Gibbs energy of mixing surfaces for both phases over the whole range of temperatures which facilitates the geometrical interpretation of the vapor-liquid equilibrium.

Author Biographies

María del Mar Olaya, University of Alicante

María del Mar Olaya completed her B.S. in chemistry in 1992 and Ph.D. in chemical engineering in 1996. She teaches a wide range of courses from freshman to senior level at the University of Alicante, Spain. Her research interests include phase equilibria calculations and polymer structure, properties, and processing.

Juan A. Reyes-Labarta, University of Alicante

Juan A. Reyes-Labarta received both his B.S. and Ph.D. in chemical engineering in 1993 and 1998, respectively, at the University of Alicante (Spain). After post-doctoral stays at Carnegie Mellon University (USA) and the Institute of Polymer Science and Technology-CSIC (Spain), he is now a full-time lecturer in Separation Processes and Molding Design.

María Dolores Serrano, University of Alicante

María Dolores Serrano is a recent chemical engineering graduate of the University of Alicante. She is currently a post-graduate student, working on different aspects of phase equilibria.

Antonio Marcilla, University of Alicante

Antonio Marcilla is a professor of chemical engineering at Alicante University. He has presented courses in Unit Operations, Phase Equilibria, and Chemical Reactor Laboratories. His research interests are pyrolysis, liquid-liquid extraction, polymers, and rheology. He is also currently involved with the study of polymer recycling via catalytic cracking and the problem of simultaneous correlation of fluid and condensed phase equilibria.