Pitzer Equations Research Articles

Temperature Dependence of the Parameters in the Pitzer Equations

The effects of temperature on the virial coefficients in the Pitzer equations are not known in general, and this is because the vast majority of experiments performed to investigate the properties of the aqueous electrolytes were conducted only at a temperature of 25 °C. Consequently, most of the parameters in the Pitzer equations that are available in the literature were estimated at this temperature. Therefore, finding a way to estimate the virial coefficients at different temperatures is highly important. To achieve this, new equations that correlate the virial coefficients with the temperature and the properties of the ions, i.e., ionic radius and ionic charge, are derived. As a result, these new derived equations were able to accurately predict the apparent relative molal enthalpies at 25 °C, as well as the activity and osmotic coefficients at temperatures up to 150 °C for electrolytes that are unlikely to form ion pairs. Moreover, comparison plots are presented to demonstrate the good agreement betw...

Calculations of phase equilibrium parameters of the quaternary systems KBr–K2SO4–K2B4O7–H2O and NaBr–Na2SO4–Na2B4O7–H2O at 298 K

Some of the parameters and equilibrium constants of quaternary salts solutions KBr–K2SO4–K2B4O7–H2O and NaBr–Na2SO4–Na2B4O7–H2O at 298 K are calculated using the correlation equation of the Pitzer parameters. The solubilities data of the ternary subsystems were fitted by multiple linear regression method. The phase diagram was plotted. A comparison between the calculated and experimental results for the systems shows that the predicted solubilities agree well with experimental data.

CO2 absorption using aqueous solution of potassium carbonate: Experimental measurement and thermodynamic modeling

Potassium carbonate solution is a widely used solvent for CO2 removal due to its benefit in energy consumption and other economic concerns like degradation and corrosion problem. In this study, the solubility of CO2 in aqueous solutions of potassium carbonate was measured using pressure-decay method at temperatures of 313.15 K, 323.15 K, and 333.15 K, different pressures (up to 1.2 MPa), and different solution concentrations of 15 %wt., 20 %wt., and 30 %wt. Also, two equations of state were utilized to anticipate CO2 solubility in aqueous solution of potassium carbonate. The model is a combination of chemical equilibrium in the liquid phase and physical equilibrium between the liquid and vapor phases. For vapor-liquid equilibrium calculations, Peng-Robinson equation of state (PR-EOS) was used to present the fugacity coefficient in the vapor phase. The activity coefficient in the liquid phase was presented by Pitzer equation. Also, the values of the primitive interaction coefficients (λCO2,K+ and μCO2,CO2,K+) were optimized using the available literature data of the similar system. The results demonstrated that the performance of the thermodynamic modeling procedure was acceptable and the average absolute relative deviation (AARD) between the experimental and the predicted data was less than 2.7%.

Application of Surface Tension Model for Prediction of Interfacial Speciation of CO2-Loaded Aqueous Solutions of Monoethanolamine

A thermodynamic platform in combination with experimental surface tension data is used to predict the surface phase speciation of CO2-loaded aqueous solutions of 30 wt % (%) monoethanolamine (MEA) at 20, 40, and 60 °C from their corresponding bulk phase speciation. The osmotic coefficient dependency of the surface tension of an electrolyte solution has been employed to estimate the surface tension. In order to calculate the osmotic coefficients, the Pitzer equation for the excess Gibbs energy was applied. According to the results of this study, molecular MEA and to some extent protonated MEA and the MEA–carbamate have surface propensity and will accumulate at the surface phase. The carbonate ion shows nearly even distribution between bulk and surface phases, and bicarbonate displays a tendency to remain in the bulk phase that increases with CO2 loading. The differences in the behaviors of protonated MEA, MEA–carbamate, carbonate, and bicarbonate are due to differences among their sizes and polarizabilitie...

Activity Coefficients of CsCl in PEG 200–H2O and PEG 600–H2O Mixtures at 298.15 K

The mean activity coefficients of the ternary systems CsCl + polyethylene glycol (PEG) (w) + H2O (1 – w) (w = 10%, 20%, 30%, 40%) determined by the potentiometric method at T = 298.15 K are reported. The molecular weights of PEG are 200 and 600, and the CsCl molality varies from 0.01 to 4.00 mol/kg. To correlate the experimental data, the Pitzer equation, extended Debye–Huckel equation, and the modified Pitzer equation have been utilized herein. As a result, a series of thermodynamic parameters were obtained and discussed in detail, including the mean ionic activity coefficients (γ±), the osmotic coefficient (Φ), the excess Gibbs free energies (GE), the standard Gibbs free energy of transference (ΔGt0) and the primary hydration number (nhydr).

Evaluation of the solubility constants of the hydrated solid phases in the H2O-Al2O3-SO3 ternary system

During the acid processing of aluminosilicate ores, the precipitation of a solid phase principally consisting of hydrated aluminium hydroxysulfates may be observed. The experimental study of the H2O-Al2O3-SO3 ternary system at 25 ◦ C and 101 kPa enabled to describe the solid-liquid equilibria and to identify the nature, the composition and the solubility of the solid phases which may form during the acid leaching. To predict the appearance of these aluminium hydroxysulfates in more complex systems, their solubility constants were calculated by modelling the experimental solubility results, using a geochemical reaction modelling software, CHESS. A model for non-ideality correction, based on the B-dot equation, was used as it was suitable for the considered ion concentration range. The solubility constants of three out of four solid phases were calculated: 104.08 for jurbanite (Al(SO4)(OH).5H2O), 1028.09 for the solid T (Al8(SO4)5(OH)14.34H2O) and 1027.28 for the solid V (Al10(SO4)3(OH)24.20H2O). However the activity correction model was not suitable to determine the solubility constant of alunogen (Al2(SO4)3.15.8H2O), as the ion concentrations of the mixtures were too high and beyond the allowable limits of the model. Another ionic activity correction model, based on the Pitzer equation for example, must be applied to calculate the solubility constant of alunogen.

Calculating Low Temperature Phase Equilibrium of NaCl-KCl-CaCl 2 Completion Fluid Based on Pitzer Model

Crystallization point, a main performance index of composite brine completion fluids, can only be obtained through laboratory experiments because most of the articles and handbooks only give the crystallization point of the single salt. If the crystallization point of a composite brine can be calculated with mathematical model, then large amount of tedious experiment can be saved, and the optimization of composite brine completion fluid can be achieved using the calculated data. Using the Pitzer model and the Spencer model parameters, salts commonly used in completion fluids, such as NaCl, KCl and CaCl2, were calculated for their solid-liquid phase equilibrium both as single salt and binary salts. The liability of the calculation was verified using documented data and experiment data. It was shown that at temperatures below 25℃, the relative standard deviation between the calculated values and the documented data was less than 0.1, satisfying the need for completion fluid study and design. At temperatures above 25℃, the relative standard deviation for KCl became larger, and the Pitzer parameters of KCl needed to be adjusted for phase equilibrium recalculation.

Solution Chemistry for Actinide Borate Species to High Ionic Strengths: Equilibrium Constants for AmHB4O72+ And AmB9O13(OH)4(cr) and Their Importance to Nuclear Waste Management

ABSTRACTBorate is present in natural groundwaters and borate is also released into groundwaters when borosilicate glass, waste form for high level nuclear waste, is corroded. Borate can form an aqueous complex, AmHB4O72+, with actinides in +III oxidation state. In this work, we present our evaluation of the equilibrium constant for formation of AmHB4O72+ and the associated Pitzer interaction parameters at 25°C.Using Nd(III) as an analog to Am(III), solubility data of Nd(OH)3(s) in NaCl solutions in the presence of borate ion from the literature, is used to determine Am(III) interactions with borate. The log10K for the formation reaction is 37.34. This evaluation is in accordance with the Waste Isolation Pilot Plant (WIPP) thermodynamic model in which the borate species include B(OH)3(aq), B(OH)4–, B3O3(OH)4–, B4O5(OH)42–, and NaB(OH)4(aq). The WIPP thermodynamic database uses the Pitzer model to calculate activity coefficients of aqueous species.In addition, the equilibrium constant for dissolution of AmB9O13(OH)4(cr) at 25oC is evaluated from the solubility data on NdB9O13(OH)4(cr) in NaCl solutions, again using Nd(III) as an analog to Am(III). The log10K for the dissolution reaction is –79.30. In the evaluation for log10K for the dissolution reaction, AmHB4O72+ is also considered.The equilibrium constant and Pitzer parameters evaluated by this study will be important to describe the chemical behavior of Am(III) in the presence of borate in geological repositories.

Application of Pitzer and six local composition models to correlate the mean ionic activity coefficients of aqueous 1-butyl-3-methylimidazolium bromide ionic liquid solutions obtained by EMF measurements

The mean ionic activity coefficients of aqueous 1-butyl-3-methylimidazolium bromide ([BMIm]Br) solutions in the concentrations ranging from 0.008 to 0.215mol·kg−1 were determined using potentiometric measurements at T=308.15, 318.15, and 328.15K. The obtained experimental data were correlated using the Pitzer and several local composition models, such as the non-electrolyte Wilson-NRF (N-Wilson-NRF), electrolyte Wilson-NRF (E-Wilson-NRF), electrolyte Wilson (E-Wilson), electrolyte NRTL (E-NRTL), modified electrolyte NRTL (ME-NRTL), and electrolyte NRTL-NRF (E-NRTL-NRF) models. The Pitzer parameters obtained were used to calculate the osmotic coefficients and excess Gibbs free energies of the solutions being studied. The results indicate that in general all the models used here can be successfully applied to predict the mean ionic activity coefficients of the aqueous ionic liquid solutions. However, the average standard deviations of the fit show that the NRTL based models represent the mean ionic activity coefficients with better precision.

Experimental determination of solubilities of di-calcium ethylenediaminetetraacetic acid hydrate [Ca2C10H12N2O8·7H2O(s)] in NaCl and MgCl2 solutions to high ionic strengths and its Pitzer model: Applications to geological disposal of nuclear waste and other low temperature environments

In this study, solubility measurements on di-calcium ethylenediaminetetraacetic acid hydrate [Ca2C10H12N2O8·7H2O(s), abbreviated as Ca2EDTA·7H2O(s)] as a function of ionic strength are conducted in NaCl solutions up to I=4.4mol·kg−1 and in MgCl2 solutions up to I=7.5mol·kg−1, at room temperature (22.5±0.5°C). The solubility constant (logKsp0) for Ca2EDTA·7H2O(s) and formation constant (logβ10) for CaEDTA2−,Ca2EDTA·7H2O(s)=2Ca2++EDTA4−+7H2O(1)Ca2++EDTA4−=CaEDTA2−(2)are determined as −15.57±0.10 and 11.50±0.05, respectively, based on the Pitzer model with a set of Pitzer parameters describing the specific interactions in NaCl and MgCl2 media.The solubility measurements and thermodynamic modeling indicate that Ca2EDTA·7H2O(s) could become a solubility-controlling phase for EDTA in geological repositories for nuclear waste when the inventories of EDTA reach the saturation concentrations for Ca2EDTA·7H2O(s). The model developed in this work would also enable researchers to calculate the optimal EDTA concentrations to be used for remediation of soils contaminated with heavy metals, and to calculate the maximum EDTA concentrations that could be present in soils after an ETDA washing technology has been applied.

Darapskite solubility in basic solutions at 25 °C: A Pitzer model for the Na[sbnd]NO3[sbnd]SO4[sbnd]OH[sbnd]H2O system

We propose a set of Pitzer interaction parameters to describe the chemical behavior of the Na2SO4NaNO3NaOHH2O quaternary system at 25 °C. With these parameters we have been able to adequately predict the properties of Na2SO4NaNO3H2O, Na2SO4NaOHH2O and NaNO3NaOHH2O ternary and Na2SO4NaNO3NaOHH2O quaternary systems, including the solubility of different single salts and the double salt darapskite (Na2SO4·NaNO3·H2O), a mineral that is expected to form in the matrix of some radioactive waste containers. We also successfully reproduced the osmotic coefficient, the water activity and the mean activity coefficients for the Na2SO4H2O, NaNO3H2O and NaOHH2O binary systems. We obtained the set of Pitzer parameters using a step-by-step modeling approach. First, we investigated the binary systems: the NaOHH2O and Na2SO4H2O binary system interaction parameters were established in previous studies from heat capacity and osmotic coefficient data. Among the various chemical models proposed in the literature that describe the properties of the NaNO3H2O binary system, we chose the full dissociation hypothesis, since it allowed complete description of the system with the minimal number of interaction parameters. Next, from the mineral solubility data, we determined the specific interaction parameters for ternary systems. Without further parameterization, the solubility of the various salts in the quaternary system could be reproduced accurately.

Modeling the acid-base properties of molybdate(VI) in different ionic media, ionic strengths and temperatures, by EDH, SIT and Pitzer equations

This paper reports the results of a study on the determination of the protonation constants of MoO42 −, in NaClaq, NaNO3aq, KClaq, at different ionic strengths (0 < I/mol dm− 3 ≤ 5.0 in NaClaq, 0 < I/mol dm− 3 ≤ 3.0 in NaNO3aq and KClaq) and temperatures (278.15 ≤ T/K ≤ 318.15 in NaClaq, only 298.15 K in NaNO3aq and KClaq), by potentiometric (ISE-H+ glass electrode) and spectrophotometric (UV/Vis) titrations. After a critical analysis of results and literature findings, the proposed speciation model takes into account the formation of two monomeric and four heptameric species, namely: MoO4H−, MoO4H2, (MoO4)7H86 −, (MoO4)7H95 −, (MoO4)7H104 − and (MoO4)7H113 −. Due to the complexity of the system, and to discrepancies of literature findings, particular attention has been paid to the determination of the stability of monomeric species, by performing measurements at very low concentrations, in which the polymerization processes do not occur. Data obtained have then been used to model the dependence of the acid-base properties of molybdate on medium, ionic strength and temperature by models commonly used for these purposes, namely the Extended Debye-Hückel (EDH), the classical Specific ion Interaction Theory (SIT), Pitzer equations, and van't Hoff (for the dependence on temperature). These last results, some of them obtained for the first time in this work, can be exploited for the modeling of the speciation of MoO42 − in a wide range of conditions typical of natural waters and biological fluids, as well as in many aqueous systems of technological/industrial importance, where molybdate can play key roles.

Activity Coefficients of RbF in the RbF + RbBr + H2O and RbF + RbNO3 + H2O Ternary Systems Using the Potentiometric Method at 298.2 K

Thermodynamic properties of the RbF + RbBr + H2O and RbF + RbNO3 + H2O systems were determined by the potentiometric method at the total ionic strengths ranging from 0.0017 to 0.7005 mol·kg–1 for different ionic strength fractions yB of RbBr/RbNO3 with yB = 0.00, 0.30, 0.60, and 0.90, at 298.2 K. Combining the Nernst equation and Pitzer equation, the mean ionic activity coefficients of RbF and RbBr/RbNO3, the osmotic coefficients, and the excess Gibbs energies of the studied systems were calculated.

Toward a Quality-Controlled and Accessible Pitzer Model for Seawater and Related Systems

We elaborate the need for a quality-controlled chemical speciation model for seawater and related natural waters, work which forms the major focus of SCOR Working Group 145. Model development is based on Pitzer equations for the seawater electrolyte and trace components. These equations can be used to calculate activities of dissolved ions and molecules and, in combination with thermodynamic equilibrium constants, chemical speciation. The major tasks to be addressed are ensuring internal consistency of the Pitzer model parameters (expressing the interactions between pairs and triplets of species, which ultimately determines the calculated activities), assessing uncertainties, and identifying important data gaps that should be addressed by new measurements. It is recognised that natural organic matter plays an important role in many aquatic ecosystems, and options for including this material in a Pitzer-based model are discussed. The process of model development begins with the core components which include the seawater electrolyte and the weak acids controlling pH. This core model can then be expanded by incorporating additional chemical components, changing the standard seawater composition and/or broadening the range of temperature and pressure, without compromising its validity. Seven important areas of application are identified: open ocean acidification; micro-nutrient biogeochemistry and geochemical tracers; micro-nutrient behaviour in laboratory studies; water quality in coastal and estuarine waters; cycling of nutrients and trace metals in pore waters; chemical equilibria in hydrothermal systems; brines and salt lakes.

Thermodynamic Study of Aqueous Solutions of 1-Butyl-3-methylimidazolium Tetrafluoroborate Ionic Liquid Using Potentiometric Measurements at Different Temperatures

The mean ionic activity coefficients of 1-butyl-3-methylimidazolium tetrafluoroborate ionic liquid in water at a low concentration range were determined using potentiometric measurements at temperatures ranging from 298.15 to 328.15 K. The obtained experimental data were correlated by the Pitzer and nonelectrolyte Wilson nonrandom factor (N-Wilson-NRF) models. The resulted Pitzer parameters were used to estimate the osmotic coefficients and excess Gibbs free energies of the system being investigated. The results indicate that both the models could be applied to predict the activity coefficients of the aqueous ionic liquid solutions, but the Pitzer model gives much lower standard deviations than the N-Wilson-NRF model. Moreover, the obtained activity and osmotic coefficients show that their values decrease with a rise in the ionic liquid concentration and increase with the elevation of temperature.

Aqueous Partition Mechanism of Organophosphorus Extractants in Rare Earths Extraction

The aqueous partition mechanism of traditional extractants and ionic liquid for the extraction of rare earths (REs) is explored in this work. To investigate the aqueous partition of extractants, the aqueous solubility of di(2-ethylhexyl) phosphoric acid (P204), 2-ethylhexyl phosphoric acid mono-2-ethylhexyl ester (P507), di(2-ethylhexyl) phosphinic acid (P227), bis (2,4,4-trimethylpentyl) phosphinic acid (C272), and [trialkylmethylammonium][di(2-ethylhexyl)orthophosphinate] ([A336][P507]) was analyzed systemically. The results demonstrated that the solubility of extractants decreased with increase of aqueous acidity, RE loading, and electrolyte concentration. Especially, the solubility of P204, P507, P227, and C272 decreased with the increase of RE complex, indicating that aqueous partition of the extractants was accompanied by the RE coordination reaction. The electrical double layer theory and the Pitzer equation was used to explain the inhibition of electrolyte on the aqueous partition of extractants. ...

Experimental and Thermodynamic Model Study on Solid and Liquid Equilibrium of Ternary System MgBr2–MgSO4–H2O at 333.15 K

The solubilities and the refractive indices of the MgBr2–MgSO4–H2O system at 333.15 K were studied with the isothermal equilibrium solubility method. The phase diagram and refractive index diagram were plotted for this system at 333.15 K. The system belongs to hydrate II type. The phase diagram is constituted of three invariant points cosaturated with two salts, four univariant solubility isotherms saturated with one salt, and four stable crystallization fields in the ternary system corresponding to MgSO4·6H2O (Hex), MgSO4·4H2O (Tet), MgSO4·H2O (Kie), and MgBr2·6H2O (Mb). The calculated refractive index data agree well with the experimental results. Combining the experimental solubility data of the ternary system, the Pitzer binary parameters for MgBr2 and MgSO4, and the Pitzer mixing ion-interaction parameter θBr,SO4, the Pitzer parameter ψMg,Br,SO4 and the solubility equilibrium constants Ksp of solid phases in the ternary system at 333.15 K were fitted using the Pitzer and Harvie–Weare (HW) model. Then...

Estimation of the Pitzer Parameters for 1–1, 2–1, 3–1, 4–1, and 2–2 Single Electrolytes at 25 °C

The Pitzer model is one of the most important thermodynamic models to predict the behavior of aqueous electrolyte solutions, especially at high ionic strengths. However, most of the parameters in the Pitzer equations have to be obtained experimentally, and this represents an important drawback to this model. Therefore, in order to make the Pitzer equations less dependent on experimental data and more dependent on the properties of the solution, new equations that correlate the Pitzer equations with the properties of the solution have been successfully developed for 1–1, 2–1, 3–1, 4–1, and 2–2 electrolytes. In particular, these equations were developed for two cases: (i) considers the original Pitzer equations and (ii) considers some simplifications to the Pitzer equation (assuming CMXφ, BMX(2), and α2 = 0). In particular, for case (ii), the second virial coefficients BMX(0) and BMX(1) of the Pitzer equations were re-estimated using published experimental data of the osmotic coefficient obtained from the l...

Measurement and Modeling of Mean Activity Coefficients of NaCl in an Aqueous Mixed Electrolyte Solution Containing Glycine

An electrochemical cell with two ion-selective electrodes (Na\(^{+}\) glass) and (Cl\(^{-}\) solid state) was used to measure the mean ionic activity coefficient of NaCl in an aqueous mixture containing NaCl, glycine, and NaNO\(_{3}\) at 308.15 K. The experiments were conducted at fixed molality of NaNO\(_{3}\) (0.1 m) and various molalities of glycine (0–1 m) and NaCl (up to 0.8 m). The experimental data were modeled using a modified version of the Pitzer equation. Finally the activity coefficient ratio of glycine was determined based on the Maxwell equation.

A sulfate and darapskite solubility model with Pitzer interaction coefficients for aqueous solutions containing NaNO2, NaNO3, and NaOH

Alkaline nuclear waste, and many other industrial processes, have sodium sulfate salts immersed in aqueous electrolyte solutions containing nitrate, nitrite, and hydroxide ions. A model is required to predict the solubility of sulfate salts in these environments. In order to develop a model for sulfate solubility, this study developed molal-based Pitzer model coefficients for interactions between sulfate and nitrate, nitrate and hydroxide. Model parameters were determined by optimizing them until the difference between predicted and measured solubilities was minimized. The sulfate-anion binary Pitzer parameters were all found to be temperature independent. The reduced chemical potentials of the double salt darapskite (Na3NO3SO4*H2O) as a function of temperature was also required and determined here by fitting the model to solubility data. The reduced chemical potentials for darapskite and other sodium sulfate salts were converted to standard state Gibbs energies and enthalpies. These thermodynamic quantities were consistent with other estimates in the literature when available.