Gibbs–Duhem equation

About: Gibbs–Duhem equation is a research topic. Over the lifetime, 393 publications have been published within this topic receiving 6248 citations. The topic is also known as: Gibbs-Duhem equation.

Discussion of “mathematical representation of thermodynamic properties of binary system and solution of Gibbs-Duhem equation”

Abstract: The conclusion that orthogonal series is an advantageous method of representing the thermodynamics of binary solutions is examined. It is noted that at least three terms are normally required in representations but seldom more than five. The inclusion of supplementary conditions to control the smoothness would only increase the number by one or two. (JRD)

Basic Thermodynamics of Electrified Interfaces

Abstract: In this study some general aspects of the thermodynamics of systems with interfaces are discussed, and a brief treatment of interfaces within the framework of classical thermodynamics is presented. Special attention is paid to the theory of electrified interfaces. The intensive parameter conjugate to surface area (“surface tension” or “interfacial tension”) is an important parameter also in the thermodynamic theory of electrodes, because the interactions between the adjacent bulk phases take place via interfaces, for example, via the interface between a metal and an electrolyte solution. As a consequence, the thermodynamic properties of the interface region (i.e., the electronic conductor/ionic conductor interface) directly influence the electrochemical processes. First, to introduce the reader to the topic, basic concepts (such as “surface,” “interface,” “interphase,” “interfacial or interface region,” “dividing surface,” “adsorption”) are reviewed, a reasonably simple thermodynamic treatment of interfaces, together with a brief description of the models widely used in the literature, are presented, and the characteristics of the Gibbs “dividing plane” model and the Guggenheim “interphase” model are outlined. The derivation of the electrocapillary equation, the Gibbs adsorption equation, and the Lippmann equation for an ideally polarizable electrode is given. A simple illustrative example for the application of the electrocapillary equation is presented. Some important mathematical concepts (e.g., theory of homogeneous functions and partly homogeneous functions, Euler's theorem, and Legendre transformation) and various functional relationships of the thermodynamics of surfaces and interfaces are summarized.

Phase separation in multi-component mixtures: the four-component case

Abstract: Calculation of ternary phase diagrams for several mixtures formed by two salts and a neutral component is presented here. The phase diagrams are obtained by inspection of the shape of the Gibbs free energy of mixing surface (Gmix) as a function of the composition at constant temperature and pressure. The Gmix surface is calculated by the mean spherical approximation (MSA). The model for the mixtures is represented by hard spheres, with the charged components interacting via a Coulomb potential. The results are interpreted in terms of a thermodynamic analysis of the contributions to the Gibbs free energy of mixing, i.e., the configurational energy, the volume and the entropy of mixing.

The Operational Basis and Mathematical Derivation of the Gibbs Differential Equation, Which is the Fundamental Equation of Chemical Thermodynamics

Abstract: The basic thermodynamic relations for systems of variable composition were first derived by J. Willard Gibbs in his memoir entitled On the Equilibrium of Heterogeneous Substances (1874–1878). From the differential equation expressing the relation between the energy, the entropy, and the masses of the components of a homogeneous system of variable composition Gibbs then derived the conditions of equilibrium in a heterogeneous system, and from these equilibrium conditions he obtained the phase rule.