Development of a Modified Bromley's Methodology for the estimation of ionic media effects on solution equilibria: Part 3. Application to the construction of thermodynamic models

The development of the Modified Bromley's Methodology (MBM) is extended for the estimation of the activity coefficients of individual species in aqueous solution at 25°C in single and mixed ionic media. The estimation is compared with literature data of activity coefficients of mixtures of electrolytes in water and applied to (a) the prediction of the ionic product of water in aqueous solutions containing different salts which are commonly used as background electrolytes (NaCl, KNO₃ and NaClO₄) and (b) the equilibrium constants of the Cr(VI)–H₂O system.     

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.     

Prediction of solubilities of salts,osmotic coefficients and vapor–liquid equilibria for single and mixed solvent electrolyte systems using the LIQUAC model

The electrolyte model LIQUAC has been used up till now to predict osmotic coefficients, mean ion activity coefficients, the vapor–liquid equilibrium (VLE) behavior, the solubility of gases in single and mixed solvent electrolyte systems, and solubilities of salts in aqueous solutions. In this paper, the required expressions for the calculation of salt solubilities not only in aqueous systems, but also in organic solvents and water–solvent electrolyte systems were deduced in detail based on the LIQUAC model with a fixed reference state and thermodynamic relations. Four salts (NaCl, KCl, NH₄Cl and NaF) and two solvent (water and methanol) were selected to test the derived expressions. The results show that the LIQUAC model with a fixed reference state can be used to predict osmotic coefficients, solubilities of salts in aqueous solutions, vapor–liquid equilibria, and the solubilities of salts in water–organic solvent systems with strong electrolytes.     

Soret coefficients of mixed electrolytes

Practical equations are developed which relate the Soret coefficients of mixed electrolytes to the entropies and enthalpies of transport. The derived equations together with published binary thermal diffusion data can be used to estimate the Soret coefficients of mixed electrolytes. The procedure is illustrated for the systems NaCl+HCl+ water and NaCl+MgCl₂+ water. Aqueous NaCl, like most salts, diffuses to the cold plate in binary Soret experiments. In aqueous HCl solutions, however, NaCl can diffuse to the warm plate, and the magnitude of its Soret coefficient can take values twice as large as those for binary solutions. The thermal diffusion of trace amounts of a salt in a solution containing a large excess of another salt is discussed. Exceptionally large Soret effects are predicted for traces of strong acids in aqueous salt solutions.     

Mutual diffusion coefficients of aqueous MnCl2 and CdCl2, and osmotic coefficients of aqueous CdCl2 at 25°C

Volume-fixed mutual diffusion coefficients have been measured for aqueous MnCl₂ and CdCl₂ solutions from 0.004 to 4.93–5.00 mol-dm^–3 (M) at 25°C. Diffusion coefficients for MnCl₂ decrease to a minimum, rise to a maximum, and then decrease rapidly; such behavior is typical for strong electrolytes. In contrast CdCl₂ diffusion coefficients decrease continuously with concentration; similar behavior is known for certain other associated electrolytes. Since thermodynamic diffusion coefficients for both salts are qualitatively similar, diffusion differences may be primarily due to thermodynamic rather than mobility factors. Isopiestic data were measured for CdCl₂ from 1.79 to 7.29 mol- (kg H₂O)^–1, and critically compared to other isopiestic and emf data for CdCl₂. Higher quality emf data are completely consistent with isopiestic data. Recommended smoothed values of activity coefficients, osmotic coefficients, water activities, and activity derivatives are given for CdCl₂ at 25°C.Work performed under the auspices of the Office of Basic Energy Sciences (Geosciences) of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract number W-7405-ENG-48.     

Enthalpies of Dilution of N,N′-hexamethylenebisacetamide in Pure Water and Aqueous Solutions of Alkali Halide at 298.15 K

Enthalpies of dilution of N,N′-hexamethylenebisacetamide in water and aqueous alkali halide solutions at the concentration of 0.150 mol⋅kg⁻¹ (approximately the concentration of physiological saline) have been determined by isothermal titration microcalorimetry at 298.15 K. The enthalpic interaction coefficients in the solutions have been calculated according to the excess enthalpy concept based on the calorimetric data. The values of enthalpic pair-wise interaction coefficients (h ₂) of the solute in aqueous solutions of different salts were discussed in terms of the different alkali salt ions and weak interactions of the diluted component with coexistent species as well as the change in solvent structure caused by ions.     

Correlation and prediction the activity coefficients and solubility of amino acids and simple peptide in aqueous solution using the modified local composition model

In this work, the modified Wilson model was used to obtain the activity coefficients of amino acids and simple peptides in non-electrolyte aqueous solutions. The Wilson model was modified using the new local mole fraction proposed by Zhao et al. and non-random case for the reference state. The binary interaction parameters (BIP) of the modified Wilson model for amino acid–water pairs were obtained using the experimental data of the activity coefficients for amino acids available in the literature. The modified Wilson model was also used to correlate the solubility of amino acids in water and the values of Δh/R, Δs/R, and Δg/R of the solutions studied were reported. The results obtained showed that the modified Wilson model can accurately correlate the activity coefficients as well as the solubility of amino acids and simple peptides in aqueous solutions. Also the modified Wilson model was coupled with the Pazuki–Rohani model to correlate the mean ionic activity coefficients of electrolytes in aqueous amino acid solutions. The results showed that the proposed model can accurately correlate the activity coefficients of the electrolytes in aqueous amino acid solution.     

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.     

Study of the reaction Fe(CN)5(4‐CNpy)3− + S2O82− in aqueous salt and micellar solutions

The reaction Fe(CN)₅(4‐CNpy)³⁻ + S₂O₈²⁻ (4‐CNpy=4‐cyanopyridine) was studied in aqueous salt solutions in the presence of several electrolytes as well as in anionic, cationic, and nonionic surfactant solutions. In aqueous salt solutions the noncoulombic interactions seem to be important in determining the positive salt effects observed. The salting effects are influencing the activity coefficients of any participant in the reaction, including those ion pairs which can be formed between the anionic reagents and the cations which come from the added salts. The changes in surfactant concentration in anionic and nonionic surfactant solutions do not affect the reaction rate, which is similar to that in pure water at the same ionic strength. In cationic micellar solutions an increase in the rate constant compared to that in pure water is found; the reaction rate decreasing when the surfactant concentration increases. The kinetic trends can be explained assuming that the reagents are totally bound to the micelles and, therefore, an increase in the surfactant concentration results in a decrease in the reagent concentrations at the micellar phase and thus in a decrease in the observed rate constant. © 1999 John Wiley & Sons, Inc. Int J Chem Kinet: 31: 229–235, 1999     

Thermodynamic models of aqueous solutions containing inorganic electrolytes and dicarboxylic acids at 298.15 K. 1. The acids as nondissociating components

Atmospheric aerosols contain a significant fraction of water-soluble organic compounds, including dicarboxylic acids. Water activities at approximately 298.15 K (including data for highly supersaturated solutions) of oxalic, malonic, succinic, glutaric, maleic, malic, and methyl succinic acids are first correlated as a function of concentration, treating the acids as nondissociating components. Methods proposed by Clegg et al. (J. Aerosol. Sci. 2001, 32, 713-738), and by Clegg and Seinfeld (J. Phys. Chem. A 2004, 108, 1008-1017) for estimating water activities and solute activity coefficients in aqueous mixtures containing both electrolytes and uncharged solutes are then evaluated from comparisons with literature data. These data include water activities, solubilities, and determinations of the eutonic points of solutions containing up to five acids, and solutions containing one or more acids and the salts (NH(4))(2)SO(4), NH(4)NO(3), or NaCl. The extended Zdanovskii-Stokes-Robinson approach of Clegg and Seinfeld yields the more accurate predictions for aqueous mixtures containing dicarboxylic acids only, and for aqueous mixtures of the acids and salts (though by a lesser margin). A number of hybrid modeling approaches, which contain elements of both methods, are outlined.     

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.     

Diffusion of Aqueous Solutions of CoCl2, Co(NO3)2, and Cu(NO3)2 in Porous Glass Membranes

Diffusion coefficients of CoCl₂, Co(NO₃)₂, and Cu(NO₃)₂ salts, characterizing permeation of their aqueous solutions across glass membranes with predominant pore radius in the range from 70 to 4.5 nm are determined. With pores in the membranes becoming narrower, the diffusion mobility of the electrolytes decreases.     

Experimental Study on Viscosity of Colloidal Silica in Aqueous Electrolytic Solutions

The relative viscosity of colloidal silica dispersion in aqueous electrolytic solutions as the function of volume fraction of dry particles in the solutions has been experimentally determined in this work, in order to study the effects of pH and electrolytes (Na₂SO₄ and AlCl₃) on the hydration of the silica surfaces in the solutions. The results have shown that the maximum relative viscosity of the silica dispersion and the strongest hydration of the silica in aqueous solutions appeared at neutral pH, while the stronger the acidity and the alkalinity of the aqueous solution, the weaker the hydration. In the presence of the electrolytes (Na₂SO₄ and AlCl₃), the relative viscosity of the silica dispersion reduced and the hydration of the silica in aqueous solutions became weak. The higher the concentration of the electrolytes, the weaker the hydration, indicating that the destabilization of the colloidal silica dispersion in aqueous solutions might be realized through adding the high-valence electrolytes to weaken the hydration of the particle surfaces (hydration forces between the particles). Also, it has been shown that the negative zeta potentials of the colloidal silica in aqueous solutions greatly reduced in the presence of the electrolytes. Therefore, the high-valence electrolytes (Na₂SO₄ and AlCl₃) as the coagulant of colloidal silica in aqueous solutions might be originated from that the presence of the electrolytes simultaneously reduces the electrical double layer repulsive force and the hydration repulsive forces between the particles in aqueous solutions.     

Thermodynamics of ionic solid solutions. A new treatment of existing distribution data

Excess amounts of two isomorphous salts, which differ with respect to only one ion (the exchanging ions), added to water and equilibrated produce an aqueous solution of the two salts and a solid solution of one salt in the other. The ratio of the two salts in the liquid phase is, in general, different from that in the coexisting solid. Data for twenty-nine such systems, including pairs of double salts (alums and picromerites), and pairs of simple salts, at or near 25°C, have been reviewed. By making the plausible assumption that the activity coefficients of the exchanging ions in the liquid phase are equal, it has been possible to derive the activity coefficients of the salts in the solid phase in addition to the thermodynamic equilibrium constants for the distributions. The interpretation of the data is compared with that of an earlier paper which drew different conclusions and was based on what is shown to be an erroneous premise. Solid solutions of alums are found, for the most part, to be ideal or nearly so. Of nine picromerite solid solutions containing sulfate as the only anion, seven pairs deviate positively from ideality, one deviates negatively, and one shows both positive and negative deviations. Three other picromerite pairs involving exchange of sulfate, selenate, and chromate ions, show only negative deviations. For the pairs [(NH₄)₂,K₂]SO₄, (NH₄,K)Cl, Ag(Cl,Br), K(Br,Cl), Rb(Br,Cl), (Rb,K)Br, and (Rb,K)Cl the deviations are positive; those for Pb(Cl,Br)₂ are negative, and those for Ba(ClO₃)₂·H₂O are both positive and negative. Independent supporting evidence for some of the conclusions is presented.     

Nonelectrolyte NRTL-NRF model to study thermodynamics of strong and weak electrolyte solutions

An electrolyte activity coefficient model is proposed by combining non-electrolyte NRTL-NRF local composition model and Pitzer–Debye–Hückel equation as short-range and long-range contributions, respectively. With two adjustable parameters per each electrolyte, the present model is applied to correlation of the mean activity coefficients of more than 150 strong aqueous electrolyte solutions at 298.15 K. Also the results of the present model are compared with the other local composition models such as electrolyte-NRTL, electrolyte-NRTL-NRF and electrolyte-Wilson-NRF models. Moreover, the present model is used for prediction of the osmotic coefficient of several aqueous binary electrolytes systems at 298.15 K. Also the present activity coefficient model is adopted for representation of nonideality of the acid gases, as weak gas electrolytes, soluble in alkanolamine solutions. The model is applied for calculation of solubility and heat of absorption (enthalpy of solution) of acid gas in the two {(H₂O + MDEA + CO₂) and (H₂O + MDEA + H₂S)} systems at different conditions. The results demonstrate that the present model can be successfully applied to study thermodynamic properties of both strong and weak electrolyte solutions.     

Thermodynamics of ionic solid solutions: II. Discontinuous series: A new treatment of existing distribution data

A method of finding the activity coefficients of salts, anhydrous or hydrated, in binary solid solutions, described in an earlier paper as it applies to continuous series, has been applied to discontinuous series. The salts must differ with respect to only one ion. The method requires isothermal distribution data for equilibria between liquid (aqueous) and solid solutions in the ternary system consisting of the two salts and water. The following salt pairs were used for illustration: K(I/Br) at 0, 15, 25, 35, and 50°C., (NH₄/K)SCN at 0, 30, 60, and 90°C., (K/Tl)C10₃ at 10°C., and (NH₄/K)SO₃NH₂, (NH₄/K)Br, (Mg/Co)SO₄-7H₂O, and (Mn/Cu) SO₄.n H₂O-all at 25°C. Two kinds of behavior were noted and treated differently: systems in which the two series have the same, and those in which they have different crystal lattices. For two salts, A and B, which have the same lattice, and whose rational activity coefficients, f _A and f _B , can be described by 2-suffix Margules equations (regular solutions), lnf _A =B_sx _B ² and lnf _B =B_sx _A ² to be partially miscible, B_s>2, but this requirement does not apply if the lattices are different. In each series, distribution constants for the equilibria were also determined. Where possible, the calculated activities of the salts or the Gibbs excess energies of the solid solutions were compared with values reported by others who determined them by other methods. All the salt pairs studied show slight or strong positive deviations from ideality.     

Thermodynamic Properties of Aqueous Glucose–Urea–Salt Systems

In this work, the thermodynamic behavior of aqueous solutions containing the solutes NaCl, glucose, and/or urea is investigated. These substances are vital components for living bodies and further they are main components of blood serum. Osmotic coefficients were determined by cryoscopic measurements in single-solute and multi-solute aqueous solutions containing salts (NaCl, KCl, CaCl₂), glucose, and/or urea. The results show that NaCl determines the osmotic coefficients in the urea/glucose/NaCl/water system. Investigation of the effect of different salts on osmotic coefficients revealed ion-specific effects. At physiologically important solute concentrations in typical blood serum solutions, the osmotic coefficients were found to be in the range of 0.90–0.93. In a second step, the state of water in different glucose/salt/water and urea/salt/water systems was investigated. Depending on the kind of salt, the chemical potential of water in urea/salt/water is either higher or lower than in glucose/salt/water systems at equal nonelectrolyte concentrations. This result was found to be independent of the salt molality. Finally, the investigated systems were modeled with the Pitzer model and the ePC-SAFT equation of state, which allowed predicting of the properties of these multi-solute aqueous solutions.     

A new model for the activity coefficients of individual ions in aqueous electrolyte solutions

In this study, the individual ion activity coefficient in an aqueous solution is modeled with a new model. This model contains two physical significant ionic parameters regarding the ionic solvation and the closest distance of approach between ions in a solution. The present model was evaluated by the estimation of the individual activity coefficients of the ions of thirty electrolytes in aqueous solutions. The results showed that this model suitably predicts the individual ion activity coefficients in aqueous two-electrolyte solutions consisting of the binary pairs of electrolytes of NaCl, KCl, KBr and CaCl₂ in a temperature range from 298.15 to 243.15 K. The results by this model were compared to the literature values. The average absolute relative deviations of vapor pressures showed acceptable agreement between experimental data and the results of this model.     

The osmotic and activity coefficients of some guanidinium salts at 298.15 K

Osmotic and activity coefficients are reported for aqueous solutions of six guanidinium salts at (298.15 ± 0.01) K, and these coefficients are compared with those of other uni-univalent electrolytes. The results are consistent with previously reported spectral results that indicated hydrogen bonding of guanidinium ion with chloride ion in aqueous solutions.     

Activity coefficients of alkyl sulfate and alkylsulfonate ions in aqueous and water-salt premicellar solutions

Potentiometry has been employed to determine the activity coefficients of n-decyl sulfate and n-alkyl(C₅–C₁₀)sulfonate ions in aqueous solutions of their sodium salts containing NaCl or Na₂SO₄ as a background electrolyte. The selectivity factors have been estimated for ion-selective electrodes exhibiting responses to surfactant ions in the presence of inorganic salts. The pattern of the dependences of the activity coefficients of the surfactant anions on the length of their hydrocarbon radicals and the nature of functional groups has been revealed. The results obtained have been compared with the data on long-chain carboxylates.