Electric Gibbs function

To illustrate the notation and meaning of the third-order coefficients let us discuss the electric Enthalpy H2 (6.16) and the electric Gibbs function G2 (6.17). With Ek and Vab as independent variables they are important for experiments involving elastic waves arrd vibrations. 

The reaction also can be carried out reversibly if additional constraints are placed on the system, as in the cell illustrated by Figure 7.2. The H2 and CI2 electrodes are connected to a potentiometer. If the electromotive force of the cell is opposed by the eleetromotive force of the potentiometer, which is maintained at an infinitesimally lower value than that of the H2-CI2 cell, then the conversion to HCl can be carried out reversibly, although it would take an infinitely long time to obtain one mole of reaction. The change in the Gibbs function is the same for either the reversible or the explosively spontaneous path for carrying out the transformation, because the initial and final states are the same in both cases. However, the amount of useful (electrical) work is different, and, for the reversible path... 

The method of determination from measurements of cell potentials depends on the possibility of carrying out a transformation reversibly in an electrical cell. (See Fig. 7.2.) In this case, the spontaneous tendency of the transformation wUl be opposed by an opposing potential just sufficient to balance the potential in the electrical ceU produced by that spontaneous tendency. The potential observed under such circumstances is related to the change of the Gibbs function for the reaction by Equation (7.84)... 

The concept of a dielectrochemical potential introduced in the previous section is already implicit in Guggenheim s treatment of dielectrics in the presence of external fields. In order to apply the familiar criteria for reversible (equilibrium) processes and irreversible (nonequilibrium) processes in terms of an appropriate Gibbs function, Guggenheim introduced the characteristic Gibbs function in the presence of electric fields by a transformation. We may express the transformed Gibbs free energy as... 

Substituting Eq. (4.10) into (4.11) finally leads to the characteristic Gibbs function for chemically open systems in electric fields ... 

Introducing Eq. (4.19) with dnj = Vjd into Eq. (4.13) we obtain the Gibbs function of chemically reacting systems in external electric fields ... 

Fuel cells are potentially attractive for converting chemical energy directly into electrical energy, as their performance is dictated by the Gibbs function rather than the Carnot... 

As an example let us discuss the triple of independent variables defining the Gibbs function G. Temperature , the coordinates of the electric field vector and... 

The determination of the Gibbs energy of adsorption at zero surface coverage AGg=o nd of the interaction parameter A as a function of an electrical variable, may become a valuable source of information on the interactions at the interface. The value of AG°can be considered as the energy required to replace n monomolecularly adsorbed solvent molecules from a fully solvent-covered electrode surface by one monomeric molecule of the solute... 

The deviations from the Szyszkowski-Langmuir adsorption theory have led to the proposal of a munber of models for the equihbrium adsorption of surfactants at the gas-Uquid interface. The aim of this paper is to critically analyze the theories and assess their applicabihty to the adsorption of both ionic and nonionic surfactants at the gas-hquid interface. The thermodynamic approach of Butler [14] and the Lucassen-Reynders dividing surface [15] will be used to describe the adsorption layer state and adsorption isotherm as a function of partial molecular area for adsorbed nonionic surfactants. The traditional approach with the Gibbs dividing surface and Gibbs adsorption isotherm, and the Gouy-Chapman electrical double layer electrostatics will be used to describe the adsorption of ionic surfactants and ionic-nonionic surfactant mixtures. The fimdamental modeling of the adsorption processes and the molecular interactions in the adsorption layers will be developed to predict the parameters of the proposed models and improve the adsorption models for ionic surfactants. Finally, experimental data for surface tension will be used to validate the proposed adsorption models. 

The free energy functions are defined by explicit equations in which the variables are functions of the state of the system. The change of a state function depends only on the initial and final states. It follows that the change of the Gibbs free energy (AG) at fixed temperature and pressure gives the limiting value of the electrical work that could be obtained from chemical transformations. AG is the same for either the reversible or the explosively spontaneous path (e.g. H2 -I- CI2 reaction) however, the amount of (electrical) work is different. Under reversible conditions... 

Since in addition to the chemical potentials also the electrical potential 99, affects the charged species, electrochemical potentials //, must be used. We use the symbol 99 instead of -ip because this is the Galvani potential (see Section 5.5). The Gibbs-Duhem equation for changes of state functions at constant temperature is... 

As we have seen in the preceding chapter, the standard thermodynamic properties of species in aqueous solutions are functions of ionic strength when they have electric charges. Substituting equation 3.6-3 for species j and for H + in equation 4.4-9 yields the standard transformed Gibbs energy of formation of species j as a function of pH and ionic strength at 298.15 K ... 

The input speciesmat is a matrix that gives the standard Gibbs energy of formation at 298.15 K, the standard enthalpy of formation at 298.15 K, the electric charge, and the numbers of hydrogen atoms in each species. There is a row in the matrix for each species of the reactant, gfnsp is alist of the functions for the species. )... 

---