Pitzer Equations Research Articles

Thermodynamically Consistent Equations for the Accurate Description of the Logarithm of the Solvent Activity and Related Properties of Electrolyte Solutions with a Unique Set of Parameters: Critical Analysis of the Mean Activity Coefficient Evaluation

Thermodynamically consistent equations for the accurate description of the dependence on concentration of the properties of electrolyte solutions are proposed, based on a polynomial of order i/4 and a unique set of adjustable coefficients. The equation for the logarithm of the solvent activity ln a1(m) was derived first, followed by analogous expressions for the osmotic coefficient ϕ(m), the solvent activity a1(m) and activity coefficient γ1(m) and finally for the mean ionic activity coefficient $$\gamma_{ \pm }^{o} (m)$$. The descriptive capability of these equations was verified and favorably compares with the extended Pitzer equation. Finally, it was demonstrated that the evaluation of $$\ln \gamma_{ \pm }^{o} (m)$$ is strongly influenced by the fitting capability of the expression used in the correlation of ϕ(m) in the low molality region.

Thermodynamic Properties of Phases and Phase Equilibria in the H2O–HNO3–UO2(NO3)2–Th(NO3)4 System

A set of Pitzer parameters was obtained to accurately describe the thermodynamic properties of solutions in the H2O–UO2(NO3)2–Th(NO3)4–HNO3 system at 25°С and represent the thermodynamic properties of liquid phases in the H2O–Th(NO3)4–HNO3 subsystem in the temperature range 25–50°С. Solubility products were calculated for crystal hydrates Th(NO3)4 · 6H2O and UO2(NO3)2 · 3H2O to predict the solubilities of these compounds in those solutions over a wide concentration range.

Correlation and prediction of surface tension in single and mixed aqueous electrolyte solutions based on the mean ionic activity coefficient: A comparative analysis of Pitzer, E-NRTL and E-UNIQUAC models

Li and Lu's model to calculate the surface tension of single and mixed aqueous electrolyte solutions, coupled with Pitzer, e-NRTL and e-UNIQUAC activity coefficient models, is critically evaluated in this paper. Parameters of these activity coefficient models were taken from vapor-liquid equilibrium data available in the literature. The effect of the mean ionic activity coefficient model on the surface tension calculation is investigated in order to obtain low deviations from experimental data with emphasis on salt reservoir applications. An evaluation is made of the magnitude of the percentage surface tension increment relative to the surface tension of pure water, which occurs due to an increase in salt concentration. The feasibility of interpolation and extrapolation of the surface tension model with respect to the temperature was investigated for single electrolyte solutions at several temperatures. A sensitivity analysis of the initial guesses of the Li and Lu's model when adjusting the model parameters was performed. A new approach is also proposed to estimate the Pitzer parameters for some systems. This study explores the Li and Lu's model as never found in the literature before and is generally able to provide more accurate surface tension calculations compared with previous works. The results show that for single electrolyte solutions, the Pitzer and e-NRTL models provide similar deviations with an overall AAPD of 0.49%. For mixed electrolyte solutions, the e-NRTL model performed better than the Pitzer and e-UNIQUAC, providing an overall AAPD of 0.42%. The simulated increments of surface tension due to addition of salt are in accordance with the literature. The sensitivity analysis demonstrates the relevance of well adjusting the initial guesses for parameter estimation. Interpolation and extrapolation analysis yielded quite acceptable deviations with all overall AAPDs lower than 1.40% and also indicated that e-NRTL model is the most accurate. The proposed approach to fit the Pitzer model parameters provided an average deviation of 0.75%.

Activity Coefficients of NaClO4 in (PEG 4000 + H2O) Mixtures at (288.15, 298.15 and 308.15) K

The cell potential of the cell containing two ion-selective electrodes (ISE), Na-ISE | NaClO4 (m), PEG 4000 (Y), H2O (100-Y) | ClO4-ISE has been measured at temperatures of (288.15, 298.15, and 308.15) K as a function of the weight percentage Y of PEG 4000 in a mixed solvent at a 1 Mpa and the standard state for measured activity coefficients will be a solution of the salt in pure water. Y was varied between (0 and 25) wt.% in five-unit steps and the molality of the electrolyte (m) was between 0.05 mol kg-1 and almost saturation. The values of the standard cell potential were calculated using routine methods of extrapolation together with extended Debye-Huckel and Pitzer equations. The results obtained produced good internal consistency for all the temperatures studied. Once the standard electromotive force was determined, the mean ionic activity coefficients for NaClO4, the Gibbs energy of transfer from the water to the PEG 4000-water mixture, and the primary NaCl hydration number were calculated.

Measurements and calculations of solid-liquid equilibria in two quaternary systems: LiCl–NaCl–SrCl2–H2O and LiCl–KCl–SrCl2–H2O at 298 K

Using the method of isothermal dissolution equilibrium, stable phase equilibria of unreported strontium-containing systems LiCl–NaCl–SrCl2–H2O and LiCl–KCl–SrCl2–H2O at 298 K have been studied in accordance with the compositions of the underground brine in western Sichuan Basin. The experimental results show that there are no solid solution and complex salt in two quaternary systems. The phase diagram of quaternary system LiCl–NaCl–SrCl2–H2O consists of two invariant points, five isothermal dissolution curves and four crystallization regions. The quaternary system LiCl–KCl–SrCl2–H2O belongs to a simple type and the phase diagram consists of two invariant points, five isothermal dissolution curves and four crystallization regions. The solubilities of salts in the above systems were accurately calculated with Pitzer electrolyte solution theory. It was found that the calculated phase diagrams coincided basically with the experimental phase diagrams by evaluated the accuracy through the experimental results. Meanwhile, the applicability of Pitzer parameters selected in this paper was validated.

Thermodynamic phase equilibria in the aqueous ternary system NaCl–NaBO2–H2O: Experimental data and solubility calculation using the Pitzer model

Solubilities and refractive indices in the ternary system NaCl–NaBO2–H2O at 323.15 K were investigated with the dissolution equilibrium method. The phase diagram of this system consists of three single-salt crystallization regions for NaBO2·4H2O, NaCl·NaBO2·2H2O and NaCl, three univariant solubility curves and two invariant points. A comparison of the diagrams of this system from 288.15 to 323.15 K shows that area of NaBO2·4H2O region decreased whereas the areas of NaCl·NaBO2·2H2O increased obviously with temperature increasing. The Pitzer binary parameters of NaB(OH)4, Pitzer mixing parameters θCl-,BOH4-and ψNa+,Cl-,BOH4-, and the dissolution equilibrium constants of NaB(OH)4·2H2O and NaCl·NaB(OH)4 were fitted with the solubility data on the basis of Pitzer model. The variation trends for calculated solubility curves are in accordance with the experimental results. The results show that the other boron species except B(OH)4− in the solution for the system NaCl–NaB(OH)4–H2O can’t be neglected. The assumption of only one boroncontainingionicspecies B(OH)4− in the solution is not very accurate, but the calculated results with the assumption can still describe the experimental values. The Pitzer parameters and Ksp values obtained in this study are capable of solubility calculation for the system containing B(OH)4−.

Mean Activity Coefficients of KCl in KCl + SrCl2 + H2O Ternary System at 288.15 K Determined by EMF Method.

In this work, the studies of thermodynamic mean activity coefficients of KCl in the KCl-SrCl2-H2O ternary system have been made. A cell without liquid junction battery cell, K-ISE|KCl(mA), SrCl2(mB)|Cl-ISE, was used to study the activity coefficients in this mixed system KCl-SrCl2-H2O at 288.15 K by the electromotive force method. The total ionic strengths ranges are 0.0100-1.0000 mol·kg-1 with different ionic strength fractions yb of SrCl2, that is, yb = (0, 0.2, 0.4, 0.6, and 0.8). The results show that the K-ISE and Cl-ISE have a good Nernst response. Accordingly, the electromotive forces of the mixed system were measured by using the ion selective electrode listed above, and the mean activity coefficients are also determined with Nernst equation. Using the activity coefficient data, the mixed ion interaction parameters θK,Sr and ψK,Sr,Cl of Pitzer equations at 288.15 K were fitted by Matlab with linear regression method, respectively. Furthermore, those parameters were applied to calculate the values of the mean activity coefficients of SrCl2. Finally, the osmotic coefficients, water activity, and the excess Gibbs free energy of this system were evaluated by Pitzer's equations.

Activity Coefficient Measuring and Modeling for a Single and Symmetrical Mixture in a Mixed Solvent and Friedman’s Footprint of a Higher-Order Limiting Law

This study is conducted to investigate the HCl + NaCl + H2O + C2H5OH mixed electrolyte systems. The experimental activity coefficients are collected through measuring the electromotive force by using a cell containing pH and silver chloride electrodes in different alcohol mass fractions w(C2H5OH) in H2O (where w = 0.10, 0.20, and 0.50). All the used electrolyte molalities are between 0.01 and 2.5 mol kg–1, at 298.15 ± 0.01 K. Modeling is achieved using mean activity coefficients data for single and mixed HCl and NaCl in mixed solvent. A detailed study of Pitzer’s equations regarding effectiveness of nonionic species is taken into account. The result shows that this approach is a valuable aspect of the Pitzer equation for activity coefficient correlation of pure and mixed electrolytes, in mixed solvent media. The result underlines the importance of including Friedman’s higher-order limiting law (HOLL) regarding fitting the activity coefficient data for symmetric mixture, that is, not only theoretically accurate but also practically important. It seems that this work would be considered as the first experimental observation for the HOLL to correlate the activity coefficient of symmetrical mixture.

Thermodynamic properties of MCl (M = Na, K, Rb, Cs) + tetramethylurea + water ternary system at 298.2 K

For this article, a number of thermodynamic properties for MCl (M = Na, K, Rb, Cs) in tetramethylurea (TMU)-water ternary systems were investigated through potentiometric method at the temperature of 298.2 K. To fit experiment data, the Pitzer equation and the extended Debye-Hückel equation were used. The mean activity coefficients, together with excess Gibbs free energy, osmotic coefficients and standard solubility product of ternary systems are calculated. The variation of these properties in this εr-decreasing co-solvent (TMU-H2O) is discussed from the aspect of ion radius, relative permittivity, ion-ion interactions and ion-solvent in the solution.

Study and modeling of the liquid–solid equilibrium of the KCl–KNO3–HCl–H2O system at 283.15 K

AbstractIn this work, the liquid–solid equilibrium of the KCl–KNO3–HCl–H2O system at 283.15 K was investigated. To calculate the solubility product constants of KCl and KNO3 in HCl solution, the Pitzer equation was used to calculate the activity coefficient of the ionic species in aqueous solution. In addition, the thermodynamic model with the Pitzer equation was constructed to regress the temperature coefficient parameters for HCl and HNO3. The calculation and prediction of the KCl–KNO3–HCl–H2O system using the results of the regression confirmed that the regression was successful and the Pitzer equation was suitable. For the reaction KCl(s) + HNO3 → KNO3(s) + HCl, the equilibrium constant K can be obtained from the solubility product constants of KCl and KNO3. Eutectic points for the KCl–KNO3–HCl–H2O system were also predicted. These equilibrium data could be expressed by the triangular phase diagram. The process of the reaction to produce KNO3 could be explained through this triangular phase.

Activity Coefficient of Bromide Ions in the Glucoamylase Solution

In this work, the electrodynamic potential E of the sodium bromide (NaBr) solution and tetrabutyl-ammonium bromide (TBAB) solution in the presence of glucoamylase was determined with an ion selective electrode at 278.15, 288.15, and 298.15 K. In addition, the value of activity coefficient of bromide ions at three temperatures was calculated with the Debye–Huckel equation and Pitzer equation. The results showed that the maximum relative error of activity coefficient of bromide ions calculated by the two methods was 8.63%. The activity coefficient of bromide ions in the NaBr solution decreased with increasing molality of NaBr, and the activity coefficients of bromide ion first decreased and then increased with increasing molality of TBAB. The concentration of glucoamylase had different effects on the relationship between the activity coefficient of bromide ions and electrolyte concentration at different temperatures. The value of the activity coefficient of bromide ions in the TBAB solution was greater than...

Prediction of multicomponent ION exchange equilibria by using the e-NRTL model for computing the activity coefficients in solution

The e-NRTL model for computing the activity coefficients in solution of electrolytes was used for the first time, as the best of our knowledge, together with the Wilson's equation for evaluating the non-ideal behavior of the resin phase, in the prediction of multicomponent ion exchange equilibria. For this purpose, experimental data for the binary systems Ni2+/Na+ and Zn2+/Na+ and the ternary system Ni2+/Zn2+/Na+ using Amberlite IR-120 reported by Franco et al. [1] were considered. The results obtained showed that the major impact over the equilibrium modelling was caused by the inclusion of the Wilson's equation demonstrating the predominant effect of the non-ideality of the resin phase. No significant differences in the results (for the systems and ionic concentrations explored here) were observed when Bromley, Pitzer and e-NRTL equations were used to predict the activity coefficients in solution. Regarding the prediction of the multicomponent equilibria, it can be said that the most complex models: Pitzer's and e-NRTL ones, yield the best results. Again, the major impact in the improvement of the prediction was the inclusion of the Wilson's parameters. Finally, since the e-NRTL model allows to indistinctly work with both electrolytes and non-electrolytes, it could be possible to design modules for simulating the ion exchange operation in process simulations software like Aspen Plus®.

Braskem offers bio-based polymers to promote the circular economy

Using the method of isothermal dissolution equilibrium, stable phase equilibria of unreported strontium-containing systems LiCl–NaCl–SrCl2–H2O and LiCl–KCl–SrCl2–H2O at 298 K have been studied in accordance with the compositions of the underground brine in western Sichuan Basin. The experimental results show that there are no solid solution and complex salt in two quaternary systems. The phase diagram of quaternary system LiCl–NaCl–SrCl2–H2O consists of two invariant points, five isothermal dissolution curves and four crystallization regions. The quaternary system LiCl–KCl–SrCl2–H2O belongs to a simple type and the phase diagram consists of two invariant points, five isothermal dissolution curves and four crystallization regions. The solubilities of salts in the above systems were accurately calculated with Pitzer electrolyte solution theory. It was found that the calculated phase diagrams coincided basically with the experimental phase diagrams by evaluated the accuracy through the experimental results. Meanwhile, the applicability of Pitzer parameters selected in this paper was validated.

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.

Solid-liquid equilibrium in the system 2-keto-L-gulonic acid + sodium-2-keto-L-gulonate + hydrochloric acid + sodium chloride + water

The reactive solid-liquid equilibrium (SLE) in the quinary system 2-keto-l-gulonic acid (HKGA) + sodium-2-keto-l-gulonate (NaKGA) + hydrochloric acid (HCl) + sodium chloride (NaCl) + water was studied experimentally at 298 K and ambient pressure. The precipitation of three solid species was observed: HKGA monohydrate (HKGA⋅H2O), NaKGA monohydrate (NaKGA⋅H2O), and NaCl. A thermodynamic model based on the Pitzer model to calculate the activity coefficients in the liquid phase for the SLE was developed and unreported Pitzer parameters were fitted to the experimental data of this work. The equilibrium constant for the dissociation of HKGA and the solubility products of HKGA⋅H2O and NaKGA⋅H2O at 298 K were calculated from experimental data, whereas the equilibrium constant for the autoprotolysis of water and the solubility product of NaCl were adopted from literature data. The agreement between the experimental data and the results from the model is excellent, both regarding the liquid phase composition and the solid species in solid-liquid equilibrium.

Theoretical confirmation of an established experimental phase diagram of ternary system (Cu(SO4)–Zn(SO4)–H2O) at 25 °C: Pitzer parameters determination

The isotherm phase diagram of the ternary system (Cu(SO4)–Zn(SO4)–H2O) was firstly established at 25°C using a synthetic method of conductivity measurement. Then, we made use of volumetric dosing, in order to identify solid phases. The obtained isotherm has revealed the presence of two solid phases that having a stable equilibrium with the liquid phase, which are Cu(SO4)·5H2O, and the Zn(SO4)·7H2O. This study was confirmed numerically while going through the calculation of the binary and ternary Pitzer parameters for the studied salts through a Nelder Mead simplex algorithm. Indeed, the comparison of these with the bibliographic data has confirmed the accuracy of our experimental results.

Mathematical analysis to optimize crystal growth

For the production of sodium sulfate, a brine is crystallized and crystals of glauber salt are generated by this process. The phase data related to the most common sodium sulfate minerals are as follows: mirabilite (Na2SO4 ⋅ 10H2O), tenardite (Na2SO4), glauberite (Na2SO4 ⋅ CaSO4), astrakanite (Na2SO4 ⋅ MgSO4 ⋅ 4H2O). The units commonly used to express the phases are moles of salt per 1000 moles of water. These latter units simplify the construction of the commonly employed four-sided Janecke phase diagrams. The cooling temperature or the speed with which the solution is cooled has an effect on the size and purity, as well as the amount of crystals produced. We seek to establish, through the population balance equations (PBE), which process variables can be modified to obtain a specific crystal size, as well as to validate the mathematical model that best predicts the amount of crystals precipitated as a function of temperature. The adjustment by least squares, cubic splines, pitzer equations and Lagrange interpolation is tested. The experimental results agree with the characteristics of the proposed models.

Thermodynamic Modeling of Calcium Sulfate Hydrates in the CaSO4-H2O System from 273.15 to 473.15 K with Extension to 548.15 K.

Calcium sulfate is one of the most common inorganic salts with a high scaling potential. The solubility of calcium sulfate was modeled with the Pitzer equation at a temperature range from 273.15 to 473.15 K from published solubility data, which was critically evaluated. Only two Pitzer parameters, β(1) and β(2), with simple temperature dependency are required to model the solubility with excellent extrapolating capabilities up to 548.15 K. The stable temperature range for gypsum is 273.15–315.95 K, whereas above 315.95 K the stable phase is anhydrite. Hemihydrate is in the metastable phase in the whole temperature range, and the obtained metastable invariant temperature from gypsum to hemihydrate is 374.55 K. The obtained enthalpy and entropy changes at 298.15 K for the solubility reactions are in good agreement with literature values yielding solubility products of 2.40 × 10–05, 3.22 × 10–05, and 8.75 × 10–05 for gypsum, anhydrite, and hemihydrate, respectively. The obtained Pitzer model for the CaSO4–H2O system is capable of predicting the independent activity and osmotic coefficient data with experimental accuracy. The mean absolute average error of activity coefficient data at 298.15 K is less than 2.2%. Our model predicts the osmotic coefficient on the ice curve within 1.5% maximum error.

Mixed Electrolyte in Mixed Solvent: Activity Coefficient Measuring and Modeling for the HCl + NaCl + Methanol + Water System

The emf of the cell is measured to investigate the HCl + NaCl + H2O + CH3OH mixed electrolyte systems. The experimental data are obtained over the electrolyte molality ranging from 0.005 mol kg–1 up to about 3.5 mol kg–1, at 298.15 ± 0.01 K, by using a cell containing a pH and a silver chloride electrode in different alcohol mass fractions x(CH3OH) in H2O (where x = 0.10, 0.20, 0.30, 0.40, and 0.50). The mean activity coefficients of HCl in the mixtures are computed. Modeling is implemented by the classical Pitzer (CP) equation and original Pitzer (OP) equation that are included by the additional terms which are arising from interactions of neutral species and finally the modified Pitzer equation by Merida et al. (MP). The different aspects of proper parameter choosing in fitting processes especially for pure and mixed electrolytes in mixed solvent systems are signified in the results.

A thermodynamic model for solution behavior and solid-liquid equilibrium in Na-K-Mg-Ca-Al(III)-Fe(III)-Cr(III)-Cl-H2O system from low to very high concentration at 25°C

Abstract In this study we evaluated new mixing (θ and ψ) Pitzer parameters, and developed models for solution behavior and solid liquid equilibria for the following mixed systems: 1) KCl-AlCl3-H2O, 2) KCl-FeCl3-H2O, 3) KCl-CrCl3-H2O, 4) MgCl2-AlCl3-H2O, 5) MgCl2-FeCl3-H2O, 6) MgCl2-CrCl3-H2O, 7) CaCl2-AlCl3-H2O, 8) CaCl2-FeCl3-H2O, and 9) CaCl2-CrCl3-H2O at 25°C. The solubility modeling approach, implemented to the Pitzer specific interaction equations is employed. The values of the binary parameters for the binary sub-systems needed here to parameterize models for mixed systems are taken from our previous studies. Mixing solution parameters are evaluated in this study using activity (when available) and solubility data. Following an approach in our previous modeling studies on M(III) chloride and sulfate systems, in this work we accept that complex Al(III), Cr(III), and Fe(III) aqueous species do not exist in solutions. We test the new models by comparing model predictions with experimental data (activity data for unsaturated solutions and solubility data in ternary systems). The agreement between model predictions and experimental data is very good. Combining present parameterization, with our M(III) models developed previously we fully complete our at 25°C model for the 8th component system Na-K-Mg-Ca-Al(III)-Cr(III)-Fe(III)-Cl-H2O. The resulting model calculates solubilities and solution activities to high solution concentration within experimental uncertainty. Limitations of the model due to data insufficiencies are discussed. The resulting parameterization was developed for the Pitzer formalism based PHREEQC database.