(231f) The Gibbs-Helmholtz Equation in Chemical Process Technology

The family of Gibbs-Helmholtz equations connect phase and chemical equilibrium with enthalpy and volume.  This family of equations is one of the most useful – yet unappreciated and poorly understood – equations in chemical thermodynamics.  Here we present several variations of the Gibbs-Helmholtz (G-H) equation, and evaluate their use for chemical process technology.  The focus of the contribution is manner in which fundamental chemical thermodynamics can and should contribute to chemical-engineering education and the industrial practice of process technology.

Applied thermodynamics is an extremely important tool in process technology.  Chemical engineers in courses and in industry use process simulators for design, and this often means that the details of the property models are buried in the software.  While the progress in automation has enabled considerable increases in productivity, the unintended consequence is that expertise is often diminished.  So how best should we educate today’s chemical engineers?  Certainly the mathematical training is important, but an intuitive understanding and visualization are equally important. These ideal are elaborated here by focusing on the Gibbs-Helmholtz family of equations.

Somehow, the G-H equation it is not as well known and appreciated as the Gibbs-Duhem equation.  There is considerable misunderstanding about the precise form of the G-H equations, and we first present the rigorous derivations.  Next, applications of the G-H equations to pure components, vapor-liquid equilibrium, chemical absorption and reactor design are presented in order to provide insight into where and how this equation is valuable in chemical process technology.  Finally, the historical development of the G-H equation is presented because it is important to learn how new ideas and concepts in science and engineering develop over many decades.