Generalized Gibbs energy

However, as the generalized Gibbs energy is a function of state, we have, according to relation [1.19] ... 

G, Gi, [G] Gibbs energy, partial molar Gibbs energy of /, generalized Gibbs energy. 

Generalized Gibbs energy, denoted [g] is the characteristic function... 

For example, a phase defined from the set of variables P, T, and O, is an electrochemical system. The chemical phase associated would be the same phase under zero potential (or zero charge). The generalized Gibbs energy of... 

The system will be completely characterized if the function s generalized Gibbs energy. Go (relation [1.9]) is known, which is written, for a solution with N components whose generalized chemical potentials are [a,], in the differential form ... 

Equation ( A2.1.39) is the generalized Gibbs-Diihem equation previously presented (equation (A2.1.27)). Note that the Gibbs free energy is just the sum over the chemical potentials. 

The general criterion of chemical reaction equiUbria is the same as that for phase equiUbria, namely that the total Gibbs energy of a closed system be a minimum at constant, uniform T and P (eq. 212). If the T and P of a siagle-phase, chemically reactive system are constant, then the quantities capable of change are the mole numbers, n. The iadependentiy variable quantities are just the r reaction coordinates, and thus the equiUbrium state is characterized by the rnecessary derivative conditions (and subject to the material balance constraints of equation 235) where j = 1,11,.. ., r ... 

Generalized charts are appHcable to a wide range of industrially important chemicals. Properties for which charts are available include all thermodynamic properties, eg, enthalpy, entropy, Gibbs energy and PVT data, compressibiUty factors, Hquid densities, fugacity coefficients, surface tensions, diffusivities, transport properties, and rate constants for chemical reactions. Charts and tables of compressibiHty factors vs reduced pressure and reduced temperature have been produced. Data is available in both tabular and graphical form (61—72). 

Complex Clieinical-Reaction Equilibria When the composition of an equilibrium mixture is determined by a number of simultaneous reactions, calculations based on equilibrium constants become complex and tedious. A more direct procedure (and one suitable for general computer solution) is based on minimization of the total Gibbs energy G in accord with Eq. (4-271). The treatment here is... 

A more general, and for the moment, less detailed description of the progress of chemical reactions, was developed in the transition state theory of kinetics. This approach considers tire reacting molecules at the point of collision to form a complex intermediate molecule before the final products are formed. This molecular species is assumed to be in thermodynamic equilibrium with the reactant species. An equilibrium constant can therefore be described for the activation process, and this, in turn, can be related to a Gibbs energy of activation ... 

In contradiction to the usual treatment, relation (5) is not general (see below). For this reason, as well as the lack of an exact thermodynamic relation with the changes in Gibbs energy, the term compensation voltage is also recommended instead of emf, which is commonly used for... 

The partial molar Gibbs energy of mixing of a component i in a non-ideal mixture can in general be expressed in terms of activity coefficients as... 

The formalism shown above is in general easily extended to multi-component systems. All thermodynamic mixing properties may be derived from the integral Gibbs energy of mixing, which in general is expressed as... 

In general, the first derivative of the Gibbs energy is sufficient to determine the conditions of equilibrium. To examine the stability of a chemical equilibrium, such as the one described above, higher order derivatives of G are needed. We will see in the following that the Gibbs energy versus the potential variable must be upwards convex for a stable equilibrium. Unstable equilibria, on the other hand, are... 

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