Mean Ionic Activity Coefficient Data Research Articles

A new NRTL-based local composition model for thermodynamic modeling of electrolyte solutions

A new local composition model for the expression of excess Gibbs energies and activity coefficients in binary and multicomponent electrolyte solutions is presented in this work. The model is based on the nonrandom two-liquid (NRTL) theory and is developed assuming the random contribution of ions and molecules around central species at reference state. The new model provides a completely new formulation for the expression of short-range interactions in electrolyte solutions. The accuracy of developed equations is examined using the available experimental data for several aqueous electrolyte systems at vast ranges of concentration and temperature. The results are compared with those obtained from eNRTL model. Two binary interaction parameters of the model are adjusted for numerous binary salt-water systems through the accurate correlation of the mean ionic activity coefficient data. Adjusted parameters are then successfully used for the prediction of osmotic coefficients in binary systems. When compared to the eNRTL model, the new model is more accurate. That superiority is very significant for the systems which are highly non-ideal. To examine the adequacy of the model for multicomponent systems, available experimental solubility and osmotic coefficient data of different ternary aqueous electrolyte systems are compared to the values predicted by the model. Using only the previously adjusted binary interaction parameters, the predicted values are in very good agreement with the experimental data.

ECPA: An ion-specific approach to parametrization

The eCPA equation of state has been shown to be a promising electrolyte model, for which several applications have been demonstrated. The model at its current status is, however, limited by the use of salt-specific parameters for the interactions between salts and water. Having salt-specific parameters limit the applicability to simple systems of ions, as it can only be applied when a common ion is found between the salts in the solution. For more complex systems of multiple ions/salts this may not work well. In this work the main goal is to eliminate this limitation by parametrizing the model with an ion-specific parameter set. The ion-specific parameters are estimated by a simultaneous fitting of parameters for 17 ions, consisting of 10 cations and 7 anions, and with data for 55 salts. The parameters are fitted to osmotic coefficient and mean ionic activity coefficient data in a wide temperature range from 273.15 K to above 500 K and up to an ionic strength of 6 molal. The parameters are found to yield similar deviations as the salt-specific parameters, however, for a few salts cation-anion interaction parameters were needed in order to obtain reasonable accuracy.The parameters are applied to a series of systems, which include mixed salt osmotic coefficients, solid-liquid equilibrium and vapor-liquid equilibrium of water-methanol-salt, illustrating the applicability of the ion-specific parameters. Modelling of mixed salt osmotic coefficients illustrate that the parameters work well in salt mixtures, while the phase equilibria alsv o illustrate the extension to mixed solvent systems.

Predicting the thermodynamic properties of experimental mixed-solvent electrolyte systems using the SAFT-VR+DE equation of state

We apply the SAFT-VR+DE equation of state to the study of experimental mixed-solvent electrolyte solutions. In the non-primitive model based SAFT-VR+DE approach (Zhao et al., JCP 2007, 126, 244503) the ions are considered fully dissociated within the solvent that is explicitly treated within the model and the theoretical framework. Typically in the study of electrolyte systems the simpler primitive model is used, which requires knowledge of the experimental dielectric constant. With the non-primitive model the dielectric constant is calculated as part of the theory, which is a particularly attractive feature in the study of mixed-solvent electrolyte systems as data for the experimental dielectric constant of such systems is more scarce. Here for the first time as far as the authors are aware, a non-primitive based equation of state has been used for the study of mixed-solvent electrolytes. The solvents considered (water, methanol and ethanol) are modeled using the SAFT-VR+D approach (Zhao et al., JCP 2007, 127, 084514; Zhao et al., JCP 2006, 125, 104504) in which the contribution of the dipole to the thermodynamics and structure of the fluid are explicitly accounted for. The theory is found to accurately predict the vapor-liquid equilibrium, as well as dielectric properties of the salt free alcohol-water mixtures both at room and elevated temperatures. Ternary mixtures of salt/water/alcohol are then studied using the SAFT-VR+DE parameters for the salts determined in earlier work (Das et al., AIChE Journal 2015, 61, 3053-3072) and a cation-alcohol unlike dispersive energy parameter obtained by fitting to mean ionic activity coefficient data at room temperature and pressure. Thus, with only one adjustable parameter, a predictive SAFT-VR+DE equation to study mixed-solvent electrolyte systems is developed. The SAFT-VR+DE predictions are found to be in good quantitative agreement with mean ionic activity coefficient data for several mixed-solvent electrolyte systems over a wide range of molalities and different solvent ratios. The model is parameterized to allow the molecular level interactions between different cations and the surrounding solvent molecules to be explored.

Modelling of the thermodynamic and solvation properties of electrolyte solutions with the statistical associating fluid theory for potentials of variable range

An improved formulation of the extension of the statistical associating fluid theory for potentials of variable range to electrolytes (SAFT-VRE) is presented, incorporating a representation for the dielectric constant of the solution that takes into account the temperature, density and composition of the solvent. The proposed approach provides an excellent correlation of the dielectric-constant data available for a number of solvents including water, representative alcohols and carbon dioxide, and it is shown that the methodology can be used to treat mixed-solvent electrolyte solutions. Models for strong electrolytes of the metal-halide family are considered here. The salts are treated as fully dissociated and ion-specific interaction parameters are presented. Vapour pressure, density, and mean ionic activity coefficient data are used to determine the ion–ion and solvent–ion parameters, and mixed-salt electrolyte solutions (brines) are then treated predictively. We find that the resulting intermolecular potential models follow physical trends in terms of energies and ion sizes with a close relationship observed with well-established ionic diameters. A good description is obtained for the densities, mean ionic activity coefficients, and vapour pressures of the electrolyte solutions studied. The theory is also seen to provide excellent predictions of the osmotic coefficient and of the depression of the freezing temperature, and provides a qualitative estimate of the solvation free energy. The vapour pressure of aqueous brines is predicted accurately, as is the density of these solutions, although not at the highest pressures considered. Calculations for the vapour–liquid and liquid–liquid equilibria of salts in water+methanol and water+n-butan-1-ol are presented. In addition, it is shown that the salting-out of carbon dioxide in sodium chloride solutions is captured well using a predictive model.

Application of the SAFT-VR equation of state in estimation of physiochemical properties of amino acid solutions

In the present study, the SAFT-VR equation of state has been utilized to examine the phase behavior of aqueous and aqueous-electrolyte solutions of amino acids and simple peptides. The main distinguishing feature of this model, is taking into account the range of interactions as a variable, in addition to other intrinsic qualities of these biomolecules such as diameter, number of segments per chain, energy of interaction and energy and volume of association. At the first stage of the simulation process, the optimized molecular parameters of water, amino acids and simple peptides are respectively obtained by correlating the experimental data of vapor pressure and activity coefficients. Subsequently, the solubility of amino acids in a wide range of temperature is correlated by means of enthalpy and entropy of dissolvation as the adjustable parameters. Afterwards, influence of pH variation on the solubility of amino acids and the phase behavior of one amino acid in the presence of another are predicted. Regarding the importance of equilibrium vapor pressure of aqueous solutions of amino acids in designing the separation units, activity and vapor pressure of water are also predicted. In the next step, the optimized molecular parameters of electrolytes are calculated by correlating the experimental mean ionic activity coefficient data and consequently the activity coefficients and solubility of amino acids in aqueous-electrolyte solutions are predicted.

Thermodynamic Properties of 1:1 Salt Aqueous Solutions with the Electrolattice Equation of State

Thermodynamic Properties of 1:1 Salt Aqueous Solutions with the Electrolattice Equa- tion of State — The electrolattice Equation of State (EOS) is a model that extends the Mattedi- Tavares-Castier EOS (MTC EOS) to systems with electrolytes. This model considers the effect of three terms. The first one is based on a lattice-hole model that considers local composition effects derived in the context of the generalized Van der Waals theory: the MTC EOS was chosen for this term. The second and the third terms are the Born and the MSA contributions, which take into account ion charging and discharging and long-range ionic interactions, respectively. Depending only on two energy interaction parameters, the model represents satisfactorily the vapor pressure and the mean ionic activity coefficient data of single aqueous solutions containing LiCl, LiBr, LiI, NaCl, NaBr, NaI, KCl, KBr, KI, CsCl, CsBr, CsI, or RbCl. Two methods are presented and contrasted: the salt-specific and the ion-specific approaches. Therefore, the aim of this work is to calculate ther- modynamic properties that are extensively used to design, operate and optimize many industrial pro- cesses, including water desalination.

Prediction of vapor–liquid equilibrium and PVTx properties of geological fluid system with SAFT-LJ EOS including multi-polar contribution. Part II: Application to H2O–NaCl and CO2–H2O–NaCl System

The SAFT-LJ equation of state improved by Sun and Dubessy (2010) can represent the vapor–liquid equilibrium and PVTx properties of the CO2–H2O system over a wide P–T range because it accounts for the energetic contribution of the main types of molecular interactions in terms of reliable molecular based models. Assuming that NaCl fully dissociates into individual ions (spherical Na+ and Cl−) in water and adopting the restricted primitive model of mean spherical approximation to account for the energetic contribution due to long-range electrostatic forces between ions, this study extends the improved SAFT-LJ EOS to the H2O–NaCl and the CO2–H2O–NaCl systems at temperatures below 573K. The EOS parameters for the interactions between ion and ion and between ion and water were determined from the mean ionic activity coefficient data and the density data of the H2O–NaCl system. The parameters for the interactions between ion and CO2 were evaluated from CO2 solubility data of the CO2–H2O–NaCl system. Comparison with the experimental data shows that this model can predict the mean ionic activity coefficient, osmotic coefficient, saturation pressure, and density of aqueous NaCl solution and can predict the vapor–liquid equilibrium and PVTx properties of the CO2–H2O–NaCl system over the range from 273 to 573K, from 0 to 1000bar, and from 0 to 6mol/kg NaCl with high accuracy.

A new equation of state for real aqueous ionic fluids based on electrolyte perturbation theory, mean spherical approximation and statistical associating fluid theory

Based on perturbation theory, a new equation of state is developed for real electrolyte aqueous fluids, which is composed of ion–ion, ion–dipole, dipole–dipole, Lennard–Jones dispersion, hydrogen bonding association and hard sphere repulsion terms. The MSA equation from Blum is adopted instead of the perturbed electrostatic term, which simplifies the calculation. The SAFT equation is adopted for the calculation of hydrogen bond association for water molecules. For each electrolyte, only one adjustable parameter, i.e., the cation soft sphere diameter, is regressed. The experimental mean ionic activity coefficient data of 30 aqueous electrolytes (including 1:1, 2:1 and 1:2 electrolytes) were correlated. The parameters thus obtained can be used to predict the densities of these aqueous single electrolyte solutions and the mean ionic activity coefficients in mixed electrolyte aqueous solutions without any additional adjustable mixing parameters.

Study of the ionic activity coefficients in aqueous electrolytes by the non-primitive mean spherical approximation equation

In this paper, the ion-dipole non-primitive MSA model is tested with Monte Carlo simulation data, with a brief discussion, and used to calculate the activity coefficients of single strong electrolyte aqueous solutions up to 3 M (mol kg −1). The water molecule parameters are obtained by fitting the experimental saturated vapor pressure data from 298.15 to 573.15 K with an equation of state derived from the MSA. The average relative deviation in pressure is within 0.5%. The hard-sphere diameters of cations and anions are treated as the adjustable but concentration-independent parameters and are obtained by fitting simultaneously the experimental mean ionic activity coefficient data of 14 electrolyte aqueous solutions. The fitted ionic diameters are smaller than the Pauling diameters. The average relative deviation of the mean ionic activity coefficient is within 6%.

An equation of state for electrolyte solutions. 3. Aqueous solutions containing multiple salts

An equation of state for mixtures containing electrolytes was derived by taking molecule-molecule interactions, charge-charge interactions, and charge-molecule interactions into account by using perturbation expansions based on their potentials. Previous calculations for a large number of aqueous solutions containing single strong or volatile weak electrolytes demonstrated the potential of this equation of state. In this paper, we give a new physical description of this model and extend the work to aqueous systems containing multiple salts. The only adjustable parameter in the model is related to the ionic size. In our previous papers, we had one parameter for each electrolyte (i.e., each ion pair). In this work, we have used a single adjustable parameter for each ion. These parameters were determined from mean ionic activity coefficient data for a large number of single-salt aqueous systems

Simultaneous correlation of activity coefficients for 55 aqueous electrolytes using a model with ion specific parameters

The Liu-Harvey-Prausnitz model (1989a) for electrolyte solutions with ion-specific parameters is extended to simultaneously correlating the mean ionic activity coefficient data for 55 aqueous electrolytes including the H 2SO 4/H 2O system up to the H 2SO 4 concentration of 76 m. With only 1.6 adjustable parameters per aqueous electrolyte, an excellent agreement between the calculated values and the experimental data has been achieved. Ion-specific parameters are reported for 9 cations (H +, Li +, Na +, K +, Rb +, Cs +, Mg ++, Ca ++ and Zn ++) and 8 anions (F −, Cl −, Br −, I −, OH −, NO − 3, CNS − and SO − − 4). The results in this work are compared with those given by the Haghtalab-Vera model (1988) and the outcome is in favor of the Liu-Harvey-Prausnitz model.