Gibbs difference

It is strictly for convenience that certain conventions have been adopted in the choice of a standard-state fugacity. These conventions, in turn, result from two important considerations (a) the necessity for an unambiguous thermodynamic treatment of noncondensable components in liquid solutions, and (b) the relation between activity coefficients given by the Gibbs-Duhem equation. The first of these considerations leads to a normalization for activity coefficients for nonoondensable components which is different from that used for condensable components, and the second leads to the definition and use of adjusted or pressure-independent activity coefficients. These considerations and their consequences are discussed in the following paragraphs. 

In this case, there is no superscript on y because, by assumption, Y is independent of pressure. The disadvantage of this procedure is that the reference pressure p" is now different for each component, thereby introducing an inconsistency in the iso-baric Gibbs-Duhem equation [Equation (16)]. In many, but not all, cases, this inconsistency is of no practical importance. 

The treatments that are concerned in more detail with the nature of the adsorbed layer make use of the general thermodynamic framework of the derivation of the Gibbs equation (Section III-5B) but differ in the handling of the electrochemical potential and the surface excess of the ionic species [114-117]. The derivation given here is after that of Grahame and Whitney [117]. Equation III-76 gives the combined first- and second-law statements for the surface excess quantities... 

For analysing equilibrium solvent effects on reaction rates it is connnon to use the thennodynamic fomuilation of TST and to relate observed solvent-mduced changes in the rate coefficient to variations in Gibbs free-energy differences between solvated reactant and transition states with respect to some reference state. Starting from the simple one-dimensional expression for the TST rate coefficient of a unimolecular reaction a— r... 

Since equation (A3.6.4) is equal to the difference between the Gibbs free energy of... 

For a multicomponent system, it is possible to simulate at constant pressure rather than constant volume, as separation into phases of different compositions is still allowed. The method allows one to study straightforwardly phase equilibria in confined systems such as pores [166]. Configuration-biased MC methods can be used in combination with the Gibbs ensemble. An impressive demonstration of this has been the detennination by Siepmaim et al [167] and Smit et al [168] of liquid-vapour coexistence curves for n-alkane chain molecules as long as 48 atoms. 

Arguments have been presented that this difference in changes in Gibbs function, rather than the similar difference in enthalpies of activation, AHl — AH, better represents the quantity with which... 

Figure 4.3a shows schematically how the Gibbs free energy of liquid (subscript 1) and crystalline (subscript c) samples of the same material vary with temperature. For constant temperature-constant pressure processes the criterion for spontaneity is a negative value for AG, where the A signifies the difference final minus initial for the property under consideration. Applying this criterion to Fig. 4.3, we conclude immediately that above T , AGf = Gj - G. is negative... 

As in the qualitative discussion above, let 7 be the Gibbs free energy per unit area of the interface between the crystal and the surrounding hquid. This is undoubtedly different for the edges of the plate than for its faces, but we... 

There are two ways in which the volume occupied by a sample can influence the Gibbs free energy of the system. One of these involves the average distance of separation between the molecules and therefore influences G through the energetics of molecular interactions. The second volume effect on G arises from the contribution of free-volume considerations. In Chap. 2 we described the molecular texture of the liquid state in terms of a model which allowed for vacancies or holes. The number and size of the holes influence G through entropy considerations. Each of these volume effects varies differently with changing temperature and each behaves differently on opposite sides of Tg. We shall call free volume that volume which makes the second type of contribution to G. 

The difference on the left is the partial excess Gibbs energy G y the dimensionless mXio J on the right is called the activity coefficient of species i in solution, y. Thus, by definition. 

P rtl IMol r Properties. The properties of individual components in a mixture or solution play an important role in solution thermodynamics. These properties, which represent molar derivatives of such extensive quantities as Gibbs free energy and entropy, are called partial molar properties. For example, in a Hquid mixture of ethanol and water, the partial molar volume of ethanol and the partial molar volume of water have values that are, in general, quite different from the volumes of pure ethanol and pure water at the same temperature and pressure (21). If the mixture is an ideal solution, the partial molar volume of a component in solution is the same as the molar volume of the pure material at the same temperature and pressure. 

A.ctivity Coefficients. Activity coefficients in Hquid mixtures are directiy related to the molar excess Gibbs energy of mixing, AG, which is defined as the difference in the molar Gibbs energy of mixing between the real and ideal mixtures. It is typically an assumed function. Various functional forms of AG give rise to many of the different activity coefficient models found in the Hterature (1—3,18). Typically, the Hquid-phase activity coefficient is a function of temperature and composition expHcit pressure dependence is rarely included. 

There is a significant difference between rhodium and the odier metals in that rhodium forms a relatively stable oxide, RI12O3. The Gibbs energy of formation of this oxide is given by the equation... 

---