Activity Coefficients Of Solutions Research Articles

Determination of gas–liquid partition coefficients of several organic solutes in trihexyl(tetradecyl)phosphonium bromide using capillary gas chromatography columns

In this paper, we report gas-liquid partition constants for thirty-five volatile organic solutes in the room temperature ionic liquid trihexyl(tetradecyl)phosphonium bromide measured by gas-liquid chromatography using capillary columns. The relative contribution of gas-liquid partition and interfacial adsorption to retention was evaluated through the use of columns with different the phase ratio. Four capillary columns with exactly known phase ratios were constructed and employed to measure the solute retention factors at four temperatures between 313.15 and 343.15K. The partition coefficients were calculated from the slopes of the linear regression between solute retention factors and the reciprocal of phase ratio at a given temperature according to the gas-liquid chromatographic theory. Gas-liquid interfacial adsorption was detected for a few solutes and it has been considered for the calculations of partition coefficient. Reliable solute's infinite dilution activity coefficients can be obtained when retention data are determined by a unique partitioning mechanism. The partial molar excess enthalpies at infinite dilution have been estimated from the dependence of experimental values of solute activity coefficients with the column temperature. A thorough discussion of the uncertainties of the experimental measurements and the main advantages of the use of capillary columns to acquire the aforementioned relevant thermodynamic information was performed.

An Evaluation of Four Electrolyte Models for the Prediction of Thermodynamic Properties of Aqueous Electrolyte Solutions

In this work, the performance of four electrolyte models for prediction the osmotic and activity coefficients of different aqueous salt solutions at 298 K, atmospheric pressure and in a wide range of concentrations are evaluated. In two of these models, (electrolyte Non-Random Two-Liquid e-NRTL and Mean Spherical Approximation-Non-Random Two-Liquid MSA-NRTL), association between ions of opposite charges for simplification purposes is ignored and in the other two ones, (Associative Mean Spherical Approximation-Non-Random Two-Liquid AMSA-NRTL and Binding Mean Spherical Approximation BiMSA) association and solvation effects are considered. The predictions of these four models for the osmotic and activity coefficients of electrolyte solutions at 298 K and atmospheric pressure are compared with the experimental data reported in the literature. This comparison includes, 28 different aqueous salt solutions including thio-cyanates, perchlorates, nitrates, hydroxides, quaternary ammonium salts and others. The results show, the performance of models that consider association effects are better than others especially for higher salt concentrations. However, the best performance belongs to BiMSA model which has some parameters with physical meaning.

Application of Pitzer and six local composition models to correlate the mean ionic activity coefficients of aqueous 1-butyl-3-methylimidazolium bromide ionic liquid solutions obtained by EMF measurements

The mean ionic activity coefficients of aqueous 1-butyl-3-methylimidazolium bromide ([BMIm]Br) solutions in the concentrations ranging from 0.008 to 0.215mol·kg−1 were determined using potentiometric measurements at T=308.15, 318.15, and 328.15K. The obtained experimental data were correlated using the Pitzer and several local composition models, such as the non-electrolyte Wilson-NRF (N-Wilson-NRF), electrolyte Wilson-NRF (E-Wilson-NRF), electrolyte Wilson (E-Wilson), electrolyte NRTL (E-NRTL), modified electrolyte NRTL (ME-NRTL), and electrolyte NRTL-NRF (E-NRTL-NRF) models. The Pitzer parameters obtained were used to calculate the osmotic coefficients and excess Gibbs free energies of the solutions being studied. The results indicate that in general all the models used here can be successfully applied to predict the mean ionic activity coefficients of the aqueous ionic liquid solutions. However, the average standard deviations of the fit show that the NRTL based models represent the mean ionic activity coefficients with better precision.

Off-Lattice Flory–Huggins Approximations for the Tailored Calculation of Activity Coefficients of Organic Solutes in Random and Block Copolymers

Predicting activity coefficients in polymers for arbitrary solute and polymers is of general interest for packaging, environmental, and membrane applications. We examined the extensions of the proposed off-lattice approach [Gillet et al. Ind. Eng. Chem.Res. 2009, 2010] for random and block copolymers. Based on a comparison with an explicit representation of random copolymers, the principles of a mean-field approximation using only the properties of homopolymers have been established. The approach was successfully validated against the Flory–Huggins coefficients collected by Fornasiero et al. [AIChE J. 2002] for 19 aromatic solutes in ethylene-vinyl acetate with acetylation rates varying from 33% to 100%. The role of substituents and isomerism is elucidated. Previously collected data and this study suggest that the real chemical affinity of substituted aromatic compounds for water could be strongly underestimated by previous oversimplified rules and that tailored methods, such as this one, would be preferable.

An overview of the performance of the COSMO-RS approach in predicting the activity coefficients of molecular solutes in ionic liquids and derived properties at infinite dilution.

This paper reports a comprehensive evaluation of the conductor-like screening model for real solvents (COSMO-RS) in predicting infinite dilution activity coefficients (γ∞) of molecular solutes in ionic liquids (ILs). In particular, comparative analysis of two quantum chemical levels of calculations used in the COSMO part of COSMO-RS, namely, TZVP-COSMO and TZVPD-FINE, is presented and discussed. The final assessment of the model performance is established based on a comparison of its predictions with the experimental data pool consisting of 41 868 data points extracted form 182 references, covering 233 ILs (including salts belonging to 12 different cationic families) and 150 molecular solutes (including a great variety of non-polar, polar and self-associating organic compounds and water) combined with 8554 distinct binary systems. The impact of the chemical family of both IL and molecular solute on the accuracy of the COSMO-RS predictions is analyzed in terms of both quantitative and qualitative measures. Relevant thermodynamic properties derived from γ∞, namely, infinite dilution partial excess enthalpy of mixing and infinite dilution selectivity are considered and their values obtained from experimental and COSMO-RS predicted γ∞ data are confronted. Finally, the impact of the molecular conformation of cations/anions/solutes on the quality of predictions is demonstrated based on some representative systems.

ACTIVITY COEFFICIENTS OF Ti AND V IN IRON MELTS FROM NITRIDE FORMATION DATA

Thermodynamic data about the TiN and VN formation in iron melts were obtained at the National University of Science and Technology “MISIS” using advanced Sieverts apparatus based on the compensation method of gas volume and pressure measuring using high-sensitive zero reader (pressure sensor). Using of such method for gas – metal interaction investigations was early offered and realized at Chelyabinsk Institute of Metallurgy by Professor A.G. Ponomarenko. Obtained experimental data were used for the calculations of Ti and V initial activity coefficients in the iron-based solutions. Thus the refined Gibbs energy values of VN formation from elements were used. Obtained values for the Ti and V initial activity coefficients in the ironbased solutions: = 0.055 and = 0.24 are compatible with the literature data.

The Fugacity Coefficient of Non-Ideal Gas and Activity Coefficient of Non-Ideal Solution

The Fugacity Coefficient of Non-Ideal Gas and Activity Coefficient of Non-Ideal Solution

Surface, micellar, and thermodynamic properties of antidepressant drug nortriptyline hydrochloride with TX-114 in aqueous/urea solutions

This paper deals with a comprehensive study of the mixed micellization and adsorption behavior of mixed systems enclosing an amphiphilic antidepressant drug nortriptyline hydrochloride (NOT) and Triton X-114 (TX-114) (nonionic surfactant) in aqueous/urea (500 mmol·kg−1 and 1000 mmol·kg−1) solutions by tensiometric method. The NOT is used for the cure of depression. For comparison purpose cmc value of pure drug NOT was also evaluated by conductimetric technique. Different theoretical models like Clint, Rubingh, and Rosen were used to get information about the nature of interaction between the components in bulk and at the interface. Because of the occurrence of urea increase in the surface charge of the micelles was obtained resulting a delay of the micelles formation. The cmc values of the mixed systems of NOT and TX-114 were found to be in between the cmc values of pure components, which signify nonideal mixed system having attractive interactions in the absence and presence of urea. Various parameters such as micellar mole fractions of TX-114 (X1m, X1σ) in solution and at interface, interaction parameter (βm/βσ) in solution and at interface, and activity coefficient in solution and at interface were evaluated and discussed using Rubingh's and Rosen's models. Surface excess (Γmax) increases that means minimum area per head group (Amin) decreases as mole fraction (α1) of TX-114 increases in the absence/presence of urea. Different thermodynamic parameters have been calculated and discussed. The ∆G0m values achieved are all negative both in the absence and occurrence of urea.

The implementation of ion-based ePC-SAFT EOS for calculation of the mean activity coefficient of single and mixed electrolyte solutions

Following our previous work (Journal of Molecular Liquids 221 (2016) 904–913), the modified perturbed chain statistical associating fluid theory (ePC-SAFT) incorporated with Debye-Huckel term has been applied to calculate some thermodynamic properties of single and mixed electrolyte solutions. The applicability of this model has been investigated by calculation of the mean ionic activity and osmotic coefficients of electrolyte solutions as well as the water activity of regarded systems at different temperatures. Firstly, water-ion hydration has been taken into account independently by two individual strategies, i.e. ions can be considered as non-associating and associating compounds distinctly. Afterwards, a new set of ion parameters containing 31 common ions has been estimated using the experimental mean ionic activity coefficients and liquid densities of 78 binary electrolyte solutions in both strategies. The optimized parameters which have been utilized for prediction of single-salt aqueous electrolyte solutions MIACs up to 373.15 K are global and transferable to different salts. Eventually, it can be observed that not only the density of aqueous electrolyte solutions, but also MIACs, osmotic coefficients and water activity of single and mixed salt solutions are satisfactorily calculated by considering ions as association compounds over a wide range of temperature and salt concentration.

Improving Estimates of the Crystallization Driving Force: Investigation into the Dependence on Temperature and Composition of Activity Coefficients in Solution

In this work the influence of temperature and composition on the activity coefficient in solution has been investigated, based on isothermal and isobaric vapor–liquid equilibrium data for 30 binary systems classified into four groups: water–organic, polar–polar, polar–nonpolar, and nonpolar–nonpolar systems. It is shown that under most conditions the temperature dependence of the activity coefficient is clearly weaker than the composition dependence. The analysis is extended to include solid–liquid solubility data of 15 binary systems of relatively large and complex organic molecules in organic solvents. Based on this, a novel approach to estimate the thermodynamic driving force of crystallization from solution is proposed. Rather than assuming that the activity coefficient ratio equals unity, it is shown that in most cases a more accurate assumption is to neglect only the temperature dependence of the activity coefficient. This allows the activity coefficient ratio to be estimated from solid–liquid equil...

Investigation of multi-component liquid adsorption of alkylaromatics in NaX zeolite using novel gas chromatographic headspace techniques

In this study, adsorption isotherms of o-xylene, ethylbenzene and toluene liquid solutions on a commercial 13X zeolite adsorbent were measured using the gas chromatographic headspace technique. According to this technique, the vapor, in equilibrium with the liquid phase and solid adsorbent, is analyzed using a GC column. In the first part of the study, a novel technique was introduced based on liquid calibration curve procedure. In addition, the earlier introduced vapor calibration technique was further extended to measure single component isotherms of non-ideal liquid solutions. In this part of the study, both vapor and liquid calibration techniques were extended to measure liquid adsorption isotherms of the multi-component solutions involving both, ideal solutions e.g., aromatic sorbates, and non-ideal solutions, e.g., aromatic sorbates and n-decane as a solvent. Consequently, Raoult's law and extended Raoult's vapor-liquid equilibrium (VLE) law for calculations of ideal and non-ideal solutions were applied, respectively. Extended Wilson and NRTL models were used to determine the sorbates' activity coefficients in the non-ideal liquid solutions. The multicomponent isotherms involving both ideal and non-ideal liquid solutions were experimentally determined at 30, 60 and 90 °C and also predicted by the extended Sips adsorption model. Based on these results, the selectivity of the NaX zeolite towards different sorbates from the selected mixtures were determined at different temperatures and concentrations.

Activity Coefficient Modelling of Aqueous Solutions of Alkyl Ammonium Salts using the Extended UNIQUAC Model

Certain alkyl ammonium salts are called ionic liquids They can be used as green solvents without toxicity, effects on the ozone layer depletion, effects on climate change, and any other significant environmental impacts; in this regard knowledge about their thermo-physical properties are really important. In this work activity coefficients of aqueous solutions of alkyl ammonium salts at 298.15 and 293.15 K are modelled using the Extended UNIQUAC (Universal Quasi Chemical) thermodynamic model. Adjustable parameters of the Extended UNIQUAC thermodynamic model were obtained by non-linear regression between experimental data and the results calculated from the model. The results of the model are in good agreement with the experimental values in most cases, the average absolute deviation of the model being less than 2 %, which is acceptable considering the uncertainty of the experimental data. Additionally, the results gained from the Extended UNIQUAC model are also compared with the results obtained from Electrolyte NRTL and Pitzer thermodynamic methods.

Redox Stability of Uranium in High Ionic Strength Media: An Electrochemical and Spectroscopic Study

Knowledge of redox behavior of uranium in concentrated solutions of the hexary oceanic salt system is essential for the transport modeling of radioactive nuclides in repositories for the long-term disposal of radioactive wastes in rock salt formations. Especially critical is the behavior of the couple U(IV)/U(VI) in the surrounding high ionic strength saline milieu, which regulates the release of mobile U(VI) species at given redox conditions defined by the presence of trace oxygen. The redox potential (Eredox) and the solubility in brines in particular implicate the activity of the different ligand- and hydroxo-complexes (ai): Eredox = f(mi, ai, βj), where βj is the complexation constant. Thus, the prediction of transport behavior of uranium at given chemical environments needs appropriate complexation and thermodynamic models assuming the ionic activities beyond the limited Debye-Hückel theory. This latter is supplied by the Pitzer formulation1, where deviations from the limit Debye-Hückel behavior are given by specific interaction parameters among the constituting ionic species, which have to be determined experimentally. For the determination of the redox potential, an approach consisting in unfolding the redox system in two electrochemical reactions is pursued: (i) U(VI) → U(V) and (ii) U(IV) → U(V), where the kinetics of each partial reaction is studied systematically at different concentrations of the ground electrolyte. Thus ir i (Eredox) = ia ii (Eredox). In this work, we focus on the aqueous chloride system. The kinetics of the electrochemical reduction and oxidation reactions was studied in a three-electrodes type cell using a Au working electrode, Pt wire counter electrode and a Ag/AgCl in3 M KCl reference electrode. Experiments were performed under an oxygen-free atmosphere in a glove-box. Cyclic voltammetry (CV) and normal pulse voltammetry (NPV) were applied to investigate the influence of chloride concentrations in the kinetics parameters, such as reaction rate, k, and the diffusion coefficient in solutions containing U(VI) or U(IV) in HCl solutions from 0.1 to 1.3 M. The solution speciation of uranium was investigated by UV/vis absorption spectroscopy. CV and NPV experiments show that the reduction of U(VI) occurs in two steps. The first wave appearing between -0.2 V and -0.3 V vs ref. can be ascribed to the reaction U(VI) àU(V), in line with previous reports2,3,4. The second cathodic wave occurs with a simultaneous gas generation. The cathodic process involved in the second wave can be described in terms of an acceleration of hydrogen evolution reaction by adsorbed intermediary species. According to thermodynamic calculations using the extended Debye-Hückel equation as a rough ionic activity approximation and NEA-data base5, the predominating species in the systems under study are UO2 2+ and UO2Cl+. The concentration of the chloride complex increases with increasing HCl concentration, as indicated by the spectral changes on UV-vis absorption data. Spectroscopic measurements with U(IV), on the other hand, do not indicate a strong complexation effect. According to the results of voltammetric experiments, chloride complexes seem to influence the second electron transfer step. A reaction mechanism will be discussed in terms of electrochemical, spectroscopic and modeling results. References K.S. Pitzer in Activity coefficients in electrolyte solutions, Ch.3, CRC Press, Boca Raton, Florida, 1991.R.E. Dueber, A.M. Bond, P.G. Dickens, J. Electrochem. Soc. 141 (1994) 311.K. El Kacemi, B. Tyburce, S. Belcadi, Electrochim. Acta 27 (1982) 729.S. Kihara, Z. Yoshida, H. Aoyagi, K. Maeda, O. Shirai, Y. Kitatsuji, Y. Yoshida, Pure Appl. Chem. 71 (1999) 1771.I. Grenthe, J. Fuger, R.J.M. Konings, R.J. Lemire, A.B. Muller, C. Nguyen-Trung, H. Wanner, in H. Wanner and I. Forest (Ed.), NEA-Data bank, Chemical Thermodynamics of Uranium, OECD Publications, Paris, 2004.

Thermodynamic Study of Aqueous Solutions of 1-Butyl-3-methylimidazolium Tetrafluoroborate Ionic Liquid Using Potentiometric Measurements at Different Temperatures

The mean ionic activity coefficients of 1-butyl-3-methylimidazolium tetrafluoroborate ionic liquid in water at a low concentration range were determined using potentiometric measurements at temperatures ranging from 298.15 to 328.15 K. The obtained experimental data were correlated by the Pitzer and nonelectrolyte Wilson nonrandom factor (N-Wilson-NRF) models. The resulted Pitzer parameters were used to estimate the osmotic coefficients and excess Gibbs free energies of the system being investigated. The results indicate that both the models could be applied to predict the activity coefficients of the aqueous ionic liquid solutions, but the Pitzer model gives much lower standard deviations than the N-Wilson-NRF model. Moreover, the obtained activity and osmotic coefficients show that their values decrease with a rise in the ionic liquid concentration and increase with the elevation of temperature.

Ionic molal conductivities, activity coefficients, and dissociation constants of HAsO42 − and H2AsO4− from 5 to 90 °C and ionic strengths from 0.001 up to 3 mol kg− 1 and applications in natural systems

Arsenic is known to be one of the most toxic inorganic elements, causing worldwide environmental contamination. However, many fundamental properties related to aqueous arsenic species are not well known which will inhibit our ability to understand the geochemical behavior of arsenic (e.g. speciation, transport, and solubility). Here, the electrical conductivity of Na2HAsO4 solutions has been measured over the concentration range of 0.001–1molkg−1 and the temperature range of 5–90°C. Ionic strength and temperature-dependent equations were derived for the molal conductivity of HAsO42− and H2AsO4− aqueous ions. Combined with speciation calculations and the approach used by McCleskey et al. (2012b), these equations can be used to calculate the electrical conductivities of arsenic-rich waters having a large range of effective ionic strengths (0.001–3molkg−1) and temperatures (5–90°C). Individual ion activity coefficients for HAsO42− and H2AsO4− in the form of the Hückel equation were also derived using the mean salt method and the mean activity coefficients of K2HAsO4 (0.001–1molkg−1) and KH2AsO4 (0.001–1.3molkg−1). A check on these activity coefficients was made by calculating mean activity coefficients for Na2HAsO4 and NaH2AsO4 solutions and comparing them to measured values. At the same time Na-arsenate complexes were evaluated. The NaH2AsO40 ion pair is negligible in NaH2AsO4 solutions up to 1.3molkg−1. The NaHAsO4− ion pair is important in NaHAsO4 solutions >0.1molkg−1 and the formation constant of 100.69 was confirmed. The enthalpy, entropy, free energy and heat capacity for the second and third arsenic acid dissociation reactions were calculated from pH measurements. These properties have been incorporated into a widely used geochemical calculation code WATEQ4F and applied to natural arsenic waters. For arsenic spiked water samples from Yellowstone National Park, the mean difference between the calculated and measured conductivities have been improved from −18% to −1.0% with a standard deviation of 2.4% and the mean charge balances have been improved from 28% to 0.6% with a standard deviation of 1.5%.

In Silico Calculation of Infinite Dilution Activity Coefficients of Molecular Solutes in Ionic Liquids: Critical Review of Current Methods and New Models Based on Three Machine Learning Algorithms.

The aim of the paper is to address all the disadvantages of currently available models for calculating infinite dilution activity coefficients (γ(∞)) of molecular solutes in ionic liquids (ILs)-a relevant property from the point of view of many applications of ILs, particularly in separations. Three new models are proposed, each of them based on distinct machine learning algorithm: stepwise multiple linear regression (SWMLR), feed-forward artificial neural network (FFANN), and least-squares support vector machine (LSSVM). The models were established based on the most comprehensive γ(∞) data bank reported so far (>34 000 data points for 188 ILs and 128 solutes). Following the paper published previously [J. Chem. Inf. Model 2014, 54, 1311-1324], the ILs were treated in terms of group contributions, whereas the Abraham solvation parameters were used to quantify an impact of solute structure. Temperature is also included in the input data of the models so that they can be utilized to obtain temperature-dependent data and thus related thermodynamic functions. Both internal and external validation techniques were applied to assess the statistical significance and explanatory power of the final correlations. A comparative study of the overall performance of the investigated SWMLR/FFANN/LSSVM approaches is presented in terms of root-mean-square error and average absolute relative deviation between calculated and experimental γ(∞), evaluated for different families of ILs and solutes, as well as between calculated and experimental infinite dilution selectivity for separation problems benzene from n-hexane and thiophene from n-heptane. LSSVM is shown to be a method with the lowest values of both training and generalization errors. It is finally demonstrated that the established models exhibit an improved accuracy compared to the state-of-the-art model, namely, temperature-dependent group contribution linear solvation energy relationship, published in 2011 [J. Chem. Eng. Data 2011, 56, 3598-3606].

Function-Space-Based Solution Scheme for the Size-Modified Poisson-Boltzmann Equation in Full-Potential DFT.

The size-modified Poisson-Boltzmann (MPB) equation is an efficient implicit solvation model which also captures electrolytic solvent effects. It combines an account of the dielectric solvent response with a mean-field description of solvated finite-sized ions. We present a general solution scheme for the MPB equation based on a fast function-space-oriented Newton method and a Green's function preconditioned iterative linear solver. In contrast to popular multigrid solvers, this approach allows us to fully exploit specialized integration grids and optimized integration schemes. We describe a corresponding numerically efficient implementation for the full-potential density-functional theory (DFT) code FHI-aims. We show that together with an additional Stern layer correction the DFT+MPB approach can describe the mean activity coefficient of a KCl aqueous solution over a wide range of concentrations. The high sensitivity of the calculated activity coefficient on the employed ionic parameters thereby suggests to use extensively tabulated experimental activity coefficients of salt solutions for a systematic parametrization protocol.

Infinite dilution activity coefficients of solutes dissolved in anhydrous alkyl(dimethyl)isopropylammonium bis(trifluoromethylsulfonyl)imide ionic liquids containing functionalized- and nonfunctionalized-alkyl chains

Infinite dilution activity coefficients and gas-to-liquid partition coefficients have been determined for at least 42 different organic solutes of varying polarity and hydrogen-bonding character dissolved in anhydrous ionic liquids comprising propyl(dimethyl)isopropylammonium bis(trifluoromethylsulfonyl)imide, hexyl(dimethyl)isopropylammonium bis(trifluoromethylsulfonyl)imide, 2-hydroxyethyl(dimethyl)isopropylammonium bis(trifluoromethylsulfonyl)imide, cyanomethyl(dimethyl)isopropylammonium bis(trifluoromethylsulfonyl)imide, and N,N,N′,N′-tetramethyl-N,N′-diisopropyl-1,9-nonanediaminium di[bis(trifluoromethylsulfonyl)imide]. The measured gas-to-liquid partition coefficient data were converted to water-to-liquid partition coefficients using standard thermodynamic relationships. Abraham model predictive correlations were developed from both sets of partition coefficients. The derived correlations describe the observed partitioning behavior to within 0.14 (or fewer) log units.

Vapor Pressure of Aqueous Solutions of Electrolytes Reproduced with Coarse-Grained Models without Electrostatics.

The vapor pressure of water is a key property in a large class of applications from the design of membranes for fuel cells and separations to the prediction of the mixing state of atmospheric aerosols. Molecular simulations have been used to compute vapor pressures, and a few studies on liquid mixtures and solutions have been reported on the basis of the Gibbs Ensemble Monte Carlo method in combination with atomistic force fields. These simulations are costly, making them impractical for the prediction of the vapor pressure of complex materials. The goal of the present work is twofold: (1) to demonstrate the use of the grand canonical screening approach ( Factorovich , M. H. J. Chem. Phys. 2014 , 140 , 064111 ) to compute the vapor pressure of solutions and to extend the methodology for the treatment of systems without a liquid-vapor interface and (2) to investigate the ability of computationally efficient high-resolution coarse-grained models based on the mW monatomic water potential and ions described exclusively with short-range interactions to reproduce the relative vapor pressure of aqueous solutions. We find that coarse-grained models of LiCl and NaCl solutions faithfully reproduce the experimental relative pressures up to high salt concentrations, despite the inability of these models to predict cohesive energies of the solutions or the salts. A thermodynamic analysis reveals that the coarse-grained models achieve the experimental activity coefficients of water in solution through a compensation of severely underestimated hydration and vaporization free energies of the salts. Our results suggest that coarse-grained models developed to replicate the hydration structure and the effective ion-ion attraction in solution may lead to this compensation. Moreover, they suggest an avenue for the design of coarse-grained models that accurately reproduce the activity coefficients of solutions.

Calculation of activity and solubility of amino acids in aqueous solution by cubic-plus-association equation of state

Cubic plus association equation of state was applied for the first time to calculate various thermodynamic properties such as activity coefficient, solubility, density, and vapor pressure of aqueous solution of amino acids. Pure compound parameters of CPA EOS were fitted to the activity coefficient of amino acids in aqueous solution. In order to calculate the monomer fractions of amino acids and water in a binary solution of these molecules, a novel 3rd degree linear equation was proposed. The model also has been used to correlate the solubility of amino acids in different temperatures, and the values of Δh and Δs were obtained through the calculation of solubility in water. In addition, a group contribution method was applied to estimate the critical temperature. CPA in contrast with the other equation of states (e.g. SAFT EOS) that previously used to correlate thermodynamic properties of amino acids has the advantage of simplicity. Moreover, the results showed good agreement with the experimental data.