Electrolytic solutions Gibbs energy

AH , AS at, AG°at Lattice enthalpy, entropy, and Gibbs energy of the crystalline electrolyte AH v, AS V, AG°V Enthalpy, entropy, and Gibbs energy of solvation of the electrolyte AG° Gibbs energy of solution of the crystalline electrolyte. Taken from Table 1 in Ref. [3], Chapter 1. 

Electrolyte solutions ordinarily do not contain free electrons. The concept of electrochemical potential of the electrons in solution, ft , can stiU be used for those among the bound electrons that will participate in redox reactions in the solution. Consider the equilibrium Ox + ne Red in the solution. In equilibrium, the total change in Gibbs energy in the reaction is zero hence the condition for equilibrium can be formulated as... 

Analogonsiy, soinbiiity measurements yieid the mean activity of electrolyte (s = w, o), and the corresponding standard Gibbs energy AG i of solution (in the molar scale). 

The determination of the standard Gibbs energies of transfer and their importance for potential differences at the boundary between two immiscible electrolyte solutions are described in Sections 3.2.7 and 3.2.8. 

Solid electrolytes are frequently used in studies of solid compounds and solid solutions. The establishment of cell equilibrium ideally requires that the electrolyte is a pure ionic conductor of only one particular type of cation or anion. If such an ideal electrolyte is available, the activity of that species can be determined and the Gibbs energy of formation of a compound may, if an appropriate cell is constructed, be derived. A simple example is a cell for the determination of the Gibbs energy of formation of NiO ... 

As in the nonelectrolyte case, the problem of representing the thermodynamic properties of electrolyte solutions is best regarded as that of finding a suitable expression for the non-ideal part of the chemical potential, or the excess Gibbs energy, as a function of composition, temperature, dielectric constant and any other relevant variables. 

Vera and co-workers (7,W,lj ) have extended the thermodynamic correlation and made two additions. First, they have developed a semi-empirical expression for the excess Gibbs energy in place of the simple empirical equations originally used (Equations 8 and 9). Also, while they use a standard state of the electrolyte of a saturated solution, they change the standard state of water back to the conventional one of pure water. 

The work of Vera and co-workers nasHed to a semi-empirical expression for the excess Gibbs energy which is consistent with our choice of the saturated solution as the standard state for the electrolyte. Vera has, however, shown that pure water is a more convenient standard state for hLO in place of the saturated solution used by Vega and Funk (19). This is particularly convenient for ternary and higher systems since it avoids the complication of having a composition-dependent standard state. 

The differences in the solvation abilities of ions by various solvents are seen, in principle, when the corresponding values of As ivG° of the ions are compared. However, such differences are brought out better by a consideration of the standard molar Gibbs energies of transfer, AtG° of the ions from a reference solvent into the solvents in question (see further section 2.6.1). In view of the extensive information shown in Table 2.4, it is natural that water is selected as the reference solvent. The TATB reference electrolyte is again employed to split experimental values of AtG° of electrolytes into the values for individual ions. Tables of such values have been published [5-7], but are outside the scope of this text. The notion of the standard molar Gibbs energy of transfer is not limited to electrolytes or ions and can be applied to other kinds of solutes as well. This is further discussed in connection with solubilities in section 2.7. 

A definite relationship exists between y+ and (p (the Gibbs-Duhem relationship), which may be expressed by the excess Gibbs energy of the solution of an electrolyte ... 

This expression is analogous to Eiq. (2.3), in that (1 — (p) expresses the contribution of the solvent and In y+ that of the electrolyte to the excess Gibbs energy of the solution. The calculation of the mean ionic activity coefficient of an electrolyte in solution is required for its activity and the effects of the latter in solvent extraction systems to be estimated. The osmotic coefficient or the activity of the water is also an important quantity related to the ability of the solution to dissolve other electrolytes and nonelectrolytes. 

We turn our attention in this chapter to systems in which chemical reactions occur. We are concerned not only with the equilibrium conditions for the reactions themselves, but also the effect of such reactions on phase equilibria and, conversely, the possible determination of chemical equilibria from known thermodynamic properties of solutions. Various expressions for the equilibrium constants are first developed from the basic condition of equilibrium. We then discuss successively the experimental determination of the values of the equilibrium constants, the dependence of the equilibrium constants on the temperature and on the pressure, and the standard changes of the Gibbs energy of formation. Equilibria involving the ionization of weak electrolytes and the determination of equilibrium constants for association and complex formation in solutions are also discussed. 

We consider only aqueous solutions here, but the methods used are applicable to any solvent system. The standard Gibbs energy of formation of a strong electrolyte dissolved in water is obtained according to Equation (11.28). In such solutions the ions are considered as the species and we are concerned with the thermodynamic functions of the ions rather than the component itself. We express the chemical potential of the electrolyte, considered to be MVtAv, in its standard state as... 

Care must be taken to use or determine the correct change of state to which the change of entropy and enthalpy refers. The difficulty arises when one or more equilibrium reactions are present in addition to those used in determining the cell reaction. Such conditions occur when two or more phases are in equilibrium for example, the electrolytic solution may be saturated with a solid phase, or one of the electrodes may consist actually of a liquid solution that is saturated with a solid solution or with another liquid solution. Such equilibria do not alter the change of the Gibbs energy or the emf. Let the cell reaction be represented as v,Bj and an equilibrium reaction as... 

The concept of excess Gibbs free energy is useful in describing mixtures of electrolyte solutions. The excess free energy is the free energy of the mixed solution over and above that possessed by the singleelectrolyte solutions which comprise the mixture. 

Sometimes the question is asked how it is possible that the surface tension of pure water increases by the addition of electrolytes that are depleted from the surface. The answer must be found in the excess nature of molar Gibbs energies (or chemical potentials) in the Interface, as compared with those in the bulk. If, by adding a substance to the solution decreases more than, the surface tension should rise. In formulas, such as -i-0RTln(l- x), see [1.2.18.5], where 0 is... 

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