Pitzer Ion-interaction Approach Research Articles

A process-based geochemical framework for carbonate sediments during marine diagenesis

A significant proportion of marine calcium carbonate sediments are comprised of metastable minerals that are susceptible to diagenetic alterations during burial. These reactions can reset the geochemical signature of sediments and pore fluids and influence elemental cycling in the ocean. However, the timing and mechanisms by which these reactions take place are poorly constrained. This study uses cores drilled on the slope of the Great Bahama Bank to provide quantitative constraints on important diagenetic reactions; namely respiration-driven dissolution, authigenic carbonate mineral formation, and conversion of aragonite to low Mg calcite (LMC). We perform detailed mineralogical characterization using newly acquired, high resolution X-ray diffraction (XRD) data and over 1000 reanalyzed XRD scans, characterize sediments texturally and elementally using electron microprobe data, calculate pore fluid saturation state with respect to aragonite using a Pitzer ion interaction approach, and use pore fluid chemistry and experimental distribution coefficients to predict authigenic carbonate compositions. These data suggest that aerobic organic matter oxidation, enabled by the advection of oxygenated seawater throughout the upper ∼ 30 m interval of sediment, causes undersaturation and thus dissolution of biogenic high Mg calcite (HMC) and aragonite. Deeper, anaerobic organic matter oxidation takes over and causes supersaturation, promoting authigenic precipitation in the form of HMC, which in turn decreases pore fluid Mg/Ca and promotes aragonite conversion to LMC. One novel aspect of this study is the identification of three types of calcites using the newly acquired XRD and electron microprobe data. Based on their unique crystallographic characteristics and chemical compositions, these types of calcites are interpreted to represent pelagic biogenic LMC, bank-derived biogenic HMC, and authigenic HMC precipitated from pore fluids. Notably, the composition of the authigenic calcite matches that predicted to precipitate from pore fluids using an empirical Mg partition coefficient in calcite. Calcites that form authigenically and from aragonite via replacement are suggested to recrystallize with burial as evidenced by the decrease in Mg content and micro-strain. This process-based geochemical framework assigns diagenetic processes to a specific depth window within the sediment column and paves the way for a mechanistic understanding of carbonate diagenesis, one that is rooted in thermodynamic and kinetic bases.

Solubility of NaCl under anisotropic stress state.

Salt solubility is generally determined under isotropic stress conditions. Yet, in the context of salt weathering of porous media, mechanical constraints on the in-pore growth of salt crystals are likely to be orientation-dependent, resulting in an anisotropic stress state on the crystal. In this paper, we determine by molecular simulation the solubility of NaCl in water when the crystal is subjected to anisotropic stress. Such anisotropy causes the chemical potential of the crystal to be orientation-dependent, and proper thermodynamic formulation requires describing the chemical potential as a tensor. The solute and crystal chemical potentials are computed from free energy calculations using Hamiltonian thermodynamic integration, and the usual condition of solubility is reformulated to account for the tensorial nature of the crystal chemical potential. We investigate in detail how the uniaxial compression of the crystal affects its solubility. The molecular simulation results led to revisiting the Correns law under anisotropic stress. Regarding the solute, the non-ideal behavior of the liquid phase is captured using Pitzer's ion interaction approach up to high concentrations of interest for in-pore crystallization and beyond the concentrations addressed in the existing literature. Regarding NaCl crystals, the validity of the generalized Gibbs-Duhem equation for a tensorial chemical potential is carefully verified, and it is found that crystallization progresses almost orthogonally to the crystal surface even under high shear stresses. Comparing uniaxial and isotropic compression highlights the major differences in solubility caused by stress anisotropy, and the revisited Correns law offers an appropriate framework to capture this phenomenon.

High-temperature and high-pressure thermodynamic properties of aqueous zinc sulfate solutions

A new method has been proposed to estimate the osmotic and activity coefficients of aqueous electrolyte solutions under non-ambient conditions on the basis of the Pitzer ion-interaction approach using the volumetric data. Following this method, a compact set of Pitzer ion-interaction parameters, valid within the temperature range 293.15 - 373.15 K, and pressure range 0.1 - 10 MPa have been obtained for aqueous ZnSO4 solutions. These parameters helped evaluate the osmotic and activity coefficients of this system to 3.0 mol∙kg−1. The pressure dependences of osmotic and activity coefficients have also been estimated using the equations derived by Rogers and Pitzer (1982). The results obtained by the method proposed in this research agree very well with those calculated using Rogers and Pitzer approach. The advantage of the method proposed here is that it directly provides a compact set of Pitzer ion-interaction parameters required for describing the osmotic and activity coefficients, in contrast to the other method. This study also provided important insight into the ion-association behavior of aqueous ZnSO4 solution with respect to temperature and pressure. Further, the apparent molar enthalpies have been estimated using appropriate temperature derivatives of the Pitzer ion-interaction parameters obtained in this study.

Thermodynamic model for CoSO4(aq) and the related solid hydrates in the temperature range from 270 to 374 K and at atmospheric pressure

Available literature on the thermodynamic properties of binary CoSO4 – H2O system has been reviewed and used to derive a model for calculating the solution properties and phase equilibria in a thermodynamically consistent manner. The solution model is based on the Pitzer ion interaction approach and, with 10 adjustable parameters, is able reproduce the available literature data with good accuracy from 270 to 374 K. The length and exact form of temperature dependence of the model was optimised using the ”structural optimisation” scheme. Properties of the solid hydrates have been included in the model for calculation of solubilities. The model has been validated by successfully predicting metastable solubilities and solid–liquid–vapor equilibrium pressures.

Correlation of the Volumetric Properties of Uni-Univalent Electrolytes in Methanol–Water Mixed Solvent Media: A Pitzer Ion-Interaction Approach

Although for a long time considerable attention has been paid to correlating the apparent molar volumes of electrolytes using the Pitzer ion-interaction approach in aqueous solutions, no attempt has, so far, been made to describe the volumetric data of electrolytes in mixed solvent media. This is due to the lack of experimental data on the pressure dependence of the dielectric constant in mixed solvent media. These data are essential to obtain the Debye–Huckel limiting law slopes for volumes that, in turn, are required to analyze the apparent molar volume vs. molality data of electrolytes in the light of the Pitzer ion-interaction approach. Here, we develop a convenient method which helped correlate the apparent molar volumes of electrolytes and estimate the Pitzer ion-interaction parameters for volume along with the Debye–Huckel limiting law slope for volumes. In particular, we have applied this approach to the literature apparent molar volume data of a number of uni-univalent electrolytes (viz., lithium chloride, sodium chloride, potassium chloride, sodium bromide, potassium bromide, sodium iodide, and potassium iodide) in methanol–water mixed solvent media at different temperatures. The parameters (namely, the apparent molar volume of the electrolyte at infinite dilution, $$V_{{\phi {\text{,MX}}}}^{\infty }$$ , the second virial coefficient $$B_{{{\text{MX}}}}^{V}$$ , and the third virial coefficient, $$C_{{{\text{MX}}}}^{V}$$ ) obtained here satisfactorily describe the molality dependence of apparent molar volumes of the investigated electrolyte solutions. The present correlation indicates that the electrolytes exist essentially as free ions in methanol–water mixed solvent media in conformity with what inferred earlier from conductivity measurements.

Influence of High Chloride Concentration on pH Control in Hydroxide Precipitation of Heavy Metals

Removal of zinc and cadmium from highly saline solutions by hydroxide precipitation is discussed. Experimental solubilities of zinc and cadmium in highly saline solutions were compared to modeled results obtained using Pitzer’s approach. An amphoteric character of zinc and cadmium and an influence of chloride ion on the concentration of dissolved metals were investigated. In order to avoid errors linked to pH measurements in concentrated aqueous solutions, the method of calibration of glass pH electrodes was developed and evaluated. The method uses easily prepared buffers whose pHs were determined with the Pitzer ion-interaction approach. The presented investigations address two issues of high significance in industrial wastewater treatment, namely: precise pH measurements and rigorous modeling of highly saline wastewaters. The results can be implemented in the treatment of hydrometallurgical wastewaters such as zinc refinery wastewater. Additionally, an implementation of the presented investigations is not limited to wastewater treatment but can easily be extended to other high-chloride metallurgical processes wherein the pH measurements in highly saline streams are required.Graphical

Direct measurement of the boron isotope fractionation factor: Reducing the uncertainty in reconstructing ocean paleo-pH

The boron isotopic composition of calcium carbonate skeletons is a promising proxy method for reconstructing paleo-ocean pH and atmospheric CO2 from the geological record. Although the boron isotope methodology has been used extensively over the past two decades to determine ancient ocean-pH, the actual value of the boron isotope fractionation factor (εB) between the two main dissolved boron species, 11B(OH)3 and 10B(OH)−4, has remained uncertain. Initially, εB values were theoretically computed from vibrational frequencies of boron species, resulting in a value of ∼19‰. Later, spectrophotometric pH measurements on artificial seawater suggested a higher value of ∼27‰. A few independent theoretical models also pointed to a higher εB value. Here we provide, for the first time, an independent empirical fractionation factor (εB=26.0±1.0‰;25 °C), determined by direct measurements of B(OH)3 in seawater and other solutions. Boric acid was isolated by preferential passage through a reverse osmosis membrane under controlled pH conditions. We further demonstrate that applying the Pitzer ion-interaction approach, combined with ion-pairing calculations, results in a more accurate determination of species distribution in aquatic solutions of different chemical composition, relative to the traditional two-species boron-system approach. We show that using the revised approach reduces both the error in simulating ancient atmospheric CO2 (by up to 21%) and the overall uncertainty of applying boron isotopes for paleo-pH reconstruction. Combined, this revised methodology lays the foundation for a more accurate determination of ocean paleo-pH through time.

Accurate and self-consistent procedure for determining pH in seawater desalination brines and its manifestation in reverse osmosis modeling

Measuring and modeling pH in concentrated aqueous solutions in an accurate and consistent manner is of paramount importance to many R&D and industrial applications, including RO desalination. Nevertheless, unified definitions and standard procedures have yet to be developed for solutions with ionic strength higher than ∼0.7 M, while implementation of conventional pH determination approaches may lead to significant errors. In this work a systematic yet simple methodology for measuring pH in concentrated solutions (dominated by Na+/Cl−) was developed and evaluated, with the aim of achieving consistency with the Pitzer ion-interaction approach. Results indicate that the addition of 0.75 M of NaCl to NIST buffers, followed by assigning a new standard pH (calculated based on the Pitzer approach), enabled reducing measured errors to below 0.03 pH units in seawater RO brines (ionic strength up to 2 M). To facilitate its use, the method was developed to be both conceptually and practically analogous to the conventional pH measurement procedure. The method was used to measure the pH of seawater RO retentates obtained at varying recovery ratios. The results matched better the pH values predicted by an accurate RO transport model. Calibrating the model by the measured pH values enabled better boron transport prediction. A Donnan-induced phenomenon, affecting pH in both retentate and permeate streams, was identified and quantified.

Mass-based hygroscopicity parameter interaction model and measurement of atmospheric aerosol water uptake

Abstract. In this study we derive and apply a mass-based hygroscopicity parameter interaction model for efficient description of concentration-dependent water uptake by atmospheric aerosol particles with complex chemical composition. The model approach builds on the single hygroscopicity parameter model of Petters and Kreidenweis (2007). We introduce an observable mass-based hygroscopicity parameter κm which can be deconvoluted into a dilute hygroscopicity parameter (κm0) and additional self- and cross-interaction parameters describing non-ideal solution behavior and concentration dependencies of single- and multi-component systems. For reference aerosol samples of sodium chloride and ammonium sulfate, the κm-interaction model (KIM) captures the experimentally observed concentration and humidity dependence of the hygroscopicity parameter and is in good agreement with an accurate reference model based on the Pitzer ion-interaction approach (Aerosol Inorganic Model, AIM). Experimental results for pure organic particles (malonic acid, levoglucosan) and for mixed organic-inorganic particles (malonic acid – ammonium sulfate) are also well reproduced by KIM, taking into account apparent or equilibrium solubilities for stepwise or gradual deliquescence and efflorescence transitions. The mixed organic-inorganic particles as well as atmospheric aerosol samples exhibit three distinctly different regimes of hygroscopicity: (I) a quasi-eutonic deliquescence & efflorescence regime at low-humidity where substances are just partly dissolved and exist also in a non-dissolved phase, (II) a gradual deliquescence & efflorescence regime at intermediate humidity where different solutes undergo gradual dissolution or solidification in the aqueous phase; and (III) a dilute regime at high humidity where the solutes are fully dissolved approaching their dilute hygroscopicity. For atmospheric aerosol samples collected from boreal rural air and from pristine tropical rainforest air (secondary organic aerosol) we present first mass-based measurements of water uptake over a wide range of relative humidity (1–99.4%) obtained with a new filter-based differential hygroscopicity analyzer (FDHA) technique. For these samples the concentration dependence of κm can be described by a simple KIM model equation based on observable mass growth factors and a total of only six fit parameters summarizing the combined effects of the dilute hygroscopicity parameters, self- and cross-interaction parameters, and solubilities of all involved chemical components. One of the fit parameters represents κm0 and can be used to predict critical dry diameters for the activation of cloud condensation nuclei (CCN) as a function of water vapor supersaturation according to Köhler theory. For sodium chloride and ammonium sulfate reference particles as well as for pristine rainforest aerosols consisting mostly of secondary organic matter, we obtained good agreement between the KIM predictions and measurement data of CCN activation. The application of KIM and mass-based measurement techniques shall help to bridge gaps in the current understanding of water uptake by atmospheric aerosols: (1) the gap between hygroscopicity parameters determined by hygroscopic growth measurements under sub-saturated conditions and by CCN activation measurements at water vapor supersaturation, and (2) the gap between the results of simplified single parameter models widely used in atmospheric or climate science and the results of complex multi-parameter ion- and molecule-interaction models frequently used in physical chemistry and solution thermodynamics (e.g., AIM, E-AIM, ADDEM, UNIFAC, AIOMFAC).

Modeling of the Ternary NH4Cl + ROH + Water Electrolyte Systems (with R = Me, Et, 1-Pr, and 2-Pr) by the Pitzer−Simonson−Clegg Approach and Its Modified Forms

Literature data on electrolyte modeling in nonaqueous and in mixed solvent systems are still relatively scarce. In addition, contrary to the currently used Pitzer ion-interaction approach, modeling of the ternary systems containing electrolyte, nonelectrolyte, and water by the more refined Pitzer−Simonson−Clegg (PSC) ion-interaction approach is limited only to the work of three research groups. In this context, we have recently reported the use of Pitzer and Pitzer−Simonson−Clegg (PSC) ion-interaction approaches for modeling the ternary HCl + ROH + water electrolyte systems (with R = Me, Et, 1-Pr, and 2-Pr). The present investigation describes also the results obtained by the application of the simplified PSC, original PSC, and previously reported modified PSC, as well as another proposed modified PSC approach (presented in this work), for modeling the nonideal behavior of the ternary NH4Cl + ROH + water mixture. The calculations were achieved based on the experimental potentiometric data previously obtained in our laboratory. Accordingly, the present calculations were performed for NH4Cl electrolyte molalities ranging from 0.01 up to about 4 mol·kg−1 in several alcohols (ROH) with different percent mass fractions, x = (10, 20, 30, 40, and 50) %, for R = Me, Et, 1-Pr, and up to 30 % for 2-Pr, at (298.15 ± 0.05) K.

Modeling of ammonia speciation in anaerobic digesters

Anaerobic digestion of high-nitrogen wastes such as animal manure can be inhibited by high concentrations of un-ionized ammonia, NH 3 (aq). Understanding the toxicity of NH 3 (aq) to anaerobic digestion requires a method for determining its concentration. Previous work on ammonia toxicity in anaerobic digesters has utilized a simple equilibrium calculation for estimating NH 3 (aq) concentration from total ammonia, temperature, and pH. This approach is not appropriate for concentrated solutions. In this work, a speciation model for major solutes in anaerobic digesters, based on Pitzer's ion-interaction approach, is presented. Model simulations show that the simple equilibrium calculation (without corrections for non-ideal behavior) substantially overestimates NH 3 (aq) concentration for all but dilute digesters. This error in concentration determination increases with total solids content and is estimated to be greater than 40% for a digester fed dairy manure with 5% total solids or swine manure with 3% total solids. However, including an estimate of the activity coefficient for NH 4 + in the simple equilibrium calculation results in much more accurate estimates of NH 3 (aq) concentration. In this case, the estimated error is less than 10% in the absence of struvite precipitation at the highest total solids contents considered.

Chromium(III) Hydroxide Solubility in the Aqueous K+-H+-OH−-CO2-HCO 3 − -CO 3 2− -H2O System: A Thermodynamic Model

Chromium(III)-carbonate reactions are expected to be important in managing high-level radioactive wastes. Extensive studies on the solubility of amorphous Cr(III) hydroxide solid in a wide range of pH (3–13) at two different fixed partial pressures of CO2(g) (0.003 or 0.03 atm.), and as functions of K2CO3 concentrations (0.01 to 5.8 mol⋅kg−1) in the presence of 0.01 mol⋅dm−3 KOH and KHCO3 concentrations (0.001 to 0.826 mol⋅kg−1) at room temperature (22±2 °C) were carried out to obtain reliable thermodynamic data for important Cr(III)-carbonate reactions. A combination of techniques (XRD, XANES, EXAFS, UV-Vis-NIR spectroscopy, thermodynamic analyses of solubility data, and quantum mechanical calculations) was used to characterize the solid and aqueous species. The Pitzer ion-interaction approach was used to interpret the solubility data. Only two aqueous species [Cr(OH)(CO3) 2 2− and Cr(OH)4CO 3 3− ] are required to explain Cr(III)-carbonate reactions in a wide range of pH, CO2(g) partial pressures, and bicarbonate and carbonate concentrations. Calculations based on density functional theory support the existence of these species. The log 10 K° values of reactions involving these species [{Cr(OH)3(am) + 2CO2(g)⇌Cr(OH)(CO3) 2 2− +2H+} and {Cr(OH)3(am) + OH−+CO 3 2− ⇌Cr(OH)4CO 3 3− }] were found to be −(19.07±0.41) and −(4.19±0.19), respectively. No other data on any Cr(III)-carbonato complexes are available for comparisons.

An improved model incorporating Pitzer’s equations for calculation of thermodynamic properties of pore solutions implemented into an efficient program code

Salts in porous building materials are not only considered as a major cause of damage but also strongly affect the hygric and capillary transport properties of such materials. This paper describes a model implemented into an efficient computer code that can be used for predicting the non-ideal behavior of pore solutions of complex composition. The model is based on the Pitzer ion interaction approach. Model parameters are provided and validated for the system Na+–K+–Cl-–NO3-–SO42-–H2O in the temperature range relevant to most buildings, i.e. from the temperature of freezing to 45 °C. This offers a number of potential applications including the incorporation in chemical equilibrium and humidity and moisture transport models.

Thermodynamics of electrolytes in mixed solvent media — Application of the Pitzer ion interaction approach

Although for a long time considerable attention has been paid to the application of the Pitzer ion interaction approach to describe the thermodynamic properties of a variety of aqueous electrolyte solutions, such studies in mixed solvent media are still scarce. The present paper discusses the application of the Pitzer ion interaction approach in the case of electrolyte solutions in mixed solvent media. In particular, a comprehensive equation for the thermodynamic properties of hydrochloric acid in dioxane–water mixtures within the temperature range 273.15 to 323.15 K has been generated in the ion interaction (Pitzer) equation form on the basis of electrochemical cell measurements of the hydrochloric acid available in the literature. It was necessary to set varying values of the exponential coefficients α1 and α2 of the standard Pitzer model in different mixed solvent media to achieve a satisfactory fit. The present model quantitatively reproduces the experimental cell electromotive forces over the entire concentration and temperature range used for the experiments. The Pitzer ion interaction approach is, thus, proved to be a very valuable method for the correlation and prediction of thermodynamic properties of electrolytes in mixed solvent media. The implications of the Pitzer ion interaction parameters (β(0), β(1) β(2), and Cϕ) have also been discussed in terms of interionic forces. The present study also stresses the need for additional emf measurements to help interpolation through the dioxane composition. Key words: Pitzer's equations, Pitzer ion interaction parameter, activity coefficients, emf, hydrochloric acid.

Modeling Alkaline Silicate Solutions at 25 °C

A thermodynamic model is developed to describe silicate behavior in solutions containing high concentrations of both NaOH and NaNO3. Experimental solubility data in such solutions are also presented. The model itself applies Pitzer's ion-interaction approach and involves several aqueous polymeric species. Model predictions compare well with a variety of experimental datasolubilities, NMR results, and pH measurements.

Comprehensive Thermodynamic Model Applicable to Highly Acidic to Basic Conditions for Isosaccharinate Reactions with Ca(II) and Np(IV)

Isosaccharinate (ISA−), a degradation product of cellulose codisposed in low-level nuclear wastes, is expected to be one of the dominant complexing ligands for radionuclides, especially tetravalent actinides. This paper presents a comprehensive thermodynamic model for isosaccharinate reactions with Ca(II) and Np(IV). The model is valid for a wide range of pH values (∼2–14), ISA− concentrations (ranging up to 0.1 m), and ionic strengths (ranging up to 6.54 m), and is based on (1) NMR investigations of HISA(aq) (α-D-isosaccharinic acid) and ISL(aq) [dehydration product of HISA(aq)], and the solubility of Ca(ISA)2(c) as a function of pH and concentrations of Ca and ISA−; (2) NpO2(am) solubility in a wide range of pH values (∼2–14) and total ISA concentrations of 0.0016 and 0.008 m and at fixed pH values of approximately 5 and 12 with total ISA concentrations ranging from 0.0001 to 0.1 m; and (3) solvent extraction of Np-ISA solutions, containing fixed NaClO4 concentrations ranging from 0.103 to 6.54 m and at fixed pC H+ values ranging from 1.5 to 1.9, with dibenzoylmethane. Pitzer's ion-interaction approach was used to interpret the data. The different aqueous species required to explain these data included HISA(aq), ISL(aq), Ca(ISA)+, Np(OH)3(ISA)(aq), Np(OH)3(ISA)2 −, Np(OH)4(ISA)−, and Np(OH)4(ISA)2 2−. The values of equilibrium constants for reactions involving these species and determined from these data provided close agreements between the observed and predicted concentrations in all of the systems investigated in this study and those reported previously.

Estimation of the Solubility Constant of Calcite, Aragonite, and Vaterite at 25�C Based on Primary Data Using the Pitzer Ion Interaction Approach

Experimentally determined values of the solubility constant of anhydrous calcium carbonate species were compiled from primary literature. The data were processed using a least-squares technique and the activity coefficients were calculated using the Pitzer ion interaction model. It was shown that the literature data considered can be divided into two data sets which are internally consistent, but mutually inconsistent. The first data set was consistent with the existence of the CaHCO3 + ion pair, while the second data set was not. It was assumed that the difference between the two data sets might be due to surface charge effects.

An investigation of the volumetric properties of [formula omitted] -alanine and sodium bromide in water at elevated temperatures and pressures

An optically coupled vibrating tube densimeter has been used to measure the relative densities of aqueous solutions ofl-alanine and sodium bromide in the ranges 397⩽T/K⩽ 521 and 10 ⩽p/MPa⩽ 30. For the solutel-alanine, the reported relative densities have been used to calculate apparent molar volumes which, in turn, have been used in the calculation of partial molar volumes at infinite dilution. The latter data are modeled using an equation of state of the type reported by Helgeson, Kirkham, and Flowers. This model is compared to those recently reported by Clarke and Tremaine. The reported model for the temperature and pressure dependence of the apparent molar volume ofl-alanine in water is used to derive expressions for the apparent molar compressibility and expansibility of this system. Calculated data for the latter property are compared to those available in the literature. In addition, the partial molar volume at infinite dilution for the alanine side chain is calculated by combining the volumetric results reported in this manuscript for aqueousl-alanine solutions with those previously reported for aqueous solutions of glycine. Volumetric results for aqueous sodium bromide solutions have been compared to those calculated from a program by Archer that utilizes the Pitzer Ion Interaction approach.

Thermodynamics of the HBr+NiBr2+H2O system from 5°C to 55°C

Abstract The emf of the following cell (A) without liquid junction was used to investigate the HBr+NiBr2+H2O mixed electrolyte system. Pt , H 2 ( g ,1 atm )| HBr (m A ), NiBr 2 (m B )| AgBr , Ag Measurements of the emf were performed for solutions at constant total ionic strengths of 0.05, 0.1, 0.25, 0.5, 1.0, 1.5 and 2.0 mol kg−1 at temperatures ranging from 5°C to 55°C, except for I=2.0 mol kg−1, where measurements were only made at 25°C. The mean activity coefficients of HBr in the mixtures were calculated using the Nernst equation. The thermodynamic properties of unsymmetrical mixtures are interpreted in terms of the simpler Harned's rule, as well as the comprehensive Pitzer's ion-interaction approach including higher order electrostatic effects for electrolyte mixtures. The Harned interaction coefficients αAB and βAB were determined from the data on the HBr+NiBr2 mixture. Literature osmotic coefficient data at 25°C have been used to determine the pure electrolyte Pitzer parameters (β(0), β(1), and Cφ) for NiBr2. The results were combined with the value of ΘH,Ni=0.069 obtained from the HCl+NiCl2+H2O system to determine ΨH,Ni,Br=0.06 from our emf data at 25°C. The effect of temperature (0–55°C) on the Pitzer parameters (β(0), β(1), and Cφ) for HBr and NiBr2 was determined from the present emf measurements, assuming that the higher order electrical terms (ΘH,Ni and ΨH,Ni,Br) were independent of temperature. They were fitted to a simple polynomial function of temperature (°C): β H , Br (0) =0.2085+8.55×10 −4 (t−25)−1.8×10 −4 (t−25) 2 β H , Br (1) =0.3477+18.0×10 −4 (t−25)+3.9×10 −4 (t−25) 2 C H , Br φ =0.001517−7.10×10 −4 (t−25)+1.05×10 −4 (t−25) 2 and β Ni , Br (0) =0.4451−0.0307(t−25)−3.1×10 −4 (t−25) 2 β Ni , Br (1) =1.49+0.0855(t−25)−6.2×10 −4 (t−25) 2 C Ni , Br φ =−0.00626+0.029(t−25)+8.45×10 −4 (t−25) 2 The values of the Pitzer parameters for NiBr2 were of the same order of magnitude as found for other bivalent bromides.

Predicting Sulfate-Mineral Solubility in Concentrated Waters

Sulfate minerals participate in a variety of mineral-water reactions with waters containing elevated concentrations of dissolved solids. Reliable prediction of sulfate-mineral solubility in concentrated waters is required for a multitude of geological, hydrogeological, industrial, and meteorological applications. Precipitation of pure sulfate minerals or sulfate-bearing solid solutions can limit concentrations of dissolved metals, radionuclides, and other cations at waste-disposal sites, in marine and other naturally occurring saline waters, in industrial waters, and in smog. Formation of these solids can control the major-ion geochemistry of water and, in turn, influence the behavior of trace constituents. One of the most widely used and robust approaches for predicting mineral solubility in concentrated waters is the Pitzer ion-interaction approach as first introduced by Pitzer (1973), as applied to geological systems by Harvie and Weare (1980) and Harvie et al. (1980), and as summarized by Weare (1987). Clegg and Whitfield (1991) and Pitzer (1979a,b; 1991) provided further comprehensive discussions on the developments and application of the ion-interaction approach to predict mineral solubility in natural waters. This chapter focuses on the application of the ion-interaction approach, or its variations, for predicting sulfate-mineral solubility in a variety of geochemical settings. Included are a summary of the Pitzer approach as applied to predictions of mineral solubility, a summary of the available constants for modeling sulfate-mineral solubility, and examples of applications for natural and contaminated sites. The discussion focuses on recent additions to earlier models developed for application to near-Earth-surface temperature and pressure conditions. Applications outside this temperature and pressure range are described only briefly. ### Compositions of concentrated waters The majority of concentrated waters in nature form as a result of solar evaporation of marine and continentally-derived waters. The evaporation of seawater leads to predictable sequences of mineral formation, including precipitation of several common sulfate minerals (e.g. gypsum, …