Pitzer Ion-interaction Parameters Research Articles

A quantitative description of barite thermodynamics, nucleation and growth for reactive transport modelling

The regression of available thermodynamic data in the BaSO4–NaCl–H2O system yielded Pitzer ion interaction parameters that accurately describe the activities of aqueous species and mineral solubilities in this system. This thermodynamics description is compared with published Pitzer parameter sets, and combined with a model for the kinetics of barite nucleation and growth, based on classical nucleation theory. Both the thermodynamic and nucleation/growth models have been incorporated into the PHREEQC computer code to facilitate calculation of the extent and consequences of barite formation in natural and engineered systems. Results of geochemical modelling calculations agree adequately with the amount of barite scale thicknesses derived from calliper measurements from an oil well if the effective surface free energy of barite nuclei is assumed to be ∼50 mJ m−2. Better results, however, are achieved using a temperature dependent effective surface free energy. In contrast, calculations performed by ignoring the effects of barite nucleation lead to a substantial overestimation of the amount of scale formed in our modelled systems. The success of our mineral nucleation and growth model to describe scaling in our modelled system suggests this description of precipitation rates can be applied to many other mineral-aqueous fluid systems, in particular where supersaturation is slight and the solids forming have substantial surface free energy.

Thermodynamic properties of the ternary system (KBr + PEG 4000 + water) by potentiometric method at T = (288.2, 298.2, and 308.2) K

The goal of this research is to evaluate the mean ion activity coefficients (γ±) of the mixtures containing KBr + PEG 4000 + H2O (PEG stands for poly(ethylene glycol)) as well as some other thermodynamic quantities including solvent osmotic coefficients (φ), excess Gibbs energies (GE), standard Gibbs energies of transference (ΔGt0), and primary hydration number (nhydr). The experiment was employed by potentiometric measurement using the cell with two ion-selective electrodes (abbreviated as ISE) at (288.2, 298.2, and 308.2) K, and the mass fraction of PEG 4000 ranged from w = (0 to 0.20) with an increment of 0.05. The type of the cell is as follows:K–ISE | KBr (m), PEG 4000 (w), H2O (1-w) | Br–ISE.Nernst's equation was used to combine the Debye-Hückel and Pitzer models with potentiometric values. Pitzer ion interaction parameters (β0, β1, and Cφ) and Debye-Hückel model parameter (a) were evaluated. Moreover, the Bjerrum parameter (q) was calculated.

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.

Measurements of mean activity coefficients and solubility prediction in ternary system KBr-K2SO4-H2O at 308.15 K and 288.15 K

In this work, the mean activity coefficients of KBr in KBr-H2O binary system and KBr-K2SO4-H2O ternary system were determined at 308.15 K and 288.15 K by the cell potential method. The potassium ion selective electrode and bromide ion selective electrode are used to measure the cell potential value of single salt electrolyte solution,and the standard potential value E0 and electrode response slope k of the binary system are obtained. The experimental results showed that ion selective electrodes of used in this work had a good Nernst response. The mean activity coefficients KBr in KBr-K2SO4-H2O system are also determined, the total ionic strength in the mixed solution ranging from (0.0100 to 1.0000) mol·kg−1, and ionic strength fractions yb of K2SO4 with yb=(0.8, 0.6, 0.4, 0.2 and 0.0). Using mean activity coefficients obtained in this work and Pitzer model, the Pitzer mixed ion interaction parameters θBr,SO4 and ψK,Br,SO4are fitted respectively. Furthermore, those osmotic coefficient Φ, water activity aw, excess Gibbs free energy GE were also calculated by Pitzer’s equations. The solubilities of salts in the KBr-K2SO4-H2O system at 308.15 K and 288.15 K are predicted by using Pitzer equations and ion interaction parameters fitted in this work, and phase diagrams of the ternary system are also plotted according to the calculated solubilities. The results show that the ion interaction parameters of Pitzer equations by fitting the activity coefficients can be used for calculation thermodynamic parameters and prediction of phase equilibria.

Determination of activity coefficients and diffusion coefficients of LiClO4 in ethylene carbonate +water mixtures based on potentiometric measurements at T=(298.2, 308.2, and 318.2) K

ABSTRACT We studied the thermodynamic properties of the lithium perchlorate (LiClO4) + ethylene carbonate (EC) +water ternary system by using cell potential measurements. Thermodynamic properties reported were obtained using the electrochemical cell: Li-ISE|LiClO4(m)|ClO4-ISE in a variety of mixed solvent systems containing 0, 10, 20 and 30% mass fractions of ethylene carbonate in water + EC mixtures (wEC/wmixture% = 0, 10, 20 and 30) on the wide range of ionic strength from 0.0090 to 2.4900 mol.kg−1 at T = (298.2, 308.2 and 318.2) K. The obtained results were analysed using Extended Debye-Huckel equation and Pitzer model. The values of Pitzer ion-interaction parameters β(0), β(1) and Cϕ were used to drive the values of thermodynamic properties such as the excess Gibbs free energy, the solvent activity, mean activity coefficients, the osmotic coefficients and diffusion coefficients for this system.

Measurements and Calculations mean activity coefficients of KI in the KI–KCl–H2O ternary system at 298.15 K

Compared to the current popular methods for measuring the mean activity coefficient of the ternary aqueous solution, electromotive force method has certain advantages of rapidity and sensitivity. Herein, The electromotive force measurements were performed on the cell of the type: K–ISE|KI (m1), KCl (m2)|I–ISE, which consists of a potassium-ion combination ion selective electrode (ISE) and iodide-ion combination ion selective electrode (ISE) without a liquid junction. We chose the total ionic strength I range from 0.0100 to 1.0000 mol·kg−1 for different ionic strength fractions yb of KCl with yb = (0.0, 0.2, 0.4, 0.6, 0.8). The experimental results show that the mean activity coefficients of KI can be calculated well by using the Pitzer models and Nernstian equation. Moreover, the Pitzer ion interaction parameters of θCl,I and ψK,I,Cl were fitted using Pitzer’s equations, and the two parameters were used to calculated the mean activity coefficients of KCl in the KI–KCl–H2O ternary system. Accordingly, the osmotic coefficients, water activities, and excess Gibbs free energies in the mixtures were studied in the KI–KCl–H2O ternary system.

Measurement and modeling of mean activity coefficients in ternary electrolyte system (Nicl2/Triton X-100/H2O) at T=298.15 ± 0.1 K

In this work, the results relating to the thermodynamic properties for the ternary electrolyte system of (NiCl2 + Triton X-100 + water) using the potentiometric method were reported at T = 298.15 K. The electromotive force measurements were carried out on the galvanic cell without liquid junction of the type: Ni2+-ISE | NiCl2 (m), Triton X-100 (%wt.), H2O (100-%wt.) | AgCl|Ag over total ionic strengths from 0.0010 to 6.0000 mol.kg-1 for different percentage mass fraction of Triton X-100 (%wt. = 0.0, 1.0, 2.5, 5.0, 7.5 and 10.0). The mean activity coefficients of NiCl2 were determined by using potentiometric data. Then, the mean activity coefficients of NiCl2 were correlated with Pitzer ion interaction model and TCPC model. The Pitzer ion-interaction parameters (βo, β1 and C^∅) and the adjustable parameters (b and S) of TCPC model were determined by correlating of data for the series under investigated system. The Pitzer ion interaction parameters were used to calculating of thermodynamic properties such as the osmotic coefficients and the excess Gibbs energy of solution. The result showed that the Pitzer ion interaction model could be used to investigation of the system, successfully.

A speciated, conventional Pitzer ion-interaction model for the aqueous Nd3+–H+–Na+–K+–Ca2+–Cl−–OH− system at 298 K and 0.1 MPa

A conventional, speciated Pitzer ion-interaction model at 298 K and 0.1 MPa is presented for the NdCl3 + H2O system and mixtures containing HCl, NaCl, KCl, and CaCl2. The model uses Nd3+, NdOH2+, Nd(OH)2+, Nd(OH)30, NdCl2+, and NdCl2+ solute species and was fitted to isopiestic, electromotive force (emf), and NdCl3·6H2O solubility data. The model was then extended to pH values at which Nd(OH)3, Nd(OH)2Cl, and a speculative double salt, Nd(OH)3·NdCl3, are stable. The two hydroxychloride salts enabled the model to join the stability fields of NdCl3·6H2O and Nd(OH)3 ensuring continuity in the range 2 < pH < 13. The activity coefficient model developed from the low pH [NdCl3 + NaCl](aq) system reproduces the solubility of solid Nd(OH)3(s) in water and NaCl(aq) with only the addition of standard state free energy terms for crystalline (cr) and amorphous (am) NdOH3(s) and the Nd(OH)2+ and Nd(OH)30 solute species. No Pitzer parameters involving NdOH2+, Nd(OH)2+ and Nd(OH)30 were necessary to reproduce the full body of thermodynamic data over an ionic strength range from infinite dilution to the solubility limits of NaCl, KCl, CaCl2·6H2O, Nd(OH)3(s), the hydroxychloride salts, and for mixtures containing up to 4.5 molal HCl(aq). The model adds only five ‘binary’ and three ‘ternary’ Pitzer ion-interaction parameters to the H-Na-K-Ca-Cl-OH parameters in Harvie et al. (1984; hereafter HMW). The model is simpler, compositionally broader, and more accurate than previously published Pitzer ion-interaction models for aqueous neodymium-chloride and -hydroxide solutions containing HCl, NaCl, KCl or CaCl2. The model has ramifications for geochemical modeling and uncertainty quantification of An(III) solubilities used to support certification of evaporite hosted nuclear waste repositories.

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.

Isopiestic investigation and phase equilibrium of the high-efficient absorption refrigerants LiBr and SrBr2 at 288.15 K

Isopiestic molalities and water activities for the commercial absorption refrigerants LiBr and SrBr2 at 288.15 K were accurately measured using an improved isopiestic method. And the solubilities for the absorption refrigeration systems were determined by the isothermal dissolution equilibrium method, meanwhile, the refractive indices and densities were measured. The Pitzer and HW model was used to correlate the measured water activities and solubilities, simulate the thermodynamic properties and predict the data in the phase equilibrium process for the absorption refrigeration systems, and the predicted data agreed well with the experimental solubilities. On the basis of the Pitzer ion-interaction parameters and solubility product constant (Ksp) obtained in this work, the ion-interactions between alkali metal ions with Sr2+ and phase equilibrium behaviors were illustrated on the molecular level, which could give an essential guide for the designing of absorption refrigeration system.

Thermophysical properties of 1-ethyl-3-methylimidazolium bromide ionic liquid in water + ethylene carbonate mixtures at T = (298.2, 308.2 and 318.2) K

In this research, we studied the effect of ethylene carbonate (EC) on thermodynamic, transport and optical properties such as electrical conductance, refractive indices and activity coefficients of aqueous 1-ethyl-3-methylimidazolium bromide, [EMIm]Br solutions at T = (298.2, 308.2 and 318.2) K and 0.1 MPa. Electrical conductance was measured for [EMIm]Br ionic liquid from 0.0029 to 0.2500 mol kg−1 in different mass fractions of ethylene carbonate (EC) in water + EC mixtures (wEC/wmixture% = 10, 20 and 30). Limiting molar conductivity (Λ°) and ion association constant (KA) were calculated through Fuoss-Onsager equation and used to obtain the thermodynamic functions. Refractive index measurements were carried out for the binary and ternary water + [EmIm]Br + EC mixtures. The measured data were used to derive the refractive index changes of mixing (ΔnD) and the values were correlated by Redlich-Kister and the Cibulka equations for binary and ternary mixtures, respectively. Moreover, the results relating to the mean activity coefficient measurements for [EMIm]Br in the EC + water solvent mixtures were presented by potentiometric method. The potentiometric measurements were performed on the electrochemical cell of the type Br-ISE | [EMIm]Br (m), EC (wt.%), H2O (1-wt)%| [EMIm]-ISE, in various mass fractions of EC in water (0, 10, 20 and 30%) over total ionic strength from 0.0085 to 2.500 mol kg−1. The experimental results were correlated by the Pitzer equation and the values of Pitzer ion-interaction parameters β(0), β(1) and Cϕ were evaluated. Finally the parameters were utilized to calculate the values of the osmotic coefficients, excess Gibbs free energies and the solvent activity for the whole series of investigated system.

Thermodynamic Properties of Aqueous Sodium Nitrate Solutions Under Superambient Conditions

Use has been made of the Pitzer ion-interaction or virial coefficient approach to estimate the pressure dependence of the osmotic and activity coefficients of aqueous solutions of sodium nitrate (NaNO3) up to 423.15 K and 6.0 mol·kg−1 using published volumetric data on NaNO3(aq). In particular, volumetric Pitzer ion-interaction parameters have been evaluated from a mathematical fit of published apparent molar volume data with the appropriate Pitzer equation. The Pitzer parameters were then fitted as a function of temperature and pressure. These results were then used to calculate the change in the osmotic and activity coefficients in going from the state of an initial pressure p1 to one of a final pressure p2. These pressure dependences have been combined with the osmotic and activity coefficient values of NaNO3(aq) at 0.1 MPa or vapor-saturation pressures (psat) obtained from the model of Archer to yield a comprehensive set of thermodynamic parameters for NaNO3(aq) at temperatures from 293.15 K through 423.15 K, at pressures of (5, 10, 15, 20) MPa, and molalities to 6.0 mol·kg−1.

Effect of hydrophobicity and H-bonding abilities of ions on osmotic coefficients of aqueous diethylammonium based protic ionic liquid solutions at 298.15 K

The osmotic and activity coefficients of aqueous solutions of diethylammonium based protic ionic liquids (PILs) were determined experimentally using vapor pressure osmometry in the concentration range of (~0.02 to ~0.5) mol·kg−1 at 298.15 K. Osmotic coefficient data show positive deviation from Debye-Hückel limiting law for all the studied PILs. Also a minimum in osmotic coefficient data was observed at higher concentrations and is explained in terms of ion-pair formation. Data of experimental osmotic coefficient were used to obtain activities (aw) and activity coefficients (γ1) of water, mean molal activity coefficient (γ±) of PILs and excess Gibbs free energy change (ΔGE) due to mixing. Observed variations in osmotic coefficients data were explained in terms of hydrophobicity as well as H-bonding. The data of osmotic and activity coefficients were further subjected to analysis through Pitzer ion-interaction model to get an information of ion-ion and ion-solvent interaction to understand ion-pairing, ion hydration and hydrophobic effects in aqueous solutions of PILs. For this, Pitzer ion interaction parameters β(0) and β(1) were estimated and compared with literature data available for other relevant systems. Finally, the results are interpreted in terms ion-ion, ion-solvent interaction along with effect of hydrophobicity on ion-pairing and further discussed the effect of alkyl chain length of anions on solvation behavior of protic ionic liquids in aqueous solutions.

Determination and Modeling the Activity Coefficients of 1-Propyl-3- methylimidazolium Bromide in the Ethanol + Water Mixtures at T = (298.2, 308.2 and 318.2) K

In this work, the results relating to the mean activity coefficient measurements for ionic liquid of 1- propyl -3 methylimidazolium bromide, [PMIm]Br in ethanol+ water mixtures have been reported using potentiometric measurements at T=( 298.2, 308.2 and 318.2)K. The electromotive force (emf) measurements were performed on the galvanic cell of the type:Br-ISE│[PrMIm] (m) ethanol (wt.%), H2O (1−wt) %│ [PrMIm] -ISE, in mixed solvent system containing 0, 10, 20, 30% mass fractions of ethanol over ionic strength ranging from 0.0010 to 2.0000 mol•kg−1. The Pitzer ion-interaction model was used to analyze the activity coefficients for studied system. The Pitzer ion-interaction parameters (β(0), β(1) and Cϕ) were determined and employed to calculate the mean activity coefficients, the osmotic coefficients and excess Gibbs free energies for the whole series the studied system.

A Thermodynamic Model for ZrO2(am) Solubility at 25 °C in the Ca2+–Na+–H+–Cl−–OH−–H2O System: A Critical Review

Zirconium is an important element in the nuclear fuel cycle. Thermodynamic data and models to reliably predict Zr–OH system behavior in various conditions including high ionic strengths are required and currently are unavailable. Most available experimental data are rather old, obtained using inadequate methodologies, and provide equilibrium constant values that differ by many orders of magnitude. Previous reviews have recommended values based on available data. These reviews used all of the available data, including poor quality data, in a global fit to determine these values. This has resulted in recommended thermodynamic models with a large number of polynuclear species and a number of mononuclear species with values of thermodynamic constants for the solubility product of ZrO2(am) and Zr–OH hydrolysis constants that are many orders of magnitude different from those for the reliable analogous Hf reactions. In this critical review, we have evaluated the quality of the available data, selected only those data that are of high quality, and reinterpreted all of the high quality data using SIT and Pitzer models for applications to high ionic strength solutions. Herein for 25 °C we (1) present formation constant values for ZrOH3+, $$ {\text{Zr}}\left( {\text{OH}} \right)_{2}^{2 + } $$ , Zr(OH)4(aq), $$ {\text{Zr}}\left( {\text{OH}} \right)_{5}^{ - } $$ , and $$ {\text{Zr}}\left( {\text{OH}} \right)_{6}^{2 - } $$ , and the solubility product for ZrO2(am) which are consistent with the Hf system, (2) report a revised value for the formation constant of $$ {\text{Ca}}_{3} {\text{Zr}}\left( {\text{OH}} \right)_{6}^{4 + } $$ , (3) show that several hypothetical polynuclear species ( $$ {\text{Zr}}_{3} \left( {\text{OH}} \right)_{9}^{3 + } $$ , Zr4(OH) 15 + , and Zr4(OH)16(aq)) proposed in previous reviews are not needed, and (4) show that polynuclear species ( $$ {\text{Zr}}_{3} \left( {\text{OH}} \right)_{4}^{8 + } $$ and $$ {\text{Zr}}_{4} \left( {\text{OH}} \right)_{8}^{8 + } $$ ) are not important in a very extensive H+ concentration range (0.1–10−15.4 mol·kg−1). Our review has also resulted in SIT and Pitzer ion-interaction parameters applicable to as high ionic strength solutions as 5.6 mol·kg−1 in NaCl, 2.11 mol·kg−1 in CaCl2, and 23.5 mol·kg−1 in NaOH.

Mean Activity Coefficients of NaCl in the Mixture of 2-Hydroxyethylammonium Butyrate + H2O at 298.15 K

The main objective of this work is to continue with a series of electrochemistry studies of mixtures of ionic liquids and water as a solvent to provide accurate data for future particular applications [Amado-Gonzalez et al. J. Chem. Eng. Data 2017, 62, 752]. The mean activity coefficients for NaCl in [2-hydroxyethylammonium butyrate (2-HEAB) + H2O] as a solvent mixture were determined by cell potential measurements: Na–ion selective electrode (ISE)|NaCl (m), 2-HEAB (w), H2O (1 – w)|Cl–ion selective electrode (ISE) at molalities from 0.10 to 3.20 mol·kg–1 at 298.15 K. Different weight fractions (w) of 2-HEAB with w = 0.01, 0.05, 0.1, 0.2, 0.3, and 0.4 were used. At higher concentrations of w = 0.40, NaCl is salting out by 2-HEAB in water. The Pitzer ion interaction parameters β0, β1, and Cγ were used to find the values of osmotic coefficients, solvent activity, and the excess Gibbs free energy for the mixed electrolyte system. The results may be interpreted by the clathrate-like formation of 2-HEAB + water...

Thermodynamic Study of the NaNO3–Cd(NO3)2–H2O Ternary System at 298.15 K by the Potential Difference Method

In this work, we have made some thermodynamic investigations about the NaNO3–Cd(NO3)2–H2O ternary system. The potential difference method of the battery cell, Na–ISE|NaNO3 (m1), Cd(NO3)2 (m2)|NO3–ISE, was used to study the activity coefficients in this mixed system at 298.15 K in the total ionic strengths range 0.0100–1.0000 mol·kg–1 with different ionic strength fractions yb of Cd(NO3)2 with yb = (0, 0.2, 0.4, 0.6, and 0.8). There was a good Nernst response between Na–ISE and NO3–ISE in this work, and the mean activity coefficients of NaNO3 can be interpreted well by the Pitzer models. Furthermore, the mixing Pitzer ion interaction parameters of θNa,Cd and ψNa,Cd,NO3 were fitted from Pitzer’s equation, and the two parameters were applied to compute the values of the mean activity coefficients of Cd(NO3)2, the osmotic coefficients, the solvent activity, and the excess Gibbs free energy in this mixed system.

Mean Activity Coefficients of NaCl in NaCl–CdCl2–H2O Ternary System at 298.15 K by Potential Difference Method

In this work, in ternary mixed-electrolyte system (NaCl–CdCl2–H2O), the mean activity coefficients of NaCl were measured with the potential difference method of the cell: Na ion-selective electroed (ISE)|NaCl(m1), CdCl2(m2)|Cl ion-selective electroed (ISE) at 298.15 K. Also, we chose the total ionic strength I range from 0.0100 to 1.0000 mol·kg–1 for different ionic strength fractions yb of CdCl2 with yb = (0.8, 0.6, 0.4, 0.2, 0). The experimental results gave that the mean activity coefficients of NaCl can be interpreted well by the Pitzer models, Na-ISE and Cl-ISE had a good Nernst response. Furthermore, the mixing Pitzer ion interaction parameters of θNa,Cd and ψNa,Cd,Cl were fitted from Pitzer’s equation, and the two parameters were applied to compute the values of the mean activity coefficients of CdCl2.

Measurement and thermodynamic model study on solubility equilibrium of potassium phosphate, potassium hydrogen phosphate, and potassium carbonate in aqueous systems containing the ionic liquid [Bmim]Cl at 298.15 K

Solubilities of potassium phosphate (K3PO4), potassium hydrogen phosphate (K2HPO4) and potassium carbonate (K2CO3) in aqueous systems containing the ionic liquid 1-butyl-3-methylimidazolium chloride ([Bmim]Cl) were determined by cloud-point measurements in the temperature of 298.15K at atmospheric pressure. The solubility equilibrium data were correlated and calculated by using Extended Pitzer thermodynamic model. In addition, the new Pitzer ion interaction parameters of the mixed-electrolyte solution were obtained by using an optimization program based on Simplex Method of Nelder–Mead algorithm. Comparison of calculated results by using the new interaction parameters at 298.15K was expressed by the relative standard deviations between the regressed solubility values and the experimental data. Results indicate that predictions of the present model are in well accordance with experimental values, which supports the reliability of the model prediction.

Mean Activity Coefficients of NaCl in NaCl + SrCl2 + H2O Ternary System at 298.15 K Determined by Potential Difference Measurements

The mean activity coefficients for NaCl in the (NaCl + SrCl2 + H2O) ternary system were determined by electrode potential measurements of the cell without liquid junction: Na–ion selective electrode (ISE)|NaCl (mA), SrCl2 (mB), H2O|Cl–ion selective electrode (ISE) at the total ionic strengths ranging from (0.0100 up to 4.0000) mol·kg–1 at 298.15 K for different ionic strength fractions yB of SrCl2 with yB = (0.0, 0.2, 0.4, 0.6, and 0.8). The activity coefficient results were interpreted based on the Pitzer model. The Pitzer ion interaction parameters θNa+·Sr2+ and φNa+·Cl–·Sr2+ were calculated. Furthermore, those parameters obtained with the Pitzer model were used to calculate the values of the mean activity coefficients of SrCl2. In addition, the osmotic coefficients, solvent activity, and the excess Gibbs free energy for the mixed electrolyte system were also studied.