Electrolyte solutions, thermodynamics generalized equations

The ionization of electrolytes is clearly manifest in the thermodynamic properties of their solutions. For example, in the ideally dilute solution limit, a solution of a strong electrolyte behaves as ions, rather than molecules, interacting with solvent molecules. A NaCl solution of molality m behaves, in the limit of infinite dilution, as an ideally dilute solution of concentration 2m, as 2 mol of ions are produced from each mole of NaCl dissolved in solution. A general strong electrolyte, dissociating by the equation... 

In this chapter, mathematical procedures for the estimation of the electrical interactions between particles covered by an ion-penetrable membrane immersed in a general electrolyte solution is introduced. The treatment is similar to that for rigid particles, except that fixed charges are distributed over a finite volume in space, rather than over a rigid surface. This introduces some complexities. Several approximate methods for the resolution of the Poisson-Boltzmann equation are discussed. The basic thermodynamic properties of an electrical double layer, including Helmholtz free energy, amount of ion adsorption, and entropy are then estimated on the basis of the results obtained, followed by the evaluation of the critical coagulation concentration of counterions and the stability ratio of the system under consideration. 

The general thermodynamic approach yields the - Gibbs-Lippmann equation (- electrocapillary) for the nonpolarizable [v] and ideally polarizable [ix] ITIES. For the interface between the electrolyte solutions of RX in w and SY in o, see also - interface between two immiscible electrolyte solutions, this equation has the form [x]... 

Pitzer KS (1973) Thermodynamics of electrolytes. I Theoretical basis and general equations.-Jour.of Physical Chemistry, 77 pp 268-277 Pitzer KS (1981) Chemistry and Geochemistry of Solutions at high T and P -In RICKARD WICKMANN, 295, V 13-14... 

There are several limitations which lead to the discrepancies in Tables IV-X. First of all, no model will be better than the assumptions upon which it is based. The models compiled in this survey are based on the ion association approach whose general reliability rests on several non-thermodynamic assumptions. For example, the use of activity coefficients to describe the non-ideal behavior of aqueous electrolytes reflects our uncertain knowledge of ionic interactions and as a consequence we must approximate activity coefficients with semi-empirical equations. In addition, the assumption of ion association may be a naive representation of the true interactions of "ions" in aqueous solutions. If a consistent and comprehensive theory of electrolyte solutions were available along with a consistent set of thermodynamic data then our aqueous models should be in excellent agreement for most systems. Until such a theory is provided we should expect the type of results shown in Tables IV-X. No degree of computational or numerical sophistication can improve upon the basic chemical model which is utilized. 

In the study of the interface with two immiscible electrolyte solutions (ITIES), considerable attention has been focused on the estimation of the Galvani potential difference at the water oil interface on the basis of a reasonable extra-thermodynamic assumptions. The discussion of these estimates is often made in terms of the ionic distribution coefficient, which is defined on the basis of equations (8.9.5) and (8.9.6). Generalizing this equation for the ot P interface at which ion i with charge z,- is transferred, one may write... 

For purposes of developing general equations for the thermodynamic properties of electrolyte solutions, it is useful to recalculate experimental values to a single reference pressure. This allows experimental data for different solution properties (e.g., activities, enthalpies, and heat capacities) whose relationships with each other are defined on an isobaric basis, to be considered in the overall regression... 

From this equation, it becomes obvious that the ratio of the equilibrium ion activities in the solution is linked with the alloy composition as expressed by the bulk atom fractions of the components, Xa and Xb = 1 — Xa- In general, therefore, the establishment of complete equilibrium for an alloy electrode requires a change of composition both of the alloy phase and of the electrolyte solution [1]. For solid alloys at ambient temperature, compositional changes (due to the preferential dissolution of one alloy component) will be restricted to the uppermost atomic layers. Further equilibration between the surface and the bulk of the alloy is prevented by solid-state diffusion limitations. Complete thermodynamic equilibrium for both components is therefore expected to evolve only with liquid alloys in which the diffu-sivity at ambient temperature is extremely high (for dilute Zn-amalgams, e.g., inter-diffusion coefficients t>zn of the order of 10 cm s have been reported under these conditions [2]). 

Clegg, S.L. Pitzer, K.S. 1992, Thermodynamics of Multicomponent, Miscible, Ionic Solutions Generalized Equations for Symmetrical Electrolytes. J. Phys. Chem., 96,3513. 

Clegg SL, Pitzer KS (1992) Thermodynamics of multicomponent, miscible, ionic solutions generalized equations for symmetrical electrolytes. J Phys Chem 96 3513-3520... 

Dolar D, Kozak D (1970) Osmotic coefficients of polyelectrolyte solutions with mono and divalent counterions. Proc Leiden Symp 11 363 366 Katchalsky A (1971) Polyelectrolytes. Pure Appl Chem 26 327 374 Pitzer KS (1973) Thermodynamics of electrolytes I. Theoretical basis and general equations. J Phys Chem 77 268 277... 

The conventional picture of the interface of simple aqueous salt solutions is based on thermodynamic analysis of the equilibrium surface tension isotherm. Valuable sources for the equilibrium surface tension isotherm of a simple aqueous electrolyte solution are the papers of Jarvis and Scheiman, and P. Weissenborn and Robert J. Pugh (See Chap. 1, Fig. 8). In general, ions increase the surface tension in a specific manner. However, it is worth mentioning that certain combinations of ions decrease the surface tension or have a negligible effect on it. The thermodynamic analysis of the surface isotherm leads to the picture that the interfacial zone is depleted of ions. The surface deficiency is calculated using Gibbs equation as the derivative of the surface tension isotherm with a dividing plane chosen at a location that the surface excess of water vanishes. 

An alternative description of a molecular solvent in contact with a solute of arbitrary shape is provided by the 3D generalization of the RfSM theory (3D-RISM) which yields the 3D correlation functions of interaction sites of solvent molecules near the solute. It was first proposed in a general form by Chandler, McCoy, and Singer [22] and recently developed by several authors for various systems by Cortis, Rossky, and Friesner [23] for a one-component dipolar molecular liquid, by Beglov and Roux [24, 25] for water and a number of organic molecules in water, and by Hirata and co-workers for water [26, 27], metal-water [26, 28] and metal oxide-water [31] interfaces, orientationally dependent potentials of mean force between molecular ions in a polar molecular solvent [29], ion pairs in aqueous electrolyte [30], and hydration of hydrophobic and hydrophilic solutes alkanes [32], polar molecule of carbon monoxide [33], simple ions [34], protein [35], amino acids and polypeptides [36, 37]. It should be noted that accurate calculation of the solvation thermodynamics for ionic and polar solutes in a polar molecular liquid requires special corrections to the 3D-RISM equations to eliminate the electrostatic artifacts of the supercell treatment employed in the 3D-RISM approach [30, 34]. 

One can imagine limiting circumstances for which the latter equations are decoupled. Explicitly, for an almost ion-free (almost nonconductive) solution, one can see that 1 = 0, while Eq. (lb) reproduces Darcy s law. In the other extreme case of a solid (infinitely viscous) electrolyte, one has U = 0, and Eq. (la) reduces to the familar Ohm s law. In general, one can show that a = p, by virtue of the Onsager thermodynamic theorem [3] p denotes the transpose of the tensor p. 

This is the exact expression for the equilibrium constant K, as given in Equation 1.113 it has been derived from thermodynamic considerations alone, without the assumption of the law of mass action. It may be simplified for systems which do not depart appreciably from ideal behaviour, i.e. for reactions in solution mole fractions. In dilute solutions, concentrations may be employed. In general, however, with concentrated solutions such as cell electrolytes, it is best to use activities. 

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