Pitzer Ion Interaction Research Articles

Stability constants for the formation of rare earth-inorganic complexes as a function of ionic strength

Recent studies have been made on the distribution of the rare earths (La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu) in natural waters relative to their concentration in shales. These metals have also been used as models for the behavior of the trivalent actinides. The speciation of the rare earths in natural waters is modelled by using ionic interaction models which require reliable stability constants. In this paper the stability constants for the formation of lanthanide complexes ( k mx ∗ ) with Cl −, NO 3 −, SO 4 2−, OH −, HCO 3 −, H 2PO 4 −, HPO 4 2−, and CO 3 2− determined in NaClO 44 at various ionic strengths have been extrapolated to infinite dilution using the Pitzer interaction model. The activity coefficients for free ions ( γM, γx) needed for this extrapolation have been estimated from the Pitzer equations. The thermodynamic stability constants ( K MX ) and activity coefficients of the various ion pairs ( γ MX ) were determined from In ( solK MX ∗ γ Mγ x ) = In K mx+ In (γ MX ). The activity coefficients of the ion pairs have been used to determine Pitzer parameters ( B MX ) for the rare earth complexes. The values of B MX were found to be the same for complexes of the same charge. These results make it possible to estimate the stability constants for the formation of rare earth complexes over a wide range of ionic strengths. The stability constants have been used to determine the speciation of the lanthanides in seawater and in brines. The carbonate complexes dominate for all natural waters where the carbonate alkalinity is greater than 0.001 eq/L at a pH near 8.

Aqueous partial molar heat capacities and volumes for NaTcO4 and NaReO4

A flow microcalorimeter/densimeter system has been commissioned to measure heat capacities and densities of solutions containing radioactive species as a function of temperature. Measurements were made for NaTcO4(aq) at six temperatures (189.15 K to 373.15 K for the heat capacities, 287.43 K to 396.67 K for the densities) over the molality range 0.01 to 0.29 mol-kg−1. Measurements for NaReO4(aq) (NaReO4 is a common nonradioactive analogue for NaTcO4) were made under similar conditions, but for eight temperatures and a more extensive range of molalities, 0.05 to 0.65 mol-kg−1. Heat capacities of NaCl(aq) reference solutions were also measured from 293.15 K to 398.15 K. The heat capacity and density data are analysed using Pitzer's ioninteraction model. Equations for the apparent molar heat capacities and volumes are reported. Values of the NaReO4(aq) partial molar heat capacities are compared to literature values based on integral heats of solution. The agreement between the two sets of NaReO4 results is good below 330 K, but only fair at the higher temperatures. Values of the partial molar volumes have also been derived. Using literature values and the results of our experiments, it is calculated that the disproportionation of hydrated TcO2(s) to form TcO 4 − (aq) and Tc(cr) occurs more readily at high temperatures. The uncertainties introduced by using thermodynamic values for ReO 4 − (aq), in the absence of values for TcO 4 − (aq), are discussed.

Aluminum speciation and equilibria in aqueous solution: I. The solubility of gibbsite in the system Na-K-Cl-OH-Al(OH) 4 from 0 to 100°C

The solubility of gibbsite, Al(OH) 3, has been measured in a large number of solutions in the system Na-K-Cl-OH-Al(OH) 4 from 6.4 to 80°C and 0.01 to 5.0 molal ionic strength. These results have been coupled with selected literature data and modeled using the Pitzer ion interaction treatment. An eight-parameter expression is derived for the molal concentration quotient of the reaction Al(OH) 4 −↔ Al(OH) 3 + OH − in this system from which the equilibrium constant at infinite dilution, log K 4, and the stoichiometric molal activity coefficient ratio, log ( γOH − γAl(OH) 4 −) , can be evaluated over the range 0–100°C and 0–12 molal ionic strength at 1 bar with a precision of approximately ±0.02 log units. Standard thermodynamic properties of the reaction at 25°C and 1 bar are log K 4 = 1.143 ± 0.006, ΔH° = −22.5 ± 0.3 kJ/mol, ΔS° = −54 ± 1 J/K/mol, and ΔC p 0 = −148 ± 6 J/K/mol. From these quantities and the standard thermodynamic properties of gibbsite, the values of ΔG f 0, ΔH f 0, and S 0 of [Al(OH) 4 −] aq at 25°C and 1 bar are computed to be −1305.6 ± 1.2 kJ/mol, −1500.6 ± 1.5 kJ/mol, and 111.4 J/K/mol, respectively. Approximate values of the pure electrolyte parameters β 0, β 1, and Cφ for NaAl(OH) 4 and KAl(OH) 4 as well as the mixing parameters for aluminate ion with OH −, OH − + Na +, and OH − + K + are also obtained.

Aluminum speciation and equilibria in aqueous solution: II. The solubility of gibbsite in acidic sodium chloride solutions from 30 to 70°C

The solubility of gibbsite in aqueous solutions was measured at ten ionic strengths made up of NaCl, HCl, and AlCl 3 at 30, 50, and 70°C with the initial acidity controlled by addition of HCl. The aluminum concentration was determined by ion chromatography, while the final equilibrium pH was measured at temperature. The equilibrium quotients for the reaction Al(OH) 3 + 3H + ai Al 3+ + 3H 2O were modeled using both an empirical equation including the Debye-Hückel term and the Pitzer ion interaction treatment which incorporated the relevant single electrolyte and mixing interaction parameters currently available in the literature. In the latter treatment only four independent variables, including θA a , ψA acl , and two terms describing the equilibrium constant at infinite dilution, were needed to fit the data well within the projected experimental error. In general, these new equilibrium quotients differ markedly from results of all but the most recently published solubility studies. The thermodynamic parameters at infinite dilution are compared with those calculated from the individual components of the reaction available in the literature. These calculations lead to recommended thermodynamic values for the Gibbs energy of reaction at 25°C of −44.2 ± 0.3 kJ mol −1 , a ΔG f 0(Al 3+, aq) of −487.7 ± 1.5 kJ mol −1 , and a ΔH f 0(Al 3+, aq) of −540.9 kJ mol −1 . No evidence for aluminum chloride complexation was found by comparing solubility experiments in the presence of varying concentrations of sodium trifluoromethanesulfonate and sodium chloride at 50°C and ca. 5 molal ionic strength.

High-temperature thermodynamics of aqueous alkali-metal salts

Heat capacities and densities of aqueous solutions of four alkali-metal halides (NaF, KF, KCl, and KI) and two alkali-metal sulfates (Na2SO4 and K2SO4) have been measured at temperatures from 298.15 K to 373.15 K and at the pressure 0.6 MPa over the molality ranges 0.03 mol·kg−1 to 0.44 mol·kg−1, 0.10 mol·kg−1 to 2.10 mol·kg−1, 0·03 mol·kg−1 to 2.01 mol·kg−1, 0.04 mol·kg−1 to 0.60 mol·kg−1, 0.05 mol·kg−1 to 1.53 mol·kg−1, and 0.03 mol·kg−1 to 0.40 mol·kg−1, respectively. The measurements were done using a flow differential-heat-capacity calorimeter in series with a vibrating-tube densimeter. Pitzer's ion-interaction model was used to analyse these results and literature values of comparable precision. Equations for the apparent molar heat capacities and volumes are reported, and consistent sets of ionic partial molar heat capacities and volumes at 298.15 K and 373.15 K, relative to the conventions: C∞p, 2(H+,qa) = 0 and V∞2(H+,aq) = 0, were calculated. Activity coefficients were also calculated for NaF and KF for the temperature range from 298.15 K to 473 K.

Thermodynamic model for aqueous Cd2+?CO 3 2? ionic interactions in high-ionic-strength carbonate solutions, and the solubility product of crystalline CdCO3

The aqueous solubility of CdCO3(c) was studied in 0.01M NaClO4, in solutions equilibrated with N2-CO2(g) mixtures that contained 0.0003, 0.001, or 0.138 atmospheres of CO2(g). The pH ranged from about 4.5 to 9, and the studies were conducted from both the oversaturation and the undersaturation directions, with the equilibration periods ranging from 6 to 57 d. To determine the carbonato complexes of Cd(II), the solubility of CdCO3(c) was also studied in 0.0016 to 1.00M Na2CO3 solutions at fixed hydroxide ion concentration, and in solutions with fixed aqueous C concentrations (0.1 and 0.01M C) over a range of OH− from 1×10−5 to 1.0M. The equilibrium Cd concentrations were reached in less than about 6 d. Pitzer's ion-interaction model was used to interpret these solubility data, as well as CdCO3(c) solubility data reported in the literature, which extended to 5.0M K2CO3 with an ionic strength of approximately 18.6 m. Our thermodynamic model required the introduction of two aqueous Cd2+-CO32− complexes, CdCO3(aq) and Cd(CO3)22−, as well as ion-interaction parameters for Cd(CO3)22− with the bulk cations Na+ and K+. This model gave excellent agreement with all available experimental data extending to 5.0M K2CO3. The logarithms of the thermodynamic equilibrium constants for the reactions: $$\begin{gathered} CdCO_3 \left( c \right) \rightleftarrows Cd^{2 + } + CO_3^{2 - } \hfill \\ Cd^{2 + } + CO_3^{2 - } \rightleftarrows CdCO_3 \left( {aq} \right) \hfill \\ Cd^{2 + } + 2CO_3^{2 - } \rightleftarrows Cd\left( {CO_3 } \right)_2^{2 - } \hfill \\ \end{gathered} $$ were found to be −12.24±0.1, 4.71±0.1, and 6.49±0.1, respectively. The β0 ion-interaction parameters for Cd(CO3)22−−Na+ and Cd(CO3)22−−K+ were found to be −0.14 and −0.06, respectively.

Aluminum potassium sulfate dodecahydrate solubility in mixed dipotassium sulfate + aluminum sulfate solutions

Recently, the Pitzer interaction model was used to calculate aluminium potassium sulfate dodecahydrate solubility products from published solubility data. The model preformed poorly, reflected by a marked increase in values with decreasing solution potassium content. Solubility measurements at 25 o C were repeated in this study

Extracting robust and physically meaningful pitzer parameters for thermodynamic properties of electrolytes from experimental data. Ridge regression as an aid to the problem of intercorrelation

The Pitzer interaction model for thermodynamic properties of electrolytes is reevaluated in view of available regression techniques for the statistical inference of Pitzer parameters from experimental data. It is concluded that ordinary least squares regression is not generally suited, because of the intrinsic correlations among the various predictor variables in the Pitzer model. The predictor variables all are some function of the concentration of the electrolyte considered. Ridge regression, a mathematically only slightly different procedure designed to overcome the problem of intercorrelations, often yields more robust estimates for the Pitzer parameters. The potential of RR is demonstrated by some examples for the system GaCl3−HCl. The ridge estimates are expected to be closer to the physically true parameter values.

Correlation of pitzer ion interaction parameters

A new correlation predicting the activity coefficients of aqueous electrolyte solutions between Pitzer ion interaction parameters and ionc properties (ionic charge, radius and entropy) is developed. The substances include uni-uni and uni-bi type of single salts for which data are available. The results of correlation show linear relations for uni-uni type, and quadratic equations for uni-bi type. Many of the trends in the calculated activity coefficients for electrolyte solutions can be correlated with respect to the effect of the ions on the structure of the water and explained by structure-making and -breaking concept. These kinds of correlation may be useful in predicting values for salts that have no measurement of the activity coefficients.

Thermodynamics of aqueous gallium chloride. Heats of solution and dilution at 25°C

The heat of solution of GaCl3 and heats of dilution of single GaCl3 solutions in water and of mixed GaCl3−HCl solutions in HCl solutions (with a fixed HCl concentration of 0.1337 mol-kg−1 HCl) up to 4 mol-kg−1 GaCl3 were measured at 25°C. While in the acid solutions hydrolysis is suppressed to below 0.5% of total gallium concentration, the measurements in water allow evaluation of the effect of hydrolysis on the relative enthalpy. The Pitzer interaction model for excess properties of aqueous electrolytes was used to interpret the change in relative enthalpy with concentration. Pitzer parameters were derived by statistical inference using ridge regression. Their physical significance is supported by the heat of solution data. The measurements yield the following results for standard heats of formation and Pitzer parameters for the relative molar enthalpy at 25°C: $$\begin{gathered} H_{GaCl_3 }^ \circ = - 722 kJ - mol^{ - 1} ; \beta _{L,GaCl_3 }^0 = - 1.52 \times 10^{ - 3} kg - mol^{ - 1} - K^{ - 1} ; \hfill \\ \beta _{L,GaCl_3 }^1 = 1.21 \times 10^{ - 2} kg - mol^{ - 1} - K^{ - 1} ; C_{L,GaCl_3 } = - 1.42 \times 10^{ - 4} kg^2 - mol^{ - 2} - K^{ - 1} ; \hfill \\ H_{GaOHCl_2 }^ \circ = - 492 kJ - mol^{ - 1} ; H_{Ga(OH)_2 Cl}^0 = - 706 kJ - mol^{ - 1} ; \hfill \\ \end{gathered} $$ With these parameters the overall variance in the partial molar heat of solution at infinite dilution, extrapolated from the present experiments, is minimized to 0.35 kJ2-mol−2, while the experimental apparent molar heats of dilution are reproduced on average within 2.7 kJ-mol−1.

The influence of pressure on the activity coefficients of the solutes and on the solubility of minerals in the system Na-Ca-Cl-SO 4-H 2O to 200°C and 1 kbar and to high NaCl concentration

A model is presented which is used to calculate the effect of pressure on activity coefficients of aqueous solutes in the system Na-Ca-Cl-SO 4-H 2O to 200°C. Literature data for the density and compressibility of aqueous binary solutions of Na 2SO 4 and CaCl 2 to 200°C are used to calculate the first and second pressure derivatives of Pitzer's ion interaction model parameters, as well as the standard molal compressibility and volume of these two salts. Empirical correlations between the apparent molal volume and compressibility of the aqueous electrolytes are used to guide the choice of the temperature dependent expressions used for the numerical representation of the derivatives of Pitzer's parameters with respect to pressure. For sodium sulfate solutions, such correlations are used to extrapolate compressibilities to 200°C. The change in the thermodynamic properties of the-CaSO 0 4 ion pair with pressure is taken into account by the variation of its dissociation constant. The volumetric properties (partial molal volumes and compressibilities) of multicomponent solutions in the Na-Ca-Cl-SO 4-H 2O system can be predicted from the information generated here and the volumetric equations of Rogers and Pitzer (1982) for NaCl. This model is then combined with the high temperature model of Moller (1988) of the same system in order to calculate activity coefficients at high pressures to 200°C. The resulting model is validated by comparing calculated and measured solubilities of anhydrite and gypsum in pure water and in NaCl solutions up to 6 M. The agreement between the calculated and measured solubilities of the calcium sulfates is typically better than 10% up to 200°C and 1 kbar. The relevance of temperature and pressure corrections to the activity coefficients of aqueous solutes is discussed in regard to the assumed accuracy with which geochemical models are able to calculate mineral solubilities.

An ion interaction model for the determination of chemical equilibria in cement/water systems

A chemical equilibria model is proposed for the simulation of reactions between porewater and the various amorphous and crystalline minerals of cementitious materia at 25°C. The model utilizes the Pitzer Ion Interaction model as a basis for the calculation of ion activity coefficients. This allows the simulation of chemical equilibria between minerals and water to high solute concentrations. A variable compositional model for CSH based on the data of Gartner and Jennings is also incorporated into the solving relations. An example simulation of the effect of progressive additions of sulfuric acid on a cement paste are presented to illustrate the basic working of the model.

Estimation of Pitzer's ion interaction parameters for electrolytes involved in complex formation using a chemical equilibrium model

Pitzer's ion interaction model has been widely accepted for calculating the thermodynamic properties for electrolytes at high ionic strength. For weak electrolytes, a better estimation can be obtained by combining the model with chemical equilibria. The method of calculation is to treat each individual species as a single, separated ion. The concentration of each ion will be constrained by the mass balance equation and its activity will be guarded by the stability constants. Including chemical equilibria in Pitzer's model provides not only a better estimation of the thermodynamic properties of weak electrolytes but also a better understanding of the equilibrium among the complexes. The results may be used for correcting the effect from high ionic strength solution when determining the stability constants. When considering chemical equilibria, some of the parameters reported by Pitzer may have to be reestimated. The method of estimation and comparison between final results are presented. The binary system of HF, and the ternary systems of CuCl2 in NaCl and in HCl are used for demonstration.

Ionization of acetic acid in aq. sodium chloride media: a potentiometric study to 573K and 130 bar

The ionization quotients of aqueous acetic acid have been determined precisely in NaCl(aq) media to 5 mol/kg from 50 to 300{degree}C with a potentiometric cell previously developed at Oak Ridge National Laboratory. Pressure coefficients were also determined to 250{degree}C. The cell contains hydrogen electrodes in a concentration cell configuration and is operated in a flow mode. Results have been combined with selected information in the literature and modeled by both the Pitzer ion-interaction treatment and a conventional ionic strength approach. Thermodynamic quantities for the ionization reaction have been derived including the equilibrium constant, activity coefficient quotients, and pressure coefficients, along with the changes in enthalpy, entropy, heat capacity, and volume for the reaction. Dramatic increases in negative values for {Delta}H{degree}, {Delta}S{degree}, {Delta}C{sub p}{degree}, and {Delta}V{degree} are seen that appear to extrapolate to negative infinity at the critical temperature along the saturation vapor pressure curve. However, increases in pressure and salinity diminish this trend until, for example, at a density of 1 g/cm{sup 3} the quantities remain relatively constant as has been shown for other such processes involving ions. These results provide the first measurements of the activity coefficient ratio for the ionization of an organic acid at high temperatures. Themore » results provide a basis for use of acetic acid-acetate as a relatively stable buffer for physical chemical studies and as a protonated ligand for metal complexation measurements of the kind reported recently from this laboratory. A comparison of the ionization constants and enthalpies for ionization of several organic acids shows modest trends with the electron-releasing character of the carboxylate.« less

The dissociation of phosphoric acid in NaCl and NaMgCl solutions at 25�C

The pK 1 * , pK 1 * and pK 3 * for the dissociation of H3PO4 have been measured in NaCl solutions from 0.5 to 6m at 25°C. The results have been used to evaluate Pitzer interaction parameters ψ(NaClH2PO4)=−0.028±0.005, λ(NaH3PO4)=−0.075±0.025, θ(HPO4Cl)=0.105±0.009, θ(PO4Cl)=−0.59±0.02 and ψ(NaClHPO4)=−0.003±0.004, ψ(PO4NaClH)=0.110±0.008. These parameters yield values of pK 1 * , pK 2 * and pK 3 * in NaCl that agree with the measured values with average deviations of ±0.04, ±0.03 and ±0.05 in pK 1 * . Measurements of pK 1 * and pK 2 * were also made in NaMgCl solutions. These results have been used to evaluate β(O)(MgH 2 PO 4)=−3.55±0.07,β(1)(MgH 2 PO 4=−16.9±0.03, β(O)(MgH 2 PO 4=−17.5±0.03 and β(1)(MgH 2 PO 4)=27.4±0.8 at 25°C. The results for pK 2 * in NaMg−Cl solutions were also used to calculate log K MX * =3.2±0.1 for the formation of the ion pair MgHPO 4 o .

An ion interaction model for the volumetric properties of natural waters: Density of the solution and partial molal volumes of electrolytes to high concentrations at 25°C

Literature density data for binary and common ion ternary solutions in the Na-K-Ca-Mg-Cl-SO 4-HCO 3-CO3-H 2O system at 25°C have been analysed with Pitzer's ion interaction model, which provides an adequate representation of the experimental data for binary and common ion ternary solutions up to high concentration. This analysis yields Pitzer's interaction parameters for the apparent and partial molal volumes, which are the first derivatives with respect to pressure of the interaction parameters for the free energy. From this information, densities of natural waters as well as partial molal volumes of their solutes can be predicted with good accuracy, as shown by several comparisons of calculated and measured values. It is shown that V ̄ MX - V ̄ 0 mx , the excess partial molal volume of the salt MX, depends more on the type of salt than on the electrolyte itself and that it increases with the charges of the salt components. The influence of concentration and composition on the variation of activity coefficients with pressure and on the partial molal volumes of the salts is discussed, using as an example the partial molal volume of CaSO 4(aq) in solutions of various compositions. The increase of V ̄ CaSO 4 , with ionic strength is very large but is not very different for a NaCl-dominated natural water like the Red Sea lower brine than for a simple NaCl solution. Although the variation of activity coefficients with pressure is usually ignored for moderate pressures, like those found in hydrothermal environments, the present example shows that it can be as large as 30% for a 2-2 salt for a pressure increase from 1 to 500 bars at high ionic strength.

Acid association quotients of bis-tris in aqueous sodium chloride media to 125�C

The ionic strength and temperature dependencies of the molal acid association quotients of 2,2-Bis(hydroxymethyl)-2,2′,2″-nitrilotriethanol (also abbreviated as bis-tris) were determined potentiometrically in a concentration cell fitted with hydrogen electrodes. The emf was recorded for equimolal bis-tris/bis- trisHCl buffer solutions from 5 to 125°C at approximately 25°C intervals, and at nine ionic strengths from 0.05 to 5.0m (NaCl). The molal association quotients, combined with infinite dilution values from the literature, are described precisely by a seven parameter equation which yielded the following thermodynamic quantities at infinite dilution and 25°C: logK=6.481±0.003, ΔH o =−28.5±0.2 kJ-mol −1 , ΔS o =28.5±0.8 J-K −1 -mol −1 , and ΔC =−22±5 J-K −1 -mol −1 . The equation incorporates a simple three term expression for logK, but requires four terms to describe the rather complex ionic strength dependence despite the reaction being isocoulombic. The molal association quotients from this study and the literature were also subjected to the Pitzer ion interaction treatment.

The solubility of SO2 and the dissociation of H2SO3 in NaCl solutions

The pK 1 * and pK 2 * of H2SO3 have been determined in NaCl solutions as a function of ionic strength (0.1 to 6 m) and temperature (5 and 25 °C). The extrapolated values in water were found to be in good agreement with literature data. The experimental results have been used to determine the Pitzer interaction parameters for SO2, HSO 3 - and SO 3 - in NaCl solutions. The resultant parameters for NaHSO3 and Na2SO3 were found to be in reasonable agreement with the values for NaHSO4 and Na2SO4. It, thus, seems reasonable to assume that the interactions of Mg2+ and Ca2+ with HSO 3 - and SO 3 - can be estimated from the values with HSO 4 - and SO 4 - until experimental values are available. Measurements of pK 1 * and pK 2 * in artificial seawater were found to be in good agreement with the calculated values using the derived Pitzer parameters. It is, thus, possible to make reasonable estimates of the activity coefficients of HSO 3 - and SO 3 - ions and pK 1 * and pK 2 * for the ionization of H2SO3 in marine aerosols.

The solubility of celestite and barite in electrolyte solutions and natural waters at 25°C: A thermodynamic study

The solubility data of barite and celestite in NaCl, KCl, CaCl 2, MgCl 2 and Na 2SO 4 aqueous solutions at 25°C have been evaluated using Pitzer's ion interaction model. From the examples of BaSO 4 and SrSO 4 the limited influence of the binary interaction parameters for slightly soluble salts is demonstrated. Even when most of the mixing parameters are omitted the model still accurately predicts barite and celestite solubilities in various ionic media, except for the case of barite in seawater. The analysis of the role of these various parameters shows that the activity coefficients of trace elements in natural waters can be calculated by Pitzer's model using only a small number of parameters. In the case of barite solubility in seawater, the discrepancy between the calculated and measured values can be explained by the formation of a (Ba,Sr)SO 4 solid solution during the experiments performed by reaching equilibrium by precipitation (supersaturation). This phase controls the Ba content of the solution which may then be higher than pure barite solubility as calculated by the model.

Ion interaction parameters for aluminum sulfate and application to the prediction of metal sulfate solubility in binary salt systems

The Pitzer ion interaction parameters for the Al 2 (SO 4 ) 3 −H 2 O system have been reevaluated by using all published isopiestic data at 25.0 o C. An analysis of the differences between model-calculated and experimental metal sulfate solubilities reveals that the ternary interaction parameter can be set to zero for all systems considered