Comparative Evaluation of Six Electrolyte Local Composition Activity Coefficient Models Applied to Binary Aqueous Solutions of Ionic Liquids

The capability of six popular local composition models including electrolyte NRTL, modified electrolyte NRTL, electrolyte NRTL–NRF, electrolyte Wilson, modified electrolyte Wilson, and electrolyte NRF–Wilson models to predict the activity coefficients of ionic liquids in aqueous solutions was examined by correlating the experimental data of 16 ionic liquids available in the literature. The adjustable parameters and standard deviations of the fit were estimated for all of these models. Results indicate that the modified electrolyte Wilson model represents the activity coefficients with higher precision.     

A Modified Local Composition-Based Model for Correlating the Vapor-Liquid and Liquid-Liquid Phase Equilibria of Aqueous Polymer-Salt Systems

In this research, a new local composition model has been proposed to study the vapor-liquid and liquid-liquid phase equilibria of polyelectrolyte solutions. The proposed model has been used in order to obtain the activity of water in polyethylene glycol (PEG) and polypropylene glycol (PPG) solutions. The interaction parameters introduced into the proposed model have been reported. The interaction parameters between the salt and water molecule have been estimated using the experimental mean ionic activity coefficients of aqueous electrolytes studied in this work. Also, the interaction parameters between the polymer and salt molecule, and the polymer and water molecule have been computed using the experimental activity of water data in aqueous polymer solutions. The results showed that the proposed model, segment-based Wilson and segment-based NRTL models have good accuracy in correlating the vapor-liquid phase equilibria of the water-polymer and water-polymer-salt systems. Also, the liquid-liquid phase behavior of the polymer-salt aqueous two-phase systems has been correlated using the proposed model. The results show that the proposed model can more accurately correlate the phase behavior of aqueous two-phase systems than the UNIQUAC and the modified Wilson models.     

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 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.     

Investigation of 1-(2-carboxyethyl)-3-methylimidazolium chloride[HOOCEMIM][Cl] ionic liquid effect on water activity and solubility of l-serine at T = 298.15 K

Water activity measurements by the isopiestic method have been carried out on the aqueous ternary system of {l-serine + 1-(2-carboxyethyl)-3-methylimidazolium chloride[HOOCEMIM][Cl]} ionic liquid and the aqueous binary system of IL at T = 298.15 K and atmospheric pressure. The data obtained were used to calculate the vapor pressure and osmotic coefficient of solution as a function of concentration. The experimental results for the activity of water were accurately correlated with segment-based local composition models of modified NRTL and UNIQUAC. The fitting quality of the above models has been favorably compared with the NRTL and Wilson models. From these data, the corresponding activity coefficients have been calculated. For the same system, the solubility of the l-serine at various [HOOCEMIM][Cl] ionic liquid concentrations was measured at T = 298.15 K using the gravimetric method. A chemical model was employed to describe the dissociation equilibria of all amino acid species with hydrogen ions in water. Moreover, for l-serine, the chemical model indicated that the formation of cations is insignificant in the [HOOCEMIM][Cl] solution. Also the above local composition models were used to predict the solubility of l-serine in aqueous IL solutions. To provide information regarding (solute + solute) interactions, transfer Gibbs free energies (ΔG_tr) of amino acid from water to aqueous IL solutions have been determined.     

A new model for predicting activity coefficients in aqueous solutions of amino acids and peptides

A new two-parameter model based on the perturbation of a hard-sphere reference has been developed to correlate the activity coefficients of several amino acids and simple peptides in aqueous solutions. The hard-sphere equation of state used as the reference in the model was proposed recently by Ghotbi and Vera. The perturbation terms coupled with the reference hard-sphere equation of state are attributed to the dispersion forces and the dipole–dipole interactions. The Lennard-Jones and Keesom potential functions are used to represent the dispersion and dipole–dipole interactions, respectively. The results of the new model are compared with those obtained by other models. It is shown that the new model can more accurately correlate the activity coefficients of amino acids and peptides in comparison with the other available models in the literature. The model was also used to correlate the solubility of several amino acids in aqueous solutions. The results show that the model can accurately correlate the solubility of the experimental data over a wide range of temperatures with only two adjustable parameters. New values for Gibbs free energy change, Δg, and enthalpy change, Δh, of the solute, i.e., amino acid for transferring one mole of solute from a saturated solution to a hypothetical aqueous solution with an activity of one molal at temperature 298.15 K are also reported.     

Vapor pressures and apparent molal volumes of the solutions of ZnCl2 in ethanol at 298.15 K

Vapor pressures and apparent molal volumes of solutions of ZnCl₂ in ethanol are reported at 298.15 K. The vapor pressure of ethanol has been evaluated from the osmotic coefficients measured by an improved isopiestic method. The experimental osmotic coefficients have been correlated with the Pitzer model and local composition models including electrolyte non-random two liquid (e-NRTL), non-random factor (NRF), modified NRTL (MNRTL) and extended Wilson (EW) models. Apparent molal volumes have been calculated from the densities of the solutions measured by a vibrating-tube densimeter, and fitted with the volumetric equations based on the Pitzer model and the local composition models. All of the models successfully correlate the experimental osmotic coefficients and apparent molal volume data.     

Interpreting freezing point depression of stearic acid and methyl stearate

Freezing point depressions of binary systems including either stearic acid (SA) or methyl stearate (MES) were evaluated based on differential scanning calorimetry melting scans. The second binary component included a solvent from the group acetic acid, acetone, 2-butanone, and hexane. Vapor pressure as a function of liquid composition and temperature was used to measure vapor/liquid equilibrium. Activity coefficients were calculated from this data and models fit to the data to determine how well the models fit the solid–liquid equilibrium models.The Gibbs/Duhem equation and polymorphism of the melt transitions indicated that freezing point depressions were due to a combination of: (1) a reduction of activity of the triglyceride derivative in solution albeit with activity coefficients > 1.0, (2) incorporation of the solvent into the solid matrix for at least some of the mixtures, and (3) substantially different physical properties between the solid and liquid phases of the SA and MES. Different melting phenomena were observed in differential scanning calorimetry (DSC) scans depending upon the heteroatom functionality of the solvent.The empirical Margules, NRTL, and Wilson activity coefficient models fit data for the solvent activity coefficients well, while the UNIQUAC model combined with the predictive abilities of UNIFAC could not accurately predict activity coefficients. Despite questions on the fundamental interpretation of the data, modeling the activity coefficients for the solvent is sufficient to approximate the effect the solvent will have on the melting point depression. Relatively simple experiments following the total pressure of mixtures as a function of composition and temperature can be used to obtain activity coefficient model parameters for the Margules, NRTL, UNIQUAC, and Wilson.     

Correlation of phase equilibria of amino acids and peptides in aqueous solution based on the perturbation theory of equation of state

In this paper, the activity coefficients of amino acids and simple peptides in aqueous solutions were correlated by using a three parameters model based on the perturbation theory. The adjustable parameters of this model were obtained from the experimental data and a relation for calculating the activity coefficient is derived. The calculated activity coefficients of amino acids and simple peptides obtained show that the equation of state based on the perturbation model can be used to correlate the activity coefficients of amino acids more accurately than the other models. A correlation for the solubility of amino acids in aqueous solutions is also derived. The results show that this correlation can accurately correlate the solubility of amino acids in aqueous solution over a wide range of temperatures (0–100 °C).     

Thermodynamic representation of phase equilibrium behavior of aqueous solutions of amino acids by the modified Wilson model

The polymer–electrolyte Wilson model [R. Sadeghi, J. Chem. Thermodyn. 37 (2005) 323–329] which has a molecular thermodynamic framework has been extended to model the vapor–liquid and liquid–solid equilibrium behavior of amino acids and small peptides in aqueous solutions as functions of temperature, ionic strength and amino acid compositions. The utility of the model is demonstrated with a successful representation of the activity coefficients and the solubility of several amino acids in different aqueous solutions and the results are compared with those obtained from the NRTL model.     

New local composition model for electrolyte solutions

A new model for representation of the excess Gibbs energy of electrolyte solutions is proposed. The excess Gibbs energy of an electrolyte solution is expressed as a sum of contributions of a long-range and a short-range excess Gibbs energy term. The Pitzer–Debye–Hückel model is used as a long-range contribution to the excess Gibbs energy. A new expression based on the local composition concept, which is the non-random factor (NRF)–Wilson model, is developed to account for the short-range contribution to the excess Gibbs energy. The main difference between this model and the electrolyte-NRF model available in the literature is the assumption that the short-range energy parameter between species in a local cell has an enthalpic rather than Gibbs energy nature. The utility of the model is demonstrated with the successful representation of the mean ionic activity coefficient of several aqueous electrolyte solutions. The results show that with only two adjustable parameters per electrolyte, the model is valid for the whole range of electrolyte concentration, from dilute solution up to saturation. The results are compared with those obtained from the NRTL, NRF and Wilson models. The model presented in this work produces better results.     

Phase equilibria in the ternary system ethyl 1,1-dimethylethyl ether+heptane+octane

Vapor–liquid equilibrium at 94 kPa has been determined for the ternary system ethyl 1,1-dimethylethyl ether (ETBE)+heptane+octane. The system deviates slightly from ideality and no azeotrope is present. The ternary activity coefficients and the boiling points of the system have been correlated with the composition using the Redlich–Kister, Wilson, NRTL, UNIQUAC, UNIFAC, and Wisniak–Tamir relations. Most of the models allow a very good prediction of the activity coefficients of the ternary system from those of the pertinent binary systems.     

Liquid–liquid equilibrium data for binary alcohol + n-alkane (C10–C16) systems: methanol + decane,ethanol + tetradecane,and ethanol + hexadecane

Liquid–liquid equilibrium (LLE) data for three binary alcohol + n-alkane (C₁₀–C₁₆) systems—methanol + decane, ethanol + tetradecane, and ethanol + hexadecane—were measured using a laser scattering technique. The experimentally determined cloud points were satisfactorily correlated by three local composition models (NRTL, Tsuboka–Katayama’s modification of the Wilson equation, and the modified complete local composition model suggested by Nagata and Tamura). Prediction of vapor–liquid equilibria by means of these models with parameters obtained from the LLE data was also tested.     

A note on excess Gibbs energy models,equations of state and the local composition concept

A density-dependent local composition expression for the residual energy is derived from a generalized NRTL expression for the excess energy and the van der Waals fluid theory. Integration of this expression yields a volume-dependent expression for the Helmholtz energy from which equations of state utilizing the local composition concept are derived and which in the high-density limit contain the well-known activity coefficient models.The local composition versions of the Carnahan—Starling—van der Waals, the Redlich—Kwong—Soave and the Peng—Robinson equations of state are derived. It is further shown that the group contribution versions of the NRTL, the Wilson and the UNIQUAC excess models may be derived from the generalized NRTL expression for the residual energy when applied to groups instead of molecules.It is thus demonstrated that all current local composition activity-coefficient models can be derived from a local composition version of the van der Waals equation of state using different sets of assumptions. In the same way the van Laar, the Scatchard—Hildebrand and the Flory—Huggins activity coefficient models are obtained from the van der Waals equation of state using the original mixing rules.     

Isopiestic study of the solutions of MnCl2, CoCl2 and NiCl2 in methanol and ethanol at 298.15 K

Osmotic coefficients of the solutions of three divalent transition metal chlorides (MCl₂; M = Mn, Co, Ni) in methanol and ethanol have been measured by isopiestic method at 298.15 K. Vapor pressures of the solutions have been evaluated from osmotic coefficients and their depression was used for qualitative deduction of the solute–solvent interactions occurring in these solutions. The osmotic coefficients have been correlated using local composition models (including electrolyte non random two liquid (e-NRTL), non random factor (NRF) and modified NRTL (mNRTL) models) and the Pitzer model. The capability of the considered models was compared on the basis of the standard deviation in osmotic coefficients. The models give reliable results in correlation of the osmotic coefficients. However, the results show that the Pitzer and the mNRTL models successfully correlate the osmotic coefficients, however e-NRTL and NRF models give larger standard deviations.     

Isobaric vapor–liquid equilibria of three aromatic hydrocarbon-tetraethylene glycol binary systems

Isobaric vapor–liquid equilibrium data have been determined at 101.33 kPa for the binary mixtures of benzene-tetraethylene glycol (TeEG), toluene-TeEG and o-xylene-TeEG. The vapor-phase fugacity coefficients were calculated from the virial equation. The thermodynamic consistency of the data has been tested via Herington analysis. The binary parameters for four activity coefficient models (van Laar, Wilson, NRTL and UNIQUAC) have been fitted with the experimental data. A comparison of model performances has been made by using the criterion of root mean square deviations in boiling point and vapor-phase composition.     

水合物反应液中水活度系数模型研究进展

水合物反应液中水活度系数的计算对水合物相平衡特性的研究及水合物技术的应用具有重要意义。 通过调研大量的国内外资料,概括了Margules、Wilson、NRTL、UNIQUAC及UNIFAC活度系数方程及其关联式等模型及其应用,结果表明,Margules模型常用于二元体系活度系数的计算,但对高温高压体系条件下的溶液适用性较差;Wilson模型参数回归误差稍大且不适于溶质与离子不能完全互溶体系;UNIQUAC模型在含水或咪唑类离子反应液体系中误差较大;多元离子体系相平衡的研究中常选择NRTL模型;UNIFAC模型拟合效果较好,可实现较高浓度体系活度系数的精确计算,应用较广泛。 水活度关联方程参数拟合效果好,且准确度高,但在高温高压水合物反应液体系中的计算仍是一个技术难点,是今后的研究方向。     

Use of the NRTL equation for simultaneous correlation of vapour-liquid equilibria and excess enthalpy

The NRTL model has been used to correlate the data for the aqueous alkanolamine systems of (MEA+H₂O), (DEA+H₂O) and (MDEA+H₂O). The model was successfully applied to correlate simultaneously the excess enthalpy, vapour-liquid equilibria, and low temperature activity coefficients. A large database of data was collected for the investigation and it covers a wide range of composition, temperature and pressures. It was found that the form of the binary interaction parameters used by Posey (1996) with a variable non-randomness parameter gave the best results.