Chemical models of electrolyte solutions

Recent developments of the chemical model of electrolyte solutions permit the extension of the validity range of transport equations up to high concentrations (c 1 mol L"1) and permit the representation of the conductivity maximum Knm in the framework of the mean spherical approximation (MSA) theory with the help of association constant KA and ionic distance parameter a, see Ref. [87] and the literature quoted there in. 

Fig. 2. The chemical model of electrolyte solutions. O observer, i ion X, j ion Xj in an arbitrary position, fjj, with regard to the ion X, special positions (contact, separation by one or two orientated solvent molecules) are sketched with broken lines, r, a, R distance parameters W mean-force potentials and relative velocities of ions X, and Xj...

The chemical model of electrolyte solutions introduces short-range interactions by means of potentials of mean force W , which can be considered as contributions to ion-pair formation. 

In the last two decades experimental evidence has been gathered showing that the intrinsic properties of the electrolytes determine both bulk properties of the solution and the reactivity of the solutes at the electrodes. Examples covering various aspects of this field are given in Ref. [16]. Intrinsic properties may be described with the help of local structures caused by ion-ion, ion-solvent, and solvent-solvent interactions. An efficient description of the properties of electrolyte solutions up to salt concentrations significantly larger than 1 mol kg 1 is based on the chemical model of electrolytes. 

Chemical models of electrolytes take into account local structures of the solution due to the interactions of ions and solvent molecules. The underlying information stems from spectroscopic, kinetic, and electrochemical experiments, as well as from dielectric relaxation spectroscopy. The postulated structures include ion pairs, higher ion aggregates, and solvated and selectively solvated ions. 

The coefficients J R) and J2 R) depend on the cutoff distance R and thus include the influence of the short-range forces on the transport phenomenon for the activity coefficient of the chemical model, see Electrolyte Solutions,... 

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. 

Pabalan, R. T., and Pitzer, K. S. (1990) Models for Aqueous Electrolyte Mixtures for Systems Extending from Dilute Solutions to Fused Salts. In Chemical Modeling of Aqueous Systems, Vol. II, R. L. Basset and D. C. Melchior, Eds., American Chemical Society, Washington, DC. 

Kalyuzhnyi, Yu.V., and Stell, G. Solution of the polymer msa for the polymerizing primitive model of electrolytes. Chemical Physics Letters, 1995, 240, p. 157-164. 

So here, the term theory will be used in a way that embraces the typical named theories of chemistry such things as molecular orbital theory, valence shell electron pair repulsion theory, transition state theory of reactions, and Debye Hiickel theory of electrolyte solutions. No decisive distinction will be made between theory, model, and other similar terms. But there is one distinction that we do make. The term theory is considered in an epistemological sense—as an expression of oin best knowledge and belief about the way chemical systems work. 

In summary, the models discussed in this chapter focus on the physical aspects of electrolyte solutions but they ignore the chemical aspects. This is especially apparent in the treatment of ion solvation where an empirical correction to the MSA model was applied to treat the differences in behavior seen for cations and anions in water. The same problem arises in using classical electrostatics to describe ion pairing. In spite of the fact that the Bjerrum and Fuoss models give a good qualitative description of an ion association, this phenomenon can only be understood in detail by using quantum-mechanical methods. Needless to say, such calculations in condensed media are much more difficult to carry out. 

The information on the structure of electrolyte solutions provided by thermwlynamic and transport properties on the one hand and by spectroscopic, relaxation and kinetic investigations on the other, complement one another with regard to the chemical model. Thermodynamic and transport properties provide the distance parameter R, the overall association constant Ka, and the activity coeffident y linked to it. No direct information can be achieved on the structure of the region a g r R and possible regions a Rj Rj. .. R. This problem, however, can be solved by modem spectroscopic and relaxation methods. 

In connexion with dielectric and other spectroscopic relaxation methods, e.g. NMR, the group of ultrasonic relaxation, temperature- and pressure-jump methods 340 - 342) jjg mentioned. These yield information on the processes in electrolyte solution and confirm the basic chemical model of free ions and ion pairs in the solution... 

The chemical model. Section 4.2., when used to provide data of electrolyte solutions by computer-assisted methods, presupposes fire knowledge of the distance parameters a and R. These are needed in the appropriate equations as the characteristic distances of the bare or solvated single ions and of the adjacent solvent molecules. Solvent molecules may be orientated either by free electrons, by H-bonds or by their dipole moments, depending on the nature of the iom and the solvent molecule itself. 

Experimental investigations of thermodynamic properties are of importance for both examining theories and providing data for technology. The limiting values of the properties at zero concentration are of crucial interest they yield the standard values of the solution. However, ideality of electrolyte solutions, y = 1, appropriate for such extrapolations, would require experiments at such low concentrations that their execution would be either useless as a consequence of low precision or even impossible. Reliable investigations in the low-concentration region use computer-assisted data analysis of the experimental results based on appropriate statistical thermodynamic models. The chemical model (Section III.D) provides property equations of type... 

Van Luik, A.E. and Jurinak, J.J., Equilibrium chemistry of heavy metals in concentrated electrolyte solution, in Chemical Modeling in Aqueous Systems Speciation, Sorption, Solubility and Kinetics, Jenne, E.A., Ed., ACS Symp. Series 93, American Chemical Society, Washington, 1979, pp. 683-710. 

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