The quality of waters is of significant importance, as they are vital for the living organisms. Thus, they should be under permanent monitoring control. Usually, this control includes nutrients and trace metals as major inorganic pollutants [1, 2].
The chemical pollutants of natural water resources differ by type, species, concentration, occurrence, mobility, biological activity and toxicity. The transition metals are of key interest for the biochemical processes, due to their specific properties and significance as pollutants.
The natural or anthropogenic changes in the environment that have occurred in the last 30 years have affected the distributions of pollutant species and thus their toxicity and bioavailability. The increased scientific interest in speciation research has improved our knowledge of chemical species mobility, activity and toxicity but monitoring studies only consider physico-chemical parameters and the total contents of several typical pollutants [3, 4]. The reason for this is the lack of fast, inexpensive, accurate and widely applicable analytical methods [5, 6].
Thus, thermodynamic modeling can be a useful tool for non-expensive and effective evaluation of inorganic chemical species in natural waters [2, 7, 8]. Two basic thermodynamic methods, differing in activity coefficient calculation of the species, have been developed – the ion association model [9, 10] and the ion interaction model [11, 12]. The ion association model is only valid for solutions with ionic strength below 0.1 mol.kg–1. It uses the thermodynamic formation constants of the different complexes as a primary database. This method is employed for modeling the chemical species of microelements in urban  or industrially [7, 13] polluted natural waters. The ion interaction model is not limited to low ionic strength waters; its equations involve, however, a large number of semi-empirical parameters. It is mainly used for modeling the equilibriums in water saline systems; data for modeling chemical species of microcomponents are limited [12, 13].
The aim of this work is to demonstrate the possibilities of the combined ion association/ion interaction model to provide an adequate mathematical description of the complex character of the ionic interactions, and hence, to permit a precise determination of the inorganic chemical species of the micro elements in natural waters of varying ionic strength and pollution type. As the precision of the results depends on the database used, the latter was adequately extended for the case (pit2010.dat). The comparison of the results of the ion association model with those of the combined ion association/ion interaction model is illustrated in case studies of surface fresh, saline and hyper-saline waters with different type of pollution (urban, agricultural and industrial) from different regions of Bulgaria. The calculated results are evaluated by theoretical considerations on the basis of Pearson concept for “hard” and “weak” Lewis acids and bases.
The surface waters are considered as a multicomponent electrolyte system whose composition varies in a broad range, depending on the geological and biochemical features of the region, on the natural occurrence of physical, chemical and biological processes, as well as on the urban, agricultural and industrial activities taking place. All these processes affect the composition and the quality of the waters. Depending on their nature and concentration, the macro, micro and trace ions interact with one another, as well as with the water molecules. The chemical behavior of the metals and their chemical species is defined by the redox potential, pH, cationic and anionic organic and inorganic composition [e.g., OH–, CO32–, HCO3–, SO42–, Cl–, Hn PO4n–3 (n=0, 1, 2), NO2–, NO3– ions], by the ability of the metals to preferentially coordinate with some of these anions, as well as by the stability of the corresponding species. Our studies deal with inorganic chemical species only.
Methods are developed for modeling the chemical speciation in natural waters, based on chemical thermodynamics under the assumption that only the chemical processes taking place are in equilibrium, i.e., there is a minimum of free energy in the system. Two approaches to determine the activity coefficients, or modeling the chemical species, are developed: the ion associationmodel and the ion interaction model. They are based on the physico-chemical description of the interactions between the ions, as well as between the ions and the molecules of the solvent.
Ion association model
The ion association model [9, 10] deals with the weak interactions between major, between minor and between major and minor ions of different charge, leading to ion pair formation. The activity coefficients of the free ions and of the ion couples depend on the ionic strength only. The model is based on the Debye-Hückel theory and the formation of each complex is defined by an adequate chemical equation and a corresponding equilibrium formation constant. The model is easily applicable, because the only primary data needed are the thermodynamic formation constants of the different complexes. The equations are valid for solutions of low ionic strength: I< 0.1 mol.kg–1. Despite this limitation, the method is applied for both urban  and industrially [7, 14] polluted natural waters, even for marine waters (I ∼ 0.7 mol.kg–1) , but the results are disputable in the latter case.
In our studies, this method was applied using the computer software PHREEQCI, version 2.14  and the sst2008.dat database elaborated on the basis of minteq.v4.dat database. The latter was adequately extended . It includes the thermodynamic formation constants of additional 417 inorganic complexes (phosphates, nitrites, hydroxides, carbonates, sulfates, nitrates and chlorides) and 59 organic complexes that may exist in polluted natural waters and takes into account of the theoretical considerations regarding the highly coordinated sulfate complexes of Zn and Cd, as noted in the text below. All thermodynamic formation constants are at 25 oC because of lack of data for their temperature dependence.
Ion interaction model
The ion interaction model takes into account the interactions of all chemical species present in the solution, irrespectively of the sign of their charge and concentration. The activity coefficients of the solution components (single or complex; charged or neutral) depend not only on the ionic strength, but on the concentration of each component and on the so called interaction coefficients.
During the last decades, the Pitzer equations  have often been used for the mathematical description of the ion interaction model. The Pitzer theory examines two types of interactions between the components of the solution: (i) Coulomb interaction between remote ions of different charge, which depends on the ionic charge, ionic strength and dielectric permittivity of the solvent (water); and (ii) non-specific short-range interaction between ion pairs and triads. The model uses the main principles of chemical thermodynamics, developed on the basis of statistical mechanics, and reflects the interactions between ions of equal or different charge in the dielectric medium of the solvent. It is assumed that in solution the electrolytes are completely dissociated in ions which interact with one another. The so called binary (β(0), β(1), β(2),Cϕ) and ternary (Θij, Ψijk) Pitzer parameters are introduced. The binary parameters (β(0), β(1), β(2),Cϕϕ) are calculated from isopiestic data for two-component salt-water systems and are characteristic for the ionic interactions between them. The ternary parameters (Θij, Ψijk) are characteristic for the interactions between ionic pairs and triads in ternary electrolyte solutions. They can be calculated from isopiestic or solubility data for the three-component systems.
The Pitzer model is mainly used for studying the behavior of the major solution components, the equilibria between multi-component solutions and solid phases and the solubility of atmospheric gases in natural waters. The model provides an adequate description of the chemical behavior of Na+, K+, Ca2+, Mg2+, Cl–, CO32–, SO42–, which are the major ions in natural waters. The main drawbacks of this model are the limited available data for the parameters used by the model and the complexity of the equations upon increasing the number of chemical species. The model is not concentration-limited. It also can employ the computer software PHREEQCI, version 2.14 and the pitzer.dat database [13, 16].
Combined ion association/ion interaction method
We propose an integration between the ion association method (based on the extended Debye-Hückel theory ) and the ion interaction method (based on the Pitzer theory ) in a combined thermodynamic method of ion association/ion interaction, for the calculation of the inorganic chemical species of the micro elements in all types of natural waters – fresh, saline and hyper-saline. The proposed model also uses the computer software PHREEQCI, version 2.14 . As the thermodynamic pitzer.dat database included in the program PHREEQCI contains thermodynamic data (binary and ternary Pitzer parameters and stability constants) only for the aqueous species H+, Na+, K+, Ca2+, Mg2+, MgOH+, Fe2+, Mn2+, Ba2+, Sr2+, Cl–, CO32–, HCO3–, CO2, SO42–, HSO4–, B(OH)3, and B(OH)4, it is suitable for an adequate description of the chemical behavior of these major ions only and not for the micro ions in natural waters. That is why we created and used in our model a new extended database pit2010.dat that includes the sst2008.dat database  and the existing database pitzer.dat enriched by us with the Pitzer parameters for the ions Fe3+, Mn2+, Cu2+, Zn2+, Cd2+, Pb2+ and the major anions Cl–, SO42– [19–27]. The highly coordinated sulfate complexes M(SO4)34– and M(SO4)46– of Zn and Cd are of low probability and are therefore excluded from our database . Thus, along with the main components behavior described by the ion interaction model, our combined model also describes the behavior of the trace metal ions Fe2+, Mn2+, Cu2+, Zn2+, Cd2+ and Pb2+ in the studied waters even at very low concentrations (10–3 – 10–10 mol.kg). This description is more accurate in comparison with the ion association model, because it takes into account the behavior of the trace metals not only through their thermodynamic constants, but also through the interactions of the transition metals with the major anions Cl– and SO42–, as accounted for by the M-X binary Pitzer parameters.
All thermodynamic calculations are based on the following approximations: (i) only inorganic chemical species are considered; (ii) the system is in thermodynamic equilibrium only for the chemical processes of complex formation in the system under consideration; (iii) the system under treatment is highly oxidized and the redox processes (Fe2+/Fe3+; Cu+/Cu2+; Mn2+/Mn3+/Mn4+/Mn6+/Mn7+) are predicted using the couple O0/O2– [15, 28–30] (iv) only Fe3+ and Cu2+ ions are accounted for, because the concentrations of Fe2+ and Cu+ in waters saturated with oxygen can be neglected; (v) as the accuracy of thermodynamic modeling depends on the completeness of the thermodynamic database used, our combined and extended database was involved in this study; (vi) as the database contains limited temperature data the calculations are made for 25 oC.
Surface waters of two different regions of Bulgaria were the subject of our previous monitoring and thermodynamic modeling studies [7, 8]. The studied areas were chosen so as to include waters with different type (urban and mining) and level of pollution (reference stations registering the background in the examined region, the pollution sources and the affected areas), as well as surface waters of different ionic strength (fresh, saline and hyper-saline waters). In the present work, these waters are modeled according to the two thermodynamic methods – the ion association and the combined ion association/ion interaction method. The obtained results for the distribution of the inorganic chemical species of the micro elements are compared.
Mining polluted waters
In our earlier studies [7, 31] the chemical status of the waters in the Maresh and Luda Yana rivers (region of Assarel-Medet mine and Panagyurishte town, Bulgaria) was determined. The ion association model was applied using the computer software PHREEQCI, version 2.11 and the sst2008.dat database. All studied waters in this region were fresh. High acidities, high levels of SO42–, and complex sulfate species of Cu, Mg, Al and Fe were recorded at the expense of free macro and micro Me2+ ions. Their ionic strength varied from 0.003 to 0.112 and pH varied from 3.1 to 8.8. These variations led to calculations of the species of the trace metals Fe, Mn, Zn, Cd, Cu and Pb and their distribution using both the ion association (A) and the combined (B) method. The results are compared in Fig. 1. In the first case the database sst2008.dat and in the second case the database pit2010.dat was used. It was found that for waters of low ionic strength (0.003–0.03), equal or very close results are obtained (difference of 2–4%). For waters of ionic strength of 0.112, however, different results are obtained, the differences being most pronounced for Zn, Cd and Pb (up to 20%). As in the ion association method the activity coefficients are proportional to the ionic strength, the high concentration of SO42– ions predetermine the domination of the Me(SO4)22- complexes. The complex character of the interaction between the ions, pre-set in the combined method, is responsible for the calculated domination of free Me2– ions. The pH value, which varies from slightly alkaline to acidic in the water of the polluted stations, has a strong effect on the chemical speciation of the studied metals.
We explain the metal-ligand interaction by the “hardness-softness” factor and the crystal field stabilization energy (CFSE). The Pearson concept of “hard” and “soft” Lewis acids and bases , as well as the Klopman scale of hardness and softness  determine the type of ligands which form complexes in the examined water systems. According to the Pearson concept, Mn2+ (3d5, high spin), Zn2+ (3d10) and Cd2+ (5s24d10), being “soft” acids with CFSE = 0, are present in natural waters mainly as free Me2+ ions. Cu2+ (3d9) and Mn2+ (3d5, low spin), as “soft” acids with CFSE ≠ 0, preferentially coordinate with the softer CO32- ions and exist in natural waters mainly as MeCO3o, followed by free Me2+ ions and MeOH+. In the studied natural water systems Pb2+ (6s24f145d106p0) displays a behavior analogous to that of Cu2+ (3d9) probably because of the too close and partially overlapping energetic levels of its 4f, 5d and 6p orbitals that could result in CFSE ≠ 0. Fe3+, being a “hard” acid, exists in all studied waters as the hydroxy species Fe(OH)n3-n.
Urban polluted fresh, saline and hyper-saline waters
Detailed information on the sampling stations, chemical analysis and results of the studies of the fresh, saline and hyper-saline waters from the Bourgas bay, the Atanassovsko lake, the Ropotamo and Aheloi rivers, Bulgaria, can be found elsewhere . In the present work, these waters are modeled by the ion association model (A) and the combined ion association/ion interaction model (B) (Fig. 2), using the computer software and the both extended databases mentioned above.
The comparison of the results calculated according to the two models points to an insignificant difference (1–2%) for waters of low ionic strength (I = 0.01). Upon increasing the ionic strength, the differences also increase, being smallest for Fe and Cu, considerable for Mn, Zn and Cd and most significant for Pb (up to 20%). The combined method reports an increased content of free Me2+ ions at the expense of reducing or eliminating the highly coordinated species MeCln2–n and Me(SO4)22– (Me = Zn, Cd, Pb; n = 3,4), which dominate according to the ion association model.
Sea brine waters display high concentrations of SO42– and Cl– ions, which are “softer” bases than H2 O, OH– and PO43– ions. Therefore, SO42– and Cl– ions will compete with each other for coordination with the “soft” Lewis acids Zn2+, Cd2+ and Pb2+. Since Cl– ions are much “softer” than SO42– ions are, mainly chloride complexes of Cd2+, Pb2+ and Zn2+should be expected to dominate. This prognosis is also supported by the results of Millero and Hawke , who calculated the species Zn2+ and CdCln2–n (n = 1–3) as the dominating species in sea waters using the ion interaction Pitzer approach. Our Raman spectroscopic studies on the ion association in the sea-type system Mg,Na/Cl,SO4//H2 O  also showed that highly coordinated sulfate species are not typical for the “hard” Mg and Na ions even in saturated with respect to MgSO4 and to Na2 SO4 solutions with low water activity. The number of solvent-separated ionic pairs (Mg-H2 O-SO4), direct ionic pairs (Mg-OSO32–) and direct ionic pairs with more strongly deformed SO4 groups was found to increase with the decrease in water activity. On the basis of theoretical considerations it can be stated that no highly coordinated sulfate species are expected in the studied waters and the combined method permits more precise calculation of the distribution of the inorganic chemical species of the elements.
The complex character of the ionic interactions is more precisely described by the mathematical equations of the combined thermodynamic method of ion association/ion interaction, as compared with the ion association method which mainly takes into account the dependence of the activity coefficients on the ionic strength. Hence, the combined ion association/ion interaction method is recommended for speciation calculations of highly variable ionic strength waters.
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