Application of the GV-MSA model to the electrolyte solutions containing mixed salts and mixed solvents

In this work the Ghotbi–Vera mean spherical approximation (GV-MSA) model, coupled with two different expressions for the cation-hydrated diameters, was used in predicting the mean ionic activity coefficients (MIAC) of electrolytes for a number of the mixed-solvent and mixed-salt electrolyte solutions at 25 °C. In all cases the cation diameters in solutions changed with concentration of electrolyte while the anion diameters were considered to be constant and equal to the corresponding Pauling diameters. In application of the GV-MSA model to the electrolyte systems, two different expressions were used for concentration dependency of cation-hydrated diameters, i.e., the GV-MSA1 and GV-MSA2 models. In case of the electrolyte solutions containing the mixed-solvent of water and alcohol, the dielectric constants of the mixed solvents were obtained by simple regression of polynomial equations in terms of weight fraction of alcohol to the pertinent experimental data available in the literature. For the mixed-salt and mixed-solvent electrolyte solutions, in order to directly calculate the MIAC of electrolytes without introducing any new adjustable parameter, the values obtained in this work for the cation-hydrated diameters in the single aqueous electrolyte solutions were used. The results obtained in this work showed that the GV-MSA2 could more accurately correlate the MIAC of electrolytes in the single aqueous electrolyte solutions in comparison to those of the GV-MSA1 and Pitzer models. Also, the results showed that the GV-MSA-based models could accurately predict the MIAC of electrolytes in the mixed-solvent electrolyte solutions in comparison to those obtained from the model of Pitzer. In case of the mixed-salt electrolyte solutions the results of the two GV-MSA-based models studied in this work reasonably predict the MIAC of electrolytes in the mixed-salt electrolyte solutions without introducing any additional adjustable parameters compared to those obtained from the model of Pitzer with two adjustable parameters.     

Modeling aqueous electrolyte solutions. Part 2. Weak electrolytes

In this work the ePC-SAFT model is applied to weak electrolytes, such as weak acids or salts that do form ion pairs. Considering an association/dissociation equilibrium accounts for the fact that the electrolytes are not fully dissociated. Applying this approach, modeling the mean ionic activity coefficients (MIAC) as well as the water activity coefficients (WAC) is in very good agreement with experimental data for the aqueous HF system as well as for solutions of cadmium halides or alkali acetates. Experimental MIACs of ZnBr₂ and ZnI₂ reveal the formation of more than one complex in aqueous solutions. Implementing a simultaneous two-step ion-pairing mechanism also allows the modeling of the MIAC of these zinc salts in water.     

A New Gibbs Energy Model for Obtaining Thermophysical Properties of Aqueous Electrolyte Solutions

In this paper, a new Gibbs energy model is proposed to study the thermophysical properties of aqueous electrolyte solutions at various temperatures. The proposed model assumes that the electrolytes completely dissociate in solution. The model also has two temperature-independent adjustable parameters that were regressed using experimental values of the mean ionic activity coefficients (MIAC) for 87 electrolyte solutions at 298.15 K. Results from the proposed model for the MIAC were compared with those obtained from the E-Wilson, E-NRTL, Pitzer and the E-UNIQUAC models, and the adjustable model parameters were used directly to predict the osmotic coefficients at this temperature. The results showed that the proposed model can accurately correlate the MIAC and predict the osmotic coefficients of the aqueous electrolyte solutions better on the average than the other models studied in this work at 298.15 K. Also, the proposed model was examined to study the osmotic coefficient and vapor pressure for a number of aqueous electrolyte solutions at high temperatures. It should be stated that in order to calculate the osmotic coefficients for the electrolyte solutions, the regressed values of parameters obtained for the vapor pressure at high temperatures were used directly. The results obtained for the osmotic coefficients and vapor pressures of electrolyte solutions indicate that good agreement is attained between the experimental data and the results of the proposed model. In order to unequivocally compare the results, the same experimental data and same minimization procedure were used for all of the studied models.     

Modification of the GV-MSA model in obtaining the activity and osmotic coefficients of aqueous electrolyte solutions

In this work a modified form of the Ghotbi–Vera Mean Spherical Approximation model (MGV-MSA) has been used to correlate the mean ionic activity coefficients (MIAC) for a number of symmetric and asymmetric aqueous electrolyte solutions at 25 °C. In the proposed model the hard sphere as well as the electrostatic contributions to the MIAC and the osmotic coefficient of the previously GV-MSA model has been modified. The results of the proposed model for the MIAC of the electrolyte solutions studied in this work are used to directly calculate the values of the osmotic coefficients without introducing any new adjustable parameter. In the MGV-MSA model the cation diameter as well as the relative permittivity of water depends on the electrolyte concentration. Having considered such dependency for both cation and relative permittivity for water in an electrolyte solution the modification of the GV-MSA has been made. It should be stated that in the MGV-MSA model the anion diameter in the solution similar to that in the GV-MSA model remains constant and independent of the electrolyte concentration. The results obtained from the proposed model have been favorably compared with those of the GV-MSA model. The results showed that the MGV-MSA model can more accurately correlate the MIAC of the single electrolyte solutions than those of the GV-MSA model. The same comparison has been observed in case of the osmotic coefficients for the electrolyte solutions studied in this work. It should be noted that in order to do an unequivocal comparison between the results obtained from the models used in this work the same minimization procedure and the same experimental data for the MIAC and the osmotic coefficients have been used. Also it should be mentioned that in the MGV-MSA model the conversion from the McMillan–Mayer (MM) framework to that of the Lewis–Randall (LR) has been performed. It has been concluded that such transformation can affect the results in particular at higher electrolyte concentrations.     

Reconciliation of Solute Concentration Data with Water Contents and Densities of Multi-Component Electrolyte Solutions

Density and chemical masses are two of the most important parameters tracked in chemical plant flowsheets. Unfortunately, chemical plant laboratories commonly avoid density and solvent concentration measurements. Without these data, it is difficult to reconcile solute concentrations reported by the laboratories with the total mass and volume tracked in flowsheets. In this paper, the Laliberté-Cooper density model is used in conjunction with a numerical algorithm to simultaneously estimate both density and water content from measured solute concentrations for aqueous electrolyte solutions. The algorithm numerically optimizes the water content until the sum of the water and solute concentrations (in mass per volume units) equals the density predicted by the Laliberté-Cooper model for that composition. The algorithm was tested against an experimental dataset of simulated nuclear waste supernatant solutions containing mixtures of ten different electrolytes with total ionic strengths up to 8 mol⋅L⁻¹. The algorithm was able to predict the measured densities with an R² of 0.9912 and an average relative percent error of just 0.05%. The model error was not correlated to the estimated water content or any of the electrolyte concentrations. Thus, the algorithm can be successfully used to simultaneously predict density and water content of aqueous electrolyte solutions containing many electrolytes at high concentrations from analytical data reported in moles or mass of solute per volume.     

Activity Coefficients of Potassium Chloride in Water–Ethanol Mixtures

Activity coefficients of KCl were determined in water–ethanol solvents in the range 5–20% (w/w) ethanol, from experimental electromotive force (emf) data. The molalities varied from 0.1 mol-kg^–1 to near saturation and measurements were taken in the temperature range 25 to 45°C. The Pitzer model was used to describe the nonideal behavior of the electrolyte and the corresponding coefficients were determined for each solvent. The Pitzer–Simonson equations were also applied and found superior in the study of KCl in those nonaqueous solutions.     

Modeling Thermodynamics and Phase Equilibria for Aqueous Solutions of Trisodium Phosphate

A computational model is developed to calculate thermodynamic phase equilibria in alkaline solutions of trisodium phosphate up to 100°C. A variety of data are used, including isopiestic measurements, freezing point data, vapor pressure data at 100°C, heat capacities, heats of dilution, and solubility measurements. Pitzer's ion-interaction treatment is used to model electrolyte solutions and many unknown parameters are determined from existing data through nonlinear least-squares fitting. Phase equilibria are determined by minimization of total Gibbs energy using a modification of the code SOLGASMIX. Results calculated using the model accurately predict experimental data.     

Ion interaction approach to calculations of volumetric properties of aqueous multiple-solute electrolyte solutions

The ion interaction approach developed by Pitzer was used for the prediction of volumetric properties of mixed electrolyte solutions at 25°C based on parameters calculated from experimental data for single-solute electrolyte solutions. Such an approach was shown to be especially effective for application to the calculation of volumetric properties of natural hypersaline brines and of industrial electrolyte solutions of large complexity. The use of the latest recommended sets of volumetric ion interaction parameters for single electrolyte solutions and symmetrical mixing parameters for Na–K–Cl ion combinations considerably improved the precision of the density calculations of highly concentrated mixed electrolyte solutions and of various natural waters.     

The liquid–gas interface of oxygen–nitrogen solutions 2: Description in the Framework of the van der Waals gradient theory

The van der Waals gradient theory (vdW GT) is used to calculate surface tension, density profiles, adsorption, the Tolman length and to determine the position of dividing surfaces in the liquid–gas interface of an oxygen–nitrogen solution. The Helmholtz energy density (HED) is determined via an equation of state (EOS), unified for a liquid and gas, which describes stable, metastable and two-phase states of solutions. The influence parameters are calculated from data on the surface tension of pure components with the use of the mixing rule. At temperatures T > 100 K the vdW GT describes experimental data on the surface tension of oxygen–nitrogen solutions [V.G. Baidakov, A.M. Kaverin, V.N. Andbaeva, The liquid–gas interface of oxygen–nitrogen solutions: 1. Surface tension, Fluid Phase Equilib. 270 (2008) 116–120] within the experimental error. It is shown that the Tolman length, which determines the dependence of surface tension on the curvature of the dividing surface, depends considerably on the solution concentration.     

Modeling hydrate formation conditions in the presence of electrolytes and polar inhibitor solutions

In this paper, a new predictive model is proposed for prediction of gas hydrate formation conditions in the presence of single and mixed electrolytes and solutions containing both electrolyte and a polar inhibitor such as monoethylene glycol (MEG), diethylene glycol (DEG) and triethylene glycol (TEG). The proposed model is based on the γ–φ approach, which uses modified Patel–Teja equation of state (VPT EOS) for characterizing the vapor phase, the solid solution theory by van der Waals and Platteeuw for modeling the hydrate phase, the non-electrolyte NRTL-NRF local composition model and Pitzer–Debye–Huckel equation as short-range and long-range contributions to calculate water activity in single electrolyte solutions. Also, the Margules equation was used to determine the activity of water in solutions containing polar inhibitor (glycols). The model predictions are in acceptable agreement with experimental data. For single electrolyte solutions, the model predictions are similar to available models, while for mixtures of electrolytes and mixtures of electrolytes and inhibitors, the proposed model gives significantly better predictions. In addition, the absolute average deviation of hydrate formation pressures (AADP) for 144 experimental data in solutions containing single electrolyte is 5.86% and for 190 experimental data in mixed electrolytes solutions is 5.23%. Furthermore, the proposed model has an AADP of 14.13%, 5.82% and 5.28% in solutions containing (Electrolyte + MEG), (Electrolyte + DEG) and (Electrolyte + TEG), respectively.     

A nonelectrolyte local composition model and its application in the correlation of the mean activity coefficient of aqueous electrolyte solutions

The local composition models have been widely used for the correlation of activity coefficient of nonelectrolyte and electrolyte solutions. A new equation for the excess Gibbs energy function is developed based on the local composition expression of Wilson and the random reference state. This new function, the nonelectrolyte Wilson nonrandom factor (N-Wilson-NRF) model, is presented in the form of a molecular framework so that it can be used for both nonelectrolyte and electrolyte solutions. Without any particular assumptions for ionic solutions, the new function is used to described the short-range contribution of the excess Gibbs energy of electrolyte solutions. The long-range contribution is represented by Pitzer–Debye–Hückel model. With two adjustable parameters per electrolyte, the new model is applied to correlate the mean activity coefficients of more than 150 binary aqueous electrolyte solutions at 25 °C. The results are compared with various local composition models such as the electrolyte-NRTL, electrolyte NRF-Wilson and electrolyte-NRTL-NRF models. The comparison of the results with experiment demonstrates that the new model can correlate the experimental data accurately. Moreover, the model shows high precision of predictability for the osmotic coefficient of binary electrolyte solutions.     

Electrolyte-UNIQUAC-NRF model for the correlation of the mean activity coefficient of electrolyte solutions

The new electrolyte-UNIQUAC-NRF excess Gibbs function is obtained for calculation of the activity coefficient of the binary electrolyte solutions. The excess Gibbs energy of the model consists of the Pitzer–Debye–Hückel equation, describing the long-range electrostatic contribution and the electrolyte-UNIQUAC-NRF model to account for the short-range contributions. With two adjustable parameters per electrolyte, the new model is applied to correlation of the mean activity coefficients of more than 130 binary aqueous electrolyte solutions at 25 °C. Also the binary parameters, obtaining from regression of mean activity data, are used for prediction of osmotic coefficient data for the same electrolytes. The results are compared with various local composition models such as the electrolyte-NRTL, electrolyte NRF-Wilson, electrolyte-NRTL-NRF, N-Wilson-NRF models. The comparison of the results with experiment demonstrates that the new model can correlate the experimental activity coefficient data and predict the osmotic coefficient data of binary electrolytes accurately.     

Electrolyte-UNIQUAC-NRF Model Based on Ion Specific Parameters for the Correlation of Mean Activity Coefficients of Electrolyte Solutions

The Electrolyte-UNIQUAC-NRF excess Gibbs function was applied to estimate ion specific adjustable parameters of various salts by global optimization of the experimental activity coefficients of 54 electrolyte solutions. Twenty-three ion specific parameters were obtained for water and several cations and anions. The estimated individual ion parameters have been used to predict osmotic coefficient of electrolyte solutions. By using only the specific values for ions, the anion–cation and ion–water interaction parameters of different salts can be precisely estimated. Consequently, the interaction parameters of sparingly insoluble salts without experimental activity data can be easily calculated. For a case study, the solubility of CaSO₄ was predicted in relatively good agreement with experimental values over a wide range of temperatures up to 473.18 K.     

Thermodynamic Properties of NaCl Solutions at Subzero Temperatures

Heat capacities at infinite dilution of NaCl (aq) for the temperature range 0 to –25°C and apparent molar volumes at infinite dilution for 0 to –15°C have been estimated from a synthesis of experimental data collected at subzero temperatures. The parameters of the Helgeson–Kirkham–Flowers (HKF) equation for Na⁺ (aq) have been obtained, from which the Gibbs energies of Na⁺ and Cl^– have been calculated. The estimated values of Pitzer-equation parameters for thermal and activity-coefficient properties have been adjusted for subzero temperatures. The experimental phase diagram for the NaCl–H₂O system could be reproduced with these data, demonstrating the low-temperature applicability of the HKF model to extrapolate thermodynamic properties of aqueous-solution species at infinite dilution.     

Isopiestic measurements at high temperatures: I. Aqueous solutions of LiCl,CsCl, and CaCl2 at 155°C

Isopiestic measurements have been made for LiCl (aq) and CsCl (aq) at a temperature of 155°C. Equilibrium molalities ranged up to 21 mol-kg^–1. MgCl₂(aq) was chosen as the reference electrolyte. The apparatus used for the isopiestic experiments is an enhanced version of that developed by Grjotheim and co-workers. To test its precision osmotic coefficients of CaCl₂ (aq) have also been determined and compared with previously reported vapor pressure measurements at high concentrations. The results show a very good coincidence. The data can be described by the ion interaction model of Pitzer. The resulting set of parameters allows a fit of the experimental osmotic coefficients with a standard error of 0.0078 and 0.0114 for LiCl(aq) and CsCl (aq), respectively. The osmotic coefficients of LiCl are consistent with data at lower molalities, but there are discrepancies for the CsCl solutions.     

Electric properties of hydrogen iodide: Reexamination of correlation and relativistic effects

The electric dipole moment and the static dipole polarizability of the hydrogen iodide molecule were studied using sophisticated correlated and relativistic methods. Both scalar and spin–orbit relativistic effects were carefully accounted for. We conclude that the large differences between the theoretical and experimental dipole moment, the dipole moment derivative and the polarizability cannot be reconciled by improved account of electron correlation and relativistic effects. The most striking difference between theory and experiment is observed for the polarizability anisotropy. We believe that experimental data, namely the experimental dipole moment (the most recent value is 0.176 au as compared to our best theoretical estimate, 0.154±0.003 au), the parallel polarizability (44.4 and 38.47±0.05 au) and the anisotropy (11.4 and 2.33±0.05 au) must be inaccurate. Experimental and theoretical perpendicular polarizability components (33.0 and 36.14±0.05 au,) and the mean polarizability (36.8 and 36.92±0.05 au) agree better. Our vibrationally corrected relativistic CCSD(T) results represent the most sophisticated predictions of electric properties of HI obtained so far.Contribution to the Björn Roos Honorary Issue     

Silicon–air batteries

A new “metal”–air battery based on silicon–oxygen couple is described. Silicon–air battery employing EMI·2.3HF·F room temperature ionic liquid (RTIL) as an electrolyte and highly-doped silicon wafers as anodes (fuels) has an undetectable self-discharge rate and high tolerance to the environment (extreme moisture/dry conditions). Such a battery yields an effectively infinite shelf life with an average working voltage of 1–1.2 V. Silicon–air battery can support relatively high current densities (up to 0.3 mA/cm²) drawn from flat polished silicon wafers anodes. Such batteries may find immediate applications, as they can provide an internal, built-in autonomous and self sustained energy source.     

Re-evaluation of the thermodynamic activity quantities in aqueous alkali metal nitrate solutions at T = 298.15 K

The Hückel equation used in this study to correlate the experimental activities of dilute alkali metal nitrate solutions up to a molality of about 1.5 mol · kg⁻¹ contains two parameters being dependent on the electrolyte: B [that is related closely to the ion-size parameter (a∗) in the Debye–Hückel equation] and b₁ (this parameter is the coefficient of the linear term with respect to the molality and this coefficient is related to hydration numbers of the ions of the electrolyte). In more concentrated solutions up to a molality of 7 mol · kg⁻¹, an extended Hückel equation was used, and it contains additionally a quadratic term with respect to the molality and the coefficient of this term is parameter b₂. All parameter values for the Hückel equations of LiNO₃, NaNO₃, and KNO₃ were determined from the isopiestic data measured by Robinson for solutions of these salts against KCl solutions [J. Am. Chem. Soc. 57 (1935) 1165]. In these estimations, the Hückel parameters determined recently for KCl solutions [J. Chem. Eng. Data 54 (2009) 208] were used. The Hückel parameters for RbNO₃ and CsNO₃ were determined from the reported osmotic coefficients of Robinson [J. Am. Chem. Soc. 59 (1937) 84]. The resulting parameter values were tested with the vapour pressure and isopiestic data existing in the literature for alkali metal nitrate solutions. These data support well the recommended Hückel parameters up to a molality of 7.0 mol · kg⁻¹ for LiNO₃ and NaNO₃, up to 4.5 mol · kg⁻¹ for RbNO₃, up to 3.5 mol · kg⁻¹ for KNO₃, and up to 1.4 mol · kg⁻¹ for CsNO₃ solutions. Reliable activity and osmotic coefficients of alkali metal nitrate solutions can, therefore, be calculated by using the new Hückel equations, and they have been tabulated at rounded molalities. The activity and osmotic coefficients obtained from these equations were compared to the values suggested by Robinson and Stokes [Electrolyte Solutions, second ed., Butterworths Scientific Publications, London, 1959], to those calculated by using the Pitzer equations with the parameter values of Pitzer and Mayorga [J. Phys. Chem. 77 (1973) 2300], and to those calculated by using the extended Hückel equation of Hamer and Wu [J. Phys. Chem. Ref. Data 1 (1972) 1047].     

A new approach in modelling phase equilibria and gas solubility in electrolyte solutions and its applications to gas hydrates

This paper presents a new predictive model for phase equilibria and gas solubility calculations in the presence of electrolyte solutions. It treats salts as pseudo-components in an equation of state (EoS) by defining the critical properties and acentric factor for each salt. The water–salt, gas–salt and salt–salt binary interaction parameters (BIP) have been determined by using available experimental data on freezing point depression and boiling point elevation as well as gas solubility and salt solubility data in saline solutions.The methodology has been applied in modelling sodium chloride, potassium chloride and their mixtures, as well as solubility of methane and carbon dioxide in aqueous single and mixed electrolyte solutions.The developed model is capable of accurately predicting the phase behaviour, gas hydrate stability zone and potential salt precipitation in single and mixed electrolyte solutions. The model predictions are compared with available independent experimental data, including hydrate inhibition characteristics of single and mixed electrolyte solutions, and good agreement is demonstrated.     

Application of Restrictive Primitive SAFT Coupled with Different Hard-Sphere Equations to Model Mean Ionic Activity Coefficients of Electrolyte Solutions

In this work, the primitive SAFT equation of state along with three different hard-sphere equations was used to correlate and predict mean ionic activity coefficients of aqueous electrolyte solutions. The mean ionic activity coefficient of aqueous electrolyte solutions was considered as the contribution of hard-sphere and dispersion effects. The Mansoori (M), Wang-Khoshkbarchi-Vera (WKV) and Ghotbi-Vera (GV) hard-sphere equations were applied in correlating the mean ionic activity coefficient of electrolyte solutions. The comparison among above indicated equations was shown. First, vapor pressure and densities of water in the temperature range of 373.15 to 423.15 K was regressed by SAFT equation of state. In the restrictive primitive mean spherical model, ions were hard spheres without any chain structure. Neither association effects were considered in this study. Clearly, in common used five SAFT parameters were decreased to three, which were calculated by using the experimental mean ionic activity coefficients of electrolyte solutions. The comparison among three hard-sphere equations of state approved that Ghotbi-Vera hard-sphere model (GV) correlated the experimental data accurately than the others; two hard-sphere models. The mean ionic activity coefficients of some electrolyte solutions were being predicted by taking the advantage of the regressed values surely, in a wide range of molality.