Phase equilibria and the chemical potential

Abstract

It is the purpose of this article to present several graphic examples of key relationships in the subject of phase equilibria.

Using the Principles of Classical and Statistical Thermodynamics To Calculate the Melting and Boiling Points, Enthalpies and Entropies of Fusion and Vaporization of Water, and the Freezing Point Depression and Boiling Point Elevation of Ideal and Nonideal Aqueous Solutions

“…In an earlier publication in this Journal , Castellan used schematic diagrams of the molar free energy curves, μ­( T ), to illustrate transition temperatures and to rationalize how changes in the applied pressure affected the melting and boiling points of a liquid, and also how the freezing point depression and boiling point elevation resulted from the presence of a solute in an ideal solution …”

“…In an earlier publication in this Journal, Castellan used schematic diagrams of the molar free energy curves, μ(T), to illustrate transition temperatures and to rationalize how changes in the applied pressure affected the melting and boiling points of a liquid, and also how the freezing point depression and boiling point elevation resulted from the presence of a solute in an ideal solution. 1 In the preceding article, we presented the methods and tools that enable students to calculate the chemical potential, μ, of the solid, liquid, and gas phases of mercury, diiodine, and ammonia (at 1 bar) as a function of temperature. 2 Students used these results to construct graphs of μ vs T and to calculate the intersection point of the μ gas (T) and μ liq (T) curves, enabling them to obtain the standard boiling point T sbp .…”

The Gibbs Phase Rule: What Happens When Some Phases Lack Some Components?

“…It makes it appear as if the rule has a caveat, which is not true. This has seldom been brought to the notice of students, though several articles have been published on the phase rule over the years. − There could be situations that lay constraints in addition to the equilibrium condition (i.e., equal chemical potential for a component across phases) (i) peritectic system, where the two components react for a product under a specific composition and temperature, (ii) an azeotropic mixture where the composition of the liquid and vapor is the same at all temperatures, , and (iii) liquid–vapor critical point, where the density of the liquid becomes equal to that of the vapor . These conditions must be treated as additional constraints, which will further reduce the degrees of freedom.…”

Constructing the Phase Diagram of a Single-Component System Using Fundamental Principles of Thermodynamics and Statistical Mechanics: A Spreadsheet-Based Learning Experience for Students

“…The qualitative portrayal of μ­( T ) plots of the solid, liquid, and gas phases of a compound that so well captures the fundamental principles of phase equilibrium perhaps first appeared in the chemistry education literature in 1955 in an article by Castellan in this Journal . That article, and others that followed, nicely illustrates how one could apply the fundamental Gibbs equation ­(where S m and V m are the molar entropy and volume of the substance) and the partial derivatives to interpret and understand this simple diagram.…”