Strong electrolytes in the MSA

The thermodynamic properties of electrolytes in the primitive MSA have been given elsewhere [23, 24]. For the sake of generality, we will discuss individual ionic excess thermodynamic properties. The single ion activity coefficients for fixed diameters were discussed hy several authors [25]-[27]. In all previous work the implicit dependence of the sizes and dielectric constants on the concentration was not, taken into account. The discussion below [28] corrects this issue. 

The thermodynamic properties can be derived from the Helmholtz energy density A. The excess energy can be split into two terms. One defines 

Thermodynamic integration (equivalent to Gimtelberg charging process) yields an expression for the MSA contribution to A. 

The expression for the excess MSA internal energy (per unit volume) [24] 

The excess osmotic coefficient is calculated from the thermodynamic relation 

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Abstract Analytical solution of the associative mean spherical approximation (AMSA) and the modified version of the mean spherical approximation - the mass action law (MSA-MAL) approach for ion and ion-dipole models are used to revise the concept of ion association in the theory of electrolyte solutions. In the considered approach in contrast to the traditional one both free and associated ion electrostatic contributions are taken into account and therefore the revised version of ion association concept is correct for weak and strong regimes of ion association. It is shown that AMSA theory is more preferable for the description of thermodynamic properties while the modified version of the MSA-MAL theory is more useful for the description of electrical properties. The capabilities of the developed approaches are illustrated by the description of thermodynamic and transport properties of electrolyte solutions in weakly polar solvents. The proposed theory is applied to explain the anomalous properties of electrical double layer in a low temperature region and for the treatment of the effect of electrolyte on the rate of intramolecular electron transfer. The revised concept of ion association is also used to describe the concentration dependence of dielectric constant in electrolyte solutions. 

Taking the chosen set of radii, very good agreement between theory and experiment was obtained without the need of introducing the concept of ion association for the description of the variation of the conductivity with concentration of an electrolyte solution in the case of 3 different simple ionic species (strong electrolytes). This model provides analytical expressions which are easy to use. However, above the limit of 1 mol/L in total concentration, its validity becomes questionable. A further extension of the theory should involve a modification in the equilibrium model. One possibility would be the use of the HNC model or of other improvements of MSA (softs- MSA, exp- MSA, The problem is then the connection to the low concentration (limiting laws) and the increase in adjustable parameters. Moreover,... 

Here, we describe the application and typical modelling results for a G model (MSA-NRTL) as well as for an EOS (ePC-SAFT). In addition to strong electrolytes which are almost fully dissociated, we also consider some weak electrolytes (acids like HE or ion-paired electrolytes) that do only partially dissociate in aqueous solution. Here, ion pairing is accounted for by an association/dissociation equilibrium between the ion pair and the respective free ions in solution. 

Section 3.2.1 describes fiilly dissociated electrolytes. For electrolytes that do not completely dissociate into the respective ions, a chemical-reaction mechanism is implemented in the ePC-SAFT framework (Sec. 3.2.2). Modelling of systems that can form multiple ion pairs is described in Sec. 3.2.3. Finally, we will discuss the experimental behaviour of strong and weak acids and present a respective model strategy (Sec. 3.2.4). Whereas so far activity coefficients of 19 electrolyte systems have been modelled by the MSA-NRTL, the properties of more than 120 systems have been studied with ePC-SAFT. The latter contains not only activity coefficients but also solution densities, which are important quantities for both process design and validation of model parameters. 

The second parameter which is used in the electrolyte models is a parameter representing the short-range interactions between water and an ion. In Table 4, anion-water and cation-water parameters are compared for the two models. Both the ePC-SAFT ujk, as well as the MSA-NRTL TW-ion interaction parameters directly reflect the strength of ionic hydration. The higher and the more negative rw-ion are, the more strongly hydrated the ion is (strong interaction with water) within the considered alkali halides. 

The following chapters will introduce the two models we focus on the (remodel MSA-NRTL and the equation of state ePC-SAFT, both of which composed of different terms for the SR and for the LR contributions in Eq. (1). After that, we will apply the two models to electrolyte solutions in order to describe thermodynamic properties of strong and weak electrolytes. 

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