Low pressure vapor–liquid equilibrium in ethanol + congener mixtures using the Wong–Sandler mixing rule

Phase equilibrium in binary ethanol mixtures found in alcoholic beverage production has been analyzed using a cubic equation of state (EoS) and suitable mixing and combining rules. The main objective of the study is the accurate modeling of the congener concentration in the vapor phase (substances different from ethanol), considered to be an important enological parameter in the alcohol industry. The Peng–Robinson (PR) equation of state has been used and the Wong–Sandler (WS) mixing rules, that include a model for the excess Gibbs free energy, have been incorporated into the equation of state constants. In the Wong–Sandler mixing rules the van Laar (VL) model for the excess Gibbs energy has been used. This combination of equations of state, mixing rules and combining rules are commonly applied to high pressure phase equilibrium and have not yet been treated in a systematic way to complex low pressure ethanol mixtures as done in this work. Nine binary ethanol + congener mixtures have been considered for analysis. Comparison with available literature data is done and the accuracy of the calculations is discussed, concluding that the model used is accurate enough for engineering applications.     

Electrostatic solvation free energy of amino acid side chain analogs: implications for the validity of electrostatic linear response in water

Electrostatic free energies of solvation for 15 neutral amino acid side chain analogs are computed. We compare three methods of varying computational complexity and accuracy for three force fields: free energy simulations, Poisson-Boltzmann (PB), and linear response approximation (LRA) using AMBER, CHARMM, and OPLS-AA force fields. We find that deviations from simulation start at low charges for solutes. The approximate PB and LRA produce an overestimation of electrostatic solvation free energies for most of molecules studied here. These deviations are remarkably systematic. The variations among force fields are almost as large as the variations found among methods. Our study confirms that success of the approximate methods for electrostatic solvation free energies comes from their ability to evaluate free energy differences accurately.     

A method to determine the Gibbs energy of specific interactions in solutions. Hydrogen bonding of proton donating solutes in basic solvents

One of two fundamental types of solute–solvent intermolecular interactions are the specific interactions, such as hydrogen bonding complexation between solute and solvent. The Gibbs energy of specific interactions is an important quantity that determines rate and equilibrium constants in solutions, but it is difficult to obtain by direct measurement. We proposed equations allowing to determine the contribution of specific interactions to the Gibbs energy of solvation in nonelectrolyte solutions. Applying it for the case of proton donating solutes with one acidic hydrogen atom dissolved in basic solvents, we obtained the values of the Gibbs energies of 1:1 complexation in pure base. These values have been compared with the Gibbs energies of 1:1 complexation in tetrachloromethane. Most of the hydrogen bonds are found to have the same energy in pure base and in CCl₄, however, some weakly bound complexes seem to become even more weakened in pure base medium. Suggested method is applicable in a general situation when multiple associates of different stoichiometry and structure are formed.     

Calculation of acidic dissociation constants in water: solvation free energy terms. Their accuracy and impact

Three polarizable continuum models, DPCM, CPCM, and IEFPCM, have been applied to calculate free energy differences for nine neutral compounds and their anions. On the basis of solvation free energies, the pK_a values were obtained for the compounds in question by using three thermodynamic cycles: one, involving the combined experimental and calculated data, as well as two other cycles solely with calculated data. This paper deals with the influence of factors such as the SCRF model applied, choice of a particular thermodynamic cycle, atomic radii used to build a cavity in the solvent (water), optimization of geometry in water, inclusion of electron correlation, and the dimension of the basis set on the solvation free energies and on the calculated pK_a values. Electronic supplementary material The online version of this article (doi: ) contains supplementary material, which is available to authorized users.     

Excess Gibbs Energy of Mixing for Organic Carbonates from Fitting of Their Binary Phase Diagrams with Nonideal Solution Models

The excess Gibbs energies of mixing in the liquid state were evaluated for all the ten binary combinations of these five organic carbonates: ethylene carbonate (EC), propylene carbonate, dimethyl carbonate (DMC), ethyl methyl carbonate, and diethyl carbonate by fitting their measured binary phase diagrams with thermodynamic nonideal solution models based on the regular solution model. Using the results of these model fits, activity coefficients of the components in the solvent mixtures were calculated for the binary series containing EC and DMC as the common component, and the composition-averaged excess Gibbs energies of mixing were calculated by integrating the energy in the whole composition range for all the binaries. The results showed the excess Gibbs energy of mixing, and therefore the intermolecular forces, to be responsible for the changes in the phase diagrams, in the activity coefficients, and in the composition-averaged excess energy for the different binary solution combinations.     

Thermodynamics of solvation and solvophobic effect in formamide

Using semi-adiabatic calorimetry, we measured the enthalpies of solution for various low-polar compounds including alkanes, aromatic hydrocarbons and their halogenated derivatives in formamide at temperature of 298 K. For the same compounds, the values of limiting activity coefficients in formamide were determined using GC headspace analysis at 298 K, and Gibbs free energies of solution and solvation were calculated. Based on these data and the available literature values of the Gibbs free energy of solvation in formamide for a number of other low-polar solutes, a study of the solvophobic effect in this solvent is performed, and its resemblance to the hydrophobic effect in aqueous solutions is demonstrated. It is shown that the contribution of the solvophobic effect into the solvation Gibbs free energy in formamide is much higher than that in aliphatic alcohols, but lower than that in water. Like in water, the magnitude of this contribution for different solutes linearly increases with the solute molecular volume. Solvophobic effect also significantly affects the enthalpies of dissolution in formamide, causing them to be more negative in the case of alkanes and more positive in the case of arenes.     

Vapour–liquid equilibria,enthalpy of mixing of binary mixtures containing diisopropylether ‘DIPE’ and monoaromatic hydrocarbons: Experimental results and modelling

The experimental isothermal P–x–y data between 263.15 and 343.15 K at 10 K intervals of liquid binary mixtures 2,2′-oxybis[propane] (diisopropylether or DIPE) + toluene, +m-xylene and of the three pure components are reported. Data reduction by Barker's method provides correlation for excess molar Gibbs energy (G^E).     

Knudsen effusion mass spectrometric determination of mixing thermodynamic data of liquid Ag–In–Sn alloy

The vaporisation of a liquid Ag–In–Sn system has been investigated at 1273–1473 K by Knudsen effusion mass spectrometry (KEMS) and the data fitted to a Redlich–Kister–Muggianu (RKM) sub-regular solution model. Nineteen different compositions have been examined at six fixed indium mole fractions, X_In = 0.10, 0.117, 0.20, 0.30, 0.40 and 0.50. The ternary L-parameters, the thermodynamic activities and the thermodynamic properties of mixing have been evaluated using standard KEMS procedures and from the measured ion intensity ratios of Ag⁺ to In⁺ and Ag⁺ to Sn⁺, using a mathematical regression technique described by us for the first time. The intermediate data obtained directly from the regression technique are the RKM ternary L-parameters. From the obtained ternary L-parameters the integral molar excess Gibbs free energy, the excess chemical potentials, the activity coefficients and the activities have been evaluated. Using the temperature dependence of the activities, the integral and partial molar excess enthalpies and entropies were determined. In addition, for comparison, for some compositions, also the Knudsen effusion isothermal evaporation method (IEM) and the Gibbs–Duhem ion intensity ratio method (GD-IIR) were used to determine activities and good agreement was obtained with the data obtained from fitting to the RKM model.     

A new set of atomic radii for accurate estimation of solvation free energy by Poisson–Boltzmann solvent model

The Poisson–Boltzmann implicit solvent (PB) is widely used to estimate the solvation free energies of biomolecules in molecular simulations. An optimized set of atomic radii (PB radii) is an important parameter for PB calculations, which determines the distribution of dielectric constants around the solute. We here present new PB radii for the AMBER protein force field to accurately reproduce the solvation free energies obtained from explicit solvent simulations. The presented PB radii were optimized using results from explicit solvent simulations of the large systems. In addition, we discriminated PB radii for N‐ and C‐terminal residues from those for nonterminal residues. The performances using our PB radii showed high accuracy for the estimation of solvation free energies at the level of the molecular fragment. The obtained PB radii are effective for the detailed analysis of the solvation effects of biomolecules. © 2014 The Authors Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Solute–solvent interactions of acid–1,4-dioxane mixtures—By dielectric, FTIR, UV–vis and 13C NMR spectrometric methods

Results of the dielectric studies carried out on the binary mixture of n-butyric and caprylic acids with 1,4-dioxane over the entire composition range and at temperatures 303 K, 308 K, 313 K and 318 K, and FTIR, UV–vis and 13C NMR spectral studies are presented in this paper. The excess permittivity and excess free energy were fitted with the Redlich–Kister polynomial. The variation of Kirkwood correlation factors, excess permittivity and excess free energy of mixing with the concentration and temperature has been investigated in view of understanding the ordering of dipoles of solute and solvent molecules. The FTIR, UV–vis and 13C NMR spectral analysis reveals the formation of complex between solute and solvent molecules. The parallel alignment of electric dipoles of the complex predicted by dielectric studies is well supported by UV–vis spectral analysis. The structure of the complex molecule present in the clusters has been deduced.     

Vapour pressure and excess Gibbs free energy of the ternary system {x1CH3F + x2HCl + x3N2O} at temperature of 182.33 K

The equilibrium pressure of ternary mixtures of {x₁CH₃F + x₂HCl + x₃N₂O} covering the entire composition range has been measured at temperature of 182.33 K by the static method. The system exhibits a minimum pressure for the binary {x₁CH₃F + x₂HCl}. The molar excess Gibbs free energy has been calculated from the experimental equilibrium pressure. For the equimolar mixture . The (p, x, y) surface for the ternary system and the corresponding curves for the three constituent binary mixtures obtained from the Peng-Robinson equation of state are in agreement with the experimental data.     

Excess partial molar volumes and thermal expansivities in the water-rich region of aqueous 2-butanone

Excess partial molar volumes of 2-butanone V _m ^E (B) and thermal expansivities _p were measured in the water-rich region of aqueous 2-butanone. The composition derivatives of both quantities showed anomalies at about X _B =0.033 (x _B is the mole fraction of B). showed a step anomaly, while exhibited a peak anomaly. The compositions at which these anomalies occurred match those of the step anomalies observed earlier in and in aqueous 2-butanone. These results are discussed in comparison with those obtained previously for aqueous 2-butoxyethanol.Presented at the Symposium, 76^th CSC Congress, Sherbrooke, Quebec, May 30–June 3, 1993, honoring Professor Donald Patterson on the occasion of his 65^th birthday.     

Vapour pressure and excess Gibbs free energy of binary mixtures of hydrogen sulphide with ethane, propane, and n-butane at temperature of 182.33 K

The vapour pressure of binary mixtures of hydrogen sulphide with ethane, propane, and n-butane was measured at T = 182.33 K covering most of the composition range. The excess Gibbs free energy of these mixtures has been derived from the measurements made. For the equimolar mixtures for (H₂S + C₂H₆), (820.1 ± 2.4) J · mol⁻¹ for (H₂S + C₃H₈), and (818.6 ± 0.9) J · mol⁻¹ for (H₂S + n-C₄H₁₀). The binary mixtures of H₂S with ethane and with propane exhibit azeotropes, but that with n-butane does not.     

Relationship between the energy of donor–acceptor bond and the reorganization energy in molecular complexes

Donor–acceptor complexes of silicon halides with ammonia, pyridine, and 2,2′bipyridine SiX₄ · nD (X = F, Cl, Br) have been studied at the B3LYP/pVDZ level of theory. Energies of the donor–acceptor bond have been estimated taking into account the reorganization energy of the donor and acceptor fragments and basis set superposition error correction. Despite of the very low (or even negative) dissociation energy of SiX₄ · nD into free fragments, the Si–N bonding in all complexes is rather strong (75–220 kJ mol^?1). It is the reorganization energy of the acceptor SiX₄ (75–280 kJ mol^?1) that governs the dissociation energy of the complex. Thus, in contrast to the complexes of group 13 halides, the reorganization effects are crucial for the complexes of group 14 halides, and their neglecting leads to erroneous conclusions about the strength of the donor–acceptor bond in these systems. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Calculation of solvation free energy using RISM theory for peptide in salt solution

We developed a robust, highly efficient algorithm for solving the full reference interaction site model (RISM) equations for salt solutions near a solute molecule with many atomic sites. It was obtained as an extension of our previously reported algorithm for pure water near the solute molecule. The algorithm is a judicious hybrid of the Newton–Raphson and Picard methods. The most striking advantage is that the Jacobian matrix is just part of the input data and need not be recalculated at all. To illustrate the algorithm, we solved the full RISM equations for a dipeptide (NH₂(SINGLE BOND)CHCH₃(SINGLE BOND)CONH(SINGLE BOND)CHCH₃(SINGLE BOND)COOH) in a 1 M NaCl solution. The extended simple point charge (SPC/E) model was employed for water molecules. Two different conformations of the dipeptide were considered. It was assumed for each conformation that the dipeptide was present either as an un-ionized form or as a zwitterion. The structure of the salt solution near the dipeptide and salt effects on the solvation free energy were also discussed. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1724–1735, 1998     

Towards a modellisation of the solvation energy in multi-component solvents. The interesting case of a charged solute imbedded in a polymer-containing electrolyte solution

In this paper we propose a mean-field theory to calculate the solvation free energy of a charged solute imbedded in a complex multi-component solvent. We considered a solvent made up of a mixture of small (electrolyte solution) and large (polymer) components. The presence of macromolecules ensures reduced mixing entropy among the different solvent components, an effect due to polymer connectivity. The reduced entropy favours strong preferential distribution of a particular solvent even in the presence of weak preferential solute–solvent interactions. In addition, two energy terms must be considered: (a) the interaction between the solute electrostatic potential and the electrolyte solution and (b) the formation of a polymer–solute interface. Because of the different dielectric permittivity of the solvent components, the electrolyte and polymer distribution functions are strongly coupled: ions, indeed, are more solvated in regions of higher local dielectric permittivity arising from the inhomogeneous mixing of solvent and polymer. We combined together the different energy terms in the framework of the de Gennes free energy functional for polymer solutions along with a generalised Poisson–Boltzmann equation developed for inhomogeneous dielectric media. Moreover, the preferential electrolyte solvation in regions of greater polarity was considered by an extension of the Born equation. Setting the polymer dielectric permittivity smaller than the solvent one and making null the specific polymer–solute interactions, we calculated enhanced electrolyte concentration and reduced polymer concentration near the solute surface on raising the solute surface charge density. The theory shows also the breakdown of the widely used separation between electrostatic and surface tension-dependent contributions to solvation energy when non-ideal mixed solvents are considered. In fact, according to the model, the surface tension of such mixed solvents strongly depends on the solute surface charge density: at high potentials the interfacial tension may increase rather than decrease on raising the polymer volume fraction. The theoretical results have been compared with experimental data on polymer+electrolyte solution surface tension and with solubility data of colloidal particles. The comparison evidences the complex behaviour of multi-component solvents going well beyond the trivial weighted average of the dielectric permittivity and surface tension of the isolated chemical components. Deviations from the simple behaviour predicted by an average picture of multi-component solvents could be understood by developing more sophisticated, but still simple, approaches like that proposed in this paper.Contribution to the Jacopo Tomasi Honorary Issue. This paper is dedicated to Jacopo Tomasi. I learned much of the difficult art of transforming complex problems into simple models after reading his early works on solvation energy.     

A new formulation of the predictive NRTL-PR model in terms of kij mixing rules. Extension of the group contributions for the modeling of hydrocarbons in the presence of associating compounds

A generalized NRTL model was previously proposed for the modeling of non ideal systems and was extended to the prediction of phase equilibria under pressure according to the cubic NRTL-PR EoS. In this work, the model is reformulated with a predictive k_ij temperature and composition dependent mixing rule and new interaction parameters are proposed between permanent gases, ethane and nitrogen with hydrocarbons, ethane with water and ethylene glycol. Results obtained for excess enthalpies, liquid-vapor and liquid-liquid equilibria are compared with those provided by the literature models, such as VTPR, PPR78, CPA and SRKm. A wide variety of mixtures formed by very asymmetric compounds, such as hydrocarbons, water and ethylene glycols are considered and special attention is paid to the evolution of k_ij with respect to mole fractions and temperature.