Ion association aqueous models

Calculations using the aqueous model from WATEQ and an aqueous model modified from WATEQ were compared to experimental mean activity coefficients for various salts to determine the range of applicability and the sources of errors in the models. An ion-association aqueous model was derived by least-squares fitting of ion-association stability constants and individual-ion, activity-coefficient parameters to experimental mean activity coefficients for various salts at 25°C. 

The components of an ion-association aqueous model are (1) The set of aqueous species (free ions and complexes), (2) stability constants for all complexes, and (3) individual-ion activity coefficients for each aqueous species. The Debye-Huckel theory or one of its extensions is used to estimate individual-ion activity coefficients. For most general-purpose ion-association models, the set of aqueous complexes and their stability constants are selected from diverse sources, including studies of specific aqueous reactions, other literature sources, or from published tabulations (for example, Smith and Martell, (13)). In most models, stability constants have been chosen independently from the individual-ion, activity-coefficient expressions and without consideration of other aqueous species in the model. Generally, no attempt has been made to insure that the choices of aqueous species, stability constants, and individual-ion activity coefficients are consistent with experimental data for mineral solubilities or mean-activity coefficients. 

In this report, calculations made using ion-association aqueous models were compared to experimental mean activity coefficients for various salts to determine the range of applicability and the sources of errors in the models. An ion-association aqueous model must reproduce the mean activity coefficients for various salts accurately or it does not describe the thermodynamics of aqueous solutions correctly. Calculations were made using three aqueous models (1) The aqueous model obtained from WATEQ (3), WATEQF (4), and WATEQ2 (6), referred to as the WATEQ model (2) the WATEQ model with modifications to the individual-ion, activity-coefficient equations for the free ions, referred to as the amended WATEQ model and (3) an aqueous model derived from least-squares fitting of mean activity-coefficient data, referred to as the fit model. 

The results of calculations made using ion-association aqueous models are the molality, activity, and individual-ion activity coefficient for each species in the model. The mean activity coefficient, y , for a salt can be calculated as follows ... 

The mean activity coefficient for a salt can be calculated from experimental data, but the individual-ion activity coefficients used in ion-association aqueous models cannot be determined experimentally. Several formulas were used for individual-ion activity coefficients in the calculations presented in this report. Three formulas were used in the WATEQ model the extended Debye-Huckel formula including an ion-size parameter, a[ (Equation 2) modified extended Debye-Huckel formula with two fitted parameters, a[ and 6i (Equation 3) and the Davies equation (Equation 4). 

Table I are not completely dissociated in solution, then the individual-ion activity coefficients used in this report are too small. Further, the stability constants for the other salts also are too small. If the salts that are assumed to be associated in solution in this report are, in fact, completely dissociated in solution, then the ion-association aqueous model is inadequate. In this case, the ion-association aqueous model can not reproduce accurately the mean activity coefficients of all the salts and simultaneously maintain a correct physical description of the solutions.

Figure 3. Comparision of gypsum solubilities calculated by the Harvie and Weare model (23) and ion-association aqueous models in 0.5-molal NaCl solutions with varying concentrations of Na2S04.

Fourth, in ion-association aqueous models, complexation only accounts for the attractive interactions among ions. All repulsive interactions among ions are included in the expressions for the individual-ion activity coefficients. Similarly, the individual-ion activity coefficients account for any hydration effects not specifically accounted for by complexation. 

Fifth, the fit model has not been tested in mixed-salt solutions and against mineral solubility data (other than gypsum). It is not known whether an ion-association aqueous model, even with additional complexes, will be capable of accurately modeling these systems. 

Last, the necessity for complexes in strong electrolyte solutions (in particular, the OH and C104 solutions) and large hi values with no apparent physical explanation (the OH salts) may reflect fundamental problems with the ion-association aqueous models. More general geochemical models may require a more rigorous formulation and an approach that accounts for specific interactions between aqueous species. 

An ion-association aqueous model was derived by (1) Selecting the set of salts used to calculate the individual-ion activity coefficients of the free ions (2) hypothesizing an appropriate set of complexes and (3) fitting the stability constants and individual-ion, activity-coefficient parameters for the complexes using the mean- activity-coefficient data. 

Concept used in sophisticated scaling models, whereby certain ions in aqueous solution are said to associate in pairs (e.g., CaS04, CaHC03-). These ion pairs are then deducted from the total analytical value, to provide an estimate of the free ion content available for seed crystal scaling or growth agglomeration and deposition. 

It is interesting to compare the Debye-Hiickel and virial methods, since each has its own advantages and limitations. The Debye-Hiickel equations are simple to apply and readily extensible to include new species in solution, since they require few coefficients specific to either species or solution. The method can be applied as well over the range of temperatures most important to an aqueous geochemist. There is an extensive literature on ion association reactions, so there are few limits to the complexity of the solutions that can be modeled. 

Solvation Effects. Many previous accounts of the activity coefficients have considered the connections between the solvation of ions and deviations from the DH limiting-laws in a semi-empirical manner, e.g., the Robinson and Stokes equation (3). In the interpretation of results according to our model, the parameter a also relates to the physical reality of a solvated ion, and the effects of polarization on the interionic forces are closely related to the nature of this entity from an electrostatic viewpoint. Without recourse to specific numerical results, we briefly illustrate the usefulness of the model by defining a polarizable cosphere (or primary solvation shell) as that small region within which the solvent responds to the ionic field in nonlinear manner the solvent outside responds linearly through mild Born-type interactions, described adequately with the use of the dielectric constant of the pure solvent. (Our comments here refer largely to activity coefficients in aqueous solution, and we assume complete dissociation of the solute. The polarizability of cations in some solvents, e.g., DMF and acetonitrile, follows a different sequence, and there is probably some ion-association.)... 

There are five reactions that deal with ion associations (numbers 8 to 12 in Table 3.3). There are, of course, many more such associations in concentrated electrolyte solutions. But the Pitzer approach allows one to either explicitly identify an ion association (Table 3.3) or to implicitly include the interaction effect in the interaction coefficients (B, C, minor components of the aqueous phase. 

In the mean spherical approximation (MSA) treatment of the ion association in aqueous solutions, the linearity of the relative permittivity and of the hydrated cation diameters with the electrolyte concentration was taken into account and a good fit of the experimental activity and osmotic coefficient was obtained [72-75]. The MSA model was elaborated on the basis of cluster expansion considerations involving the direct correlation function the treatment can deal with the many-body interaction term and with a screening parameter and proved expedient for the interpretation of experimental results concerning inorganic electrolyte solutions [67,75-77]. 

One could use the Debye-Hiickel ionic-atmosphere model to study how ions of opposite charges attract each other, (a) Derive the radial distribution of cation ( +) and anion (nj concentration, respectively, around a central positive ion in a dilute aqueous solution of 1 1 electrolyte, (b) Plot these distributions and compare this model with Bjerrum s model ofion association. Comment on the applicability of this model in the study of ion association behavior, (c) Using the data in Table 3.2, compute the cation/anion concentrations at Debye-HUckel reciprocal lengths for NaCl concentrations of lO and 10 mol dm", respectively. Explain the applicability of the expressions derived. (Xu)... 

We have utilized a chemical model in this investigation to interpret the equilibrium behavior of iron in acid mine waters. A successful correlation between calculated and measured Eh values has been found, using WATEQ2, the computerized ion association model. This correlation supports the basic assumption of homogeneous solution equilibrium in these waters and simultaneously corroborates both the validity of the aqueous model and the quantitative interpretation of Eh measurements in these waters. This interpretation makes it possible to calculate the distribution of iron... 

The computerized aqueous chemical model of Truesdell and Jones (, 3), WATEQ, has been greatly revised and expanded to include consideration of ion association and solubility equilibria for several trace metals, Ag, As, Cd, Cu, Mn, Ni, Pb and Zn, solubility equilibria for various metastable and(or) sparingly soluble equilibrium solids, calculation of propagated standard deviation, calculation of redox potential from various couples, polysulfides, and a mass balance section for sulfide solutes. Revisions include expansion and revision of the redox, sulfate, iron, boron, and fluoride solute sections, changes in the possible operations with Fe (II, III, and II + HI), and updating the model s thermodynamic data base using critically evaluated values (81, 50, 58) and new compilations (51, 26 R. M. Siebert and... 

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. 

Models are applied to a system, or a portion of the observable universe separated by well-defined boundaries for the purpose of investigation. A chemical model is a theoretical construct that permits the calculation of chemical properties and processes, such as the thermodynamic, kinetic, or quantum mechanical properties of a system. A geochemical model is a chemical model developed for geologic systems. Geochemical models often incorporate chemical models such as ion association and aqueous speciation together with mineralogical data and assumptions about mass transfer to study water-rock interactions. 

The term speciation is used to describe the reactions that take place when an electrolyte is dissolved in water. Water dissociates, sour gases hydrolyze, some ions dissociate, and other ions associate until thermodynamic equilibrium is attained. The liquid phase of the ternary H2O-NH3-CO2 system contains at least the following nine species HjO, NH3(aq), COjiaq), H", OH, NH4, HCOj, COj , and NHjCOO. (aq) indicates that the species is in aqueous solution to avoid ambiguity. In order to adequately model this system, interaction parameters for the interaction between each pair of species need to be determined thus, speciation calculations are performed simultaneously with the parameter estimation, and the calculated amount of each species is compared with experimental data. Some models also require ternary parameters and consequently an additional amount of data to determine these parameters. 

There is considerable discussion in the literature regarding the adsorption mechanism of ions from aqueous solutions onto RPLC stationary phases [87-90]. It has been shown that, under certain conditions, organic ions are adsorbed as ion pairs [87,89,91], and that, under other conditions, they may be adsorbed as separate ions. In this case, the model derived by StMUberg [92] may be useful. In his theory of the retention mechanism in ion-pair chromatography, StMilberg focused on the derivation of the isotherm of the amphiphilic compoimd, that is, the counter-ion used in this technique to adjust the retention factors of the sample components and their separation factors e.g., the cation tetrabutulammonium). The counter-ion (Br, Cl , H2PO4 ) may not be strongly associated with the cation in a mobile phase that is a mere aqueous buffer. Other cations, rmder other experimental conditions may adsorb as true ion pairs, in which case the isotherm behavior is quite different. 

Parkhurst, D. L. 1990. Ion-association models and mean activity coefficients of various salts. In Chemical modeling of aqueous systems fl, ed D. C. Melchior and R. L. Bassett, Am. Chem. Soc. Symp. Ser. 416, pp. 30-43. Washington DC Am. Chem. Soc. 

Ion-Association and lon-Hvdration. Aqueous solutions of electrolytes have been chemically described using a variety of theories. The original theoretical approach used by geochemists to model aqueous systems was based on the concept of ion-pairing or ion-association. The ion association approach as described by Carrels and Thompson (1) accurately depicted the speciation of seawater and later many other aqueous solutions. This approach was subsequently found to be inadequate for defining the chemistry of more complex and more concentrated aqueous solutions or those solutions near the critical point of water. This deficiency led to the use of other theoretical approaches to describe these systems, such as the ion-interaction, mean salt, and ion-hydration theories. 

The ion-association concept relies on the use of Debye-Huckel based activity coefficients to calculate aqueous activities and is one that is employed most frequently in the models used today. A primary assumption of this approach is the use of the Macinnes convention such that for an aqueous solution containing equimolal concentrations of and Cl, their activities and hence activity coefficients are equivalent. This approach and convention were reexamined by Parkhurst in this volume, who explored the issue of mean salt based activity coefficients and the apparent... 

Table II. Association reaction, stability constant, ion-activity-coefficient equation, and ion-activity-coefficient parameters for each aqueous species for the WATEQ, amended WATEQ, and fit aqueous models...

The derived model reproduced the experimental mean activity coefficients for a fixed set of salts to concentrations of about 2 molal. Thus, it is possible to construct an ion-association model that is consistent with the experimental data. However, the fitting process for the derived model could not determine uniquely all of the parameters of the model. Alternative choices for the complexes included in the model and for the individual-ion, activity-coefficient parameters could fit the experimental data equally well. Further work is needed to incorporate other physical evidence for the existence of aqueous complexes into the fitting process to insure that the ion-association model provides an accurate physical description of aqueous solutions in addition to reproducing experimental mean activity coefficients. 

A revised, updated suinmary of equilibrium constants and reaction enthalpies for aqueous ion association reactions and mineral solubilities has been compiled from the literature for common equilibria occurring in natural waters at 0-100 C and 1 bar pressure. The species have been limited to those containing the elements Na, K, Li, Ca, Mg, Ba, Sr, Ra, Fe(II/III), Al, Mn(II,III,IV), Si, C, Cl, S(VI) and F. The necessary criteria for obtaining reliable and consistent thermodynamic data for water chemistry modeling is outlined and limitations on the application of equilibrium computations is described. An important limitation is that minerals that do not show reversible solubility behavior should not be assumed to attain chemical equilibrium in natural aquatic systems. 

Hie parameters ois, oos and at, reflect the disposition of ions in the soil solution after they have become incorporated into the interfacial region. Therefore, these surface charge densities represent the net charging effects of the surface speciation of the ions. By analogy with the use of speciation models (ion-association models) to estimate the distribution of ionic charge in aqueous phases like soil. solutions, surface speciation models (surface... 

Papelis, G., Hayes, K.F. and Ledde, J.O. (1988) Hydraql A Program for the Computation of Chemical EquOibrimn Composition of Aqueous Batch System Including Surface Complexation Modeling of Ion Association at the Oxide/Solution Interface. Technical Report No. 306. Stanford University, Stanford. 

Data from these models for different types of electrolytes in dilute aqueous solutions have been presented in the literature [25, 26], From those data we conclude that for symmetrical uni-univalent, both theories (Onsager and Pikal) give similar results, and they are consistent with experimental ones. In fact, if Pikal s theory is valid, AM must be the major term all other terms are much smaller and they partially cancel each other. Concerning symmetrical but polyvalent electrolytes [25, 26], we can well see that PikaTs theory is a better approximation than the Onsager-Fuoss . The ion association, taken into account in this model [27], can justify this behavior. 

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