Partial Excess Gibbs Energy Research Articles

Molecular Mechanism for Azeotrope Formation in Ethanol/Benzene Binary Mixtures through Gibbs Ensemble Monte Carlo Simulation.

Azeotropes have been studied for decades due to the challenges they impose on separation processes but fundamental understanding at the molecular level remains limited. Although molecular simulation has demonstrated its capability of predicting mixture vapor-liquid equilibrium (VLE) behaviors, including azeotropes, its potential for mechanistic investigation has not been fully exploited. In this study, we use the united atom transferable potentials for phase equilibria (TraPPE-UA) force field to model the ethanol/benzene mixture, which displays a positive azeotrope. Gibbs ensemble Monte Carlo (GEMC) simulation is performed to predict the VLE phase diagram, including an azeotrope point. The results accurately agree with experimental measurements. We argue that the molecular mechanism of azeotrope formation cannot be fully understood by studying the mixture liquid-state stability at the azeotrope point alone. Rather, azeotrope occurrence is only a reflection of the changing relative volatility between the two components over a much wider composition range. A thermodynamic criterion is thus proposed on the basis of the comparison of partial excess Gibbs energy between the components. In the ethanol/benzene system, molecular energetics shows that with increasing ethanol mole fraction, its volatility initially decreases but later plateaus, while benzene volatility is initially nearly constant and only starts to decrease when its mole fraction is low. Analysis of the mixture liquid structure, including a detailed investigation of ethanol hydrogen-bonding configurations at different composition levels, reveals the underlying molecular mechanism for the changing volatilities responsible for the azeotrope.

The Uniqueness of a Correction to Interaction Parameter Formalism in a Thermodynamically Consistent Manner

Polynomial representation of partial excess Gibbs energy (i.e., activity coefficient) in multicomponent dilute solution has been widely used after Wagner. Although Wagner’s Interaction Parameter Formalism has been known to be only strictly valid at infinite dilute concentration, it has been used often, even at finite concentration, due to its mathematical simplicity. Nevertheless, several attempts have been made to correct the formalism to be thermodynamically consistent at finite concentration. Among those, Unified Interaction Parameter Formalism proposed by Pelton and Bale, which may be considered as an extension of Darken’s quadratic formalism, has obtained much attention. However, there have been much confusion and debate about the way of the correction. Recently, a thermodynamic analysis was reported that there are infinite numbers of ways to correct Wagner’s formalism to be thermodynamically consistent, which may prevent one from using the Unified Interaction Parameter Formalism with confidence. In the present article, the correction to the Wagner’s formalism is discussed by revisiting Darken’s condition of the thermodynamic consistency. It is shown that the correction to the Wagner’s formalism can be made uniquely. It is pointed out that to ensure the thermodynamic consistency among the activity coefficients of all components, Gibbs–Duhem relation and Maxwell relation among all components including solvent–solute, must be obeyed. Derived expressions for activity coefficients of all components by path-independent integration are also shown to be the same as those obtained by differentiating a corresponding integral excess partial Gibbs energy.

Thermodynamic properties of ternary Me-Ga-In (Me = La, U) alloys in a fused Ga-In/LiCl-KCl system

This work presents the results of a study of apparent standard potentials of La-(Ga-In) and U-(Ga-In) alloys vs. Cl−/Cl2 reference electrode at the temperature range (723–823) K in fused Me(Ga-In)/LiCl-KCl (3:2 mol ratio) system by potentiometric method at zero current. Lanthanum and uranium activity coefficients and La/U separation factor in gallium-indium alloys containing 40 and 70 wt% indium were determined. Partial excess free Gibbs energy, partial enthalpy of mixing and partial excess entropy of La-(Ga-In) and U-(Ga-In) alloys were calculated. The efficiency of separation of La from U was estimated.

GREEN CHEMICAL SYNTHESIS AND PROPERTIES OF SOLID DISPERSIONS OF BENZIMIDAZOLE –Β. NAPHTHOL BINARY DRUG SYSTEM

With a view to synthesize and characterize the enhanced pharmaceutical properties of the solid-liquid dispersions of binary drug system through a green chemical technique, the present communication have been undertaken for detailed investigation of thermodynamic and interfacial properties of benzimidazole (BI) and β. naphthol (βN) binary eutectic and non-eutectic drug dispersions. Eutectic solid dispersion was observed at 0.657-mole fraction of β. naphthol (βN) and at melting temperature 90°C. Thermodynamic quantities; Partial and Integral excess Gibbs energy (gE), excess enthalpy (hE), excess entropy (sE) of eutectic and non-eutectic dispersions were determined with the help of activity coefficient data. The negative deviation from ideal behaviour has been seen in the system which refers to a stronger association between unlike molecules during the formation of the binary mix. The negative value of Gibbs free energy of mixing (DGM) refers to the mixing for all eutectic and non-eutectic dispersions are spontaneous. The solid-liquid interfacial characteristics i.e., the entropy of fusion per unit volume (DSV), solid-liquid interfacial energy (s), roughness parameter (α), grain boundary energy and roughness parameter (α) of eutectic and non-eutectic solid dispersions have been reported. The size of the critical nucleus at different undercooling has been found in nanoscale, which may be a big significance in the pharmaceutical world. The value of roughness parameter, α > 2 was observed which manifests the faceted and irregular growth leads in the system.

The effect of Al concentration on thermodynamic properties of Nd and U in Ga–Al-based alloys and the separation factor of Nd/U couple in a “molten salt-liquid metal system”

Electrochemical behavior of neodymium and uranium in a molten Nd(U)–(Ga–xAl)/3LiCl–2KCl system (x = 1.5; 5.0 and 20.0 wt% Al) between 723 and 823 K was studied. Temperature dependencies of apparent standard potentials of Nd–(Ga–Al) and U–(Ga–Al) alloys were determined versus Cl−/Cl2 reference electrode. Neodymium and uranium activity coefficients and Nd/U separation factor were calculated. Partial excess free Gibbs energy, partial enthalpy of mixing and partial excess entropy of Nd–(Ga–Al) and U–(Ga–Al) alloys were estimated.

Calorimetric and Electromotive Force Measurements of Al-Li-Zn Liquid Solutions

The solution calorimetry and electromotive force methods were used for the study of the mixing enthalpy and partial excess Gibbs energy of the Al-Li-Zn liquid solutions. Calorimetric investigations were conducted for solutions with the ratio of XLi/XAl and XLi/XZn = 0.8/0.2 and at the temperatures of 942 and 978 K, respectively. The electromotive force studies were performed at two temperatures: 873 and 923 K by the titration technique and for dilute solutions. Based on the data of the mixing enthalpy change and the partial excess Gibbs energy of Li available in the literature, together with that obtained in these studies, the ternary interaction parameters were elaborated. The comparative analysis of the experimental mixing enthalpy change generally showed a good agreement with the values calculated based on different models. The observed deviations between the experimental and the calculated values were, for most of the experimental data, lower than 1 kJ/mol. The experimental partial excess Gibbs energy of Li showed a satisfactory agreement with that modeled on the basis of the ternary parameters elaborated in this work.

Thermodynamic properties of La–Ga–Al and U–Ga–Al alloys and the separation factor of U/La couple in the molten salt–liquid metal system

The electrochemical behaviour of lanthanum and uranium was studied in fused 3LiCl–2KCl eutectic and Ga–Al eutectic liquid metal alloy between 723 and 823 K. Electrode potentials were recorded vs. Cl−/Cl2 reference electrode and the temperature dependencies of the apparent standard potentials of La-(Ga–Al) and U-(Ga–Al) alloys were determined. Lanthanum and uranium activity coefficients and U/La couple separation factor were calculated. Partial excess free Gibbs energy, partial enthalpy of mixing and partial excess entropy of La-(Ga–Al) and U-(Ga–Al) alloys were estimated.

Modeling surface tension of multicomponent liquid steel using Modified Quasichemical Model and Constrained Gibbs Energy Minimization

Surface tension of multicomponent liquid steel was calculated based on the concept proposed by Butler, which assumes a chemical equilibrium between a bulk phase and a surface phase of a monolayer. Requirement for the calculation of the surface tension was categorized as: 1) accurate description of partial excess Gibbs energies of solutes in the liquid steel, in particular for those of non-metallic solutes such as S, C, etc., 2) physical properties of pure components, such as surface tension and molar volume, and 3) possibility of solving a series of Butler equations for multicomponent liquid steel. In the present study, it is proposed to use the Modified Quasichemical Model in order to describe the partial excess Gibbs energies of solutes, and to use the Constrained Gibbs Energy Minimization in order to solve equilibrium between the bulk and the surface phases of the multicomponent liquid steel. Physical properties of non-stable pure components such as S, C, were treated as variables to reproduce known experimental data in binary systems. The proposed method can be easily extended into multicomponent liquid steel. Examples of the surface tension calculations are presented.

Estimation of extraction properties of new imidazolide anion based ionic liquids on the basis of activity coefficient at infinite dilution measurements

New ionic liquids, based on the 4,5-dicyano-2-(trifluoromethyl)imidazolide [TDI] anion proposed as a new electrolyte in Li-ion batteries, 1-butyl-3-methylimidazolium 4,5-dicyano-2-(trifluoromethyl)imidazolide, [BMIM][TDI] and the 1-butyl-3-methylpyridinium 4,5-dicyano-2-(trifluoromethyl)imidazolide, [BM3PY][TDI], were synthesized and purified. The basic thermal properties of the pure [BMIM][TDI] and [BM3PY][TDI] ionic liquids i.e. glass-transition temperatures, and the heat capacity change at glass transition have been measured using a differential scanning microcalorimetry (DSC). The densities, viscosities and surface tensions of [BMIM][TDI] and [BM3PY][TDI] in temperature range from 283.15K to 363.15K were measured. The density and viscosity correlation for these systems was tested by an empirical second-order polynomial and by the Vogel–Fucher–Tammann equation. The surface tensions of pure ionic liquid were measured at atmospheric pressure at five temperatures (298.15, 308.15, 318.15, 328.15 and 338.15)K. The surface thermodynamic functions such as surface entropy and enthalpy were derived from the temperature dependence of the surface tension values. The critical temperature, parachor and speed of sound for pure ionic liquids were described and compared with other ILs with the same cation. The activity coefficients at infinite dilution, γ13∞ were determined at the temperature range from 318.15K to 368.15K by gas–liquid chromatography in the ionic liquid [BMIM][TDI] and [BM3PY][TDI] for 67 solutes: alkanes, cycloalkanes, alkenes, alkynes, aromatic hydrocarbons, alcohols, water, thiophene, ethers, ketones and pyridine. The interaction of these 66 organic compounds and water with the ILs were described with the partial excess molar Gibbs energies, ΔG1E,∞, enthalpies ΔH1E,∞, and entropies TrefΔS1E,∞ at infinite dilution, calculated from the experimental γ13∞ values, obtained over the temperature range. The gas–liquid partition coefficients, KL were calculated for all solutes. The selectivities for different separation problems were calculated from γ13∞ and compared to literature values for N-methyl-2-pyrrolidinone (NMP), sulfolane, and other 1-butyl-3-methylimidazolium, or 1-butyl-3-methylpyridinium-based ionic liquids. Obtained values were compared to the literature values for the other ionic liquids, NMP and sulfolane. The selectivities in proposed extraction processes were not attractive in comparison with previously measured ILs, with exception of water/1-butanol system. However, in contrast with the former measured ILs, [BMIM][TDI] and [BM3PY][TDI] posses higher capacity for benzene and thiophene. The gas–liquid partition coefficients, KL were calculated for all solutes and the Abraham solvation parameter model was discussed.

Thermodynamics of liquid Au–Sb–Sn

Abstract The thermodynamic properties of liquid Au–Sb–Sn are discussed with regard to the energetics of the system. The analysis in terms of the partial excess Gibbs energies and the partial enthalpies of mixing indicates that the presence of Sb in the alloys is energetically unfavourable. In addition, this is found also to be reflected by the concentration–concentration correlations in the long-wavelength limit, S cc ij , which are representative of the fluctuations in local composition occuring in the system. It is suggested that the analysis of the partial quantities in the system might give an extremely helpful contribution to understanding the energetics of multi-component systems.

Measurements of activity coefficients at infinite dilution for organic solutes and water in the ionic liquid 1-butyl-1-methylpyrrolidinium tris(pentafluoroethyl)trifluorophosphate ([BMPYR][FAP

The activity coefficients at infinite dilution, γ13∞, for 60 solutes, including alkanes, cycloalkanes, alkenes, alkynes, aromatic hydrocarbons, alcohols, water, acetic acid, thiophene, ethers, ketones, esters, butyraldehyde and acetonitrile in the ionic liquid 1-butyl-1-methylpyrrolidinium tris(pentafluoroethyl)trifluorophosphate [BMPYR][FAP], were determined by gas–liquid chromatography at six temperatures in range of 318.15–368.15K. The interaction of these 59 organic compounds and water with the IL was described with the partial excess molar Gibbs energies, ΔG1E,∞, enthalpies ΔH1E,∞, and entropies TrefΔS1E,∞ at infinite dilution, calculated from the experimental γ13∞ values obtained over the temperature range. The gas–liquid partition coefficients, KL were calculated for all solutes. The selectivities for different separation problems were calculated from γ13∞ and compared to literature values for N-methyl-2-pyrrolidinone (NMP), sulfolane, and other tris(pentafluoroethyl)trifluorophosphate-based ionic liquids. Comparison with other 1-butyl-1-methylpyrrolidynium-based ILs shows much lower capability of [BMPYR][FAP] to reveal hydrogen bonds and interact with lone electron pairs and/or polar groups of solutes. In contrast with the former measured ILs, [BMPYR][FAP] was found to posses however very high capacity for benzene. The density of [BMPYR][FAP] in temperature range from 318.15K to 368.15K was measured.

ChemInform Abstract: Thermodynamics of Gold-Erbium Alloys.

Abstract Galvanic cells with CaF 2 as solid electrolytes were used to obtain the thermodynamic properties of the gold–erbium system between 973 and 1073 K. A complete set of thermodynamic data was obtained for the gold-rich solid solution and for the intermetallic compounds Au 4 Er, Au 3 Er, Au 2 Er, AuEr and AuEr 2 . The relative partial excess Gibbs energy of erbium at infinite dilution was determined to be −257 kJ/mol at 1073 K. Electronic and elastic effects are discussed in order to account for the pronounced deviations from ideality.

A Calphad-compatible method to calculate liquid/liquid interfacial energies in immiscible metallic systems

For the calculation of liquid/liquid interfacial energies in monotectic metallic alloys only simplified models are known, which suppose the validity of the regular solution model for the liquid solution. In the present paper a Calphad-compatible method is developed to calculate the liquid/liquid interfacial energies in binary, ternary and multicomponent liquid monotectic alloys. The method can be considered as the extension of the Butler equation to the liquid/liquid interfaces. The first order interfacial phase transition has been predicted at a certain critical temperature, which is about 18% of the bulk critical temperature. Below this critical temperature the compositions of the two sides of the liquid/liquid interface are different, while above this critical temperature the compositions at the two sides of the interface are identical. The latter case is valid for the majority of liquid metallic systems above their monotectic temperatures. The method has been validated against the experimentally measured liquid/liquid interfacial energies in the Ga–Pb and Al–Bi systems. The method is found to be very sensitive to the correctness of the Calphad-assessment of the partial excess Gibbs energies of the components in the liquid solution. The excess Gibbs energy function of the liquid Al–Bi solution was reassessed using our recent exponential temperature dependence of the interaction energies.

Constitution and thermodynamics of Pt–La alloys

A complete set of thermodynamic functions was determined for the Pt–La system from electromotive force measurements on galvanic cells in the temperature range from 923 to 1073 K using CaF 2 single crystals as solid electrolytes. The phases on the platinum-rich side show pronounced negative deviations from ideal mixing behaviour; at 1073 K and infinite dilution, for instance, the relative partial excess Gibbs energy of La was determined to be −315 kJ/mol. Two effects are discussed to account for the deviations from ideal mixing behaviour: the transfer of the valence electrons of La to the electron gas of the alloy and the lattice distortion brought about by the size difference of the components. The phase relations were investigated by means of thermal, and X-ray analyses. The thermodynamic description of the system was optimized using experimental data from the present thermodynamic and phase diagram work. The calculated thermodynamic functions as well as the calculated phase diagram turned out to be in excellent accordance with the experimental results.

The Hg—Ra (Mercury—Radium) System

AbstractFor Abstract see ChemInform Abstract in Full Text.

On the Constitution and Thermodynamics of Ni—Tb Alloys

AbstractFor Abstract see ChemInform Abstract in Full Text.

The Hg-Ra (Mercury-Radium) System

The Hg-Ra phase diagram is not known. The melting points of Hg and Ra are −38.8290 and 700 °C, respectively. Information about the crystallographic features of both metals is given in Table 1. [1910Cur] prepared ∼0.8 at.% Ra amalgam by electrolysis. It looked completely fluid at room temperature. When heated, it became solid at 400 °C and emanated the rest of the Hg at 700 °C. [1962Koz] calculated the solubility of Ra in liquid Hg of 1.1 at.% Ra at 25 °C using a semiempirical equation relating metal solubility to its entropy of melting. Calculations by the same author [1992Koz], using a regular solution approximation and the cellular model of Miedema et al. [1983Nie], resulted in solubility values both equal to 0.5 at.% Ra. In the opinion of this evaluator, these estimations give the proper order of magnitude for Ra solubility. One may predict a probable Hg-Ra phase relationships by an extrapolation of the systematic changes in the behavior of Mg, Ca, Sr, and Ba in their binary alloys with Hg [2004Gum]. A distinct tendency to formation of the Hgricher compounds is observed with an increase in the atomic number of the alkaline earth metal series. Therefore, it is not clear whether HgRa2 exists, but most probably the congruently melting HgRa and Hg2Ra compounds should be the most stable phases of the Hg-Ra system. Moreover, a formation of Hg31Ra7, Hg11Ra, and Hg∼6Ra, by analogy to the Ba-Hg compounds, is expected. [1992Koz] reported the formation of HgRa, Hg2Ra, and Hg4Ra, but the experimental evidence underlying this report is unknown. Strong affinity between Hg and Ra is manifested in the partial excess Gibbs energy of Ra in its very diluted amalgam. This energy was found to be −255 ± 10 kJ/mol Ra near room temperature, and −243.8 kJ/mol Ra at 25 °C, respectively, according to [1975Nug] and [1990Kor]. These values point to stronger Hg-Ra interactions in the Hg-rich RaHg alloys than was observed in the Ba-Hg system [2000Gum]. The partial excess Gibbs energy was calculated from the difference between the standard potential of Ra/ Ra(II) and the polarographic half-wave potential of Ra, which was experimentally determined by a radiopolarographic method [1975Nug]. [1977Koz] reported the partial excess Gibbs energy (−250 kJ/mol) and enthalpy (−313 kJ/ mol) of Ra in its diluted amalgam by an extrapolation of the corresponding values for Ca, Sr, and Ba compared with the electronegativity or atom radii of these elements to the position of Ra. Because neither the electronegativity nor the atomic radius of Ra is precisely known, the strongly negative partial enthalpy value should be treated very tentatively. The activity coefficient of Ra in a dilute amalgam was estimated by [1989Gum] to be on the order of 10. This also points to a very strong interaction between Hg and Ra.

Thermodynamic and phase diagram investigation of Pb–BiIn section in Pb–Bi–In ternary system

The results of thermodynamic study of Pb–BiIn section of Pb–Bi–In system done experimentally by Oelsen calorimetry and calculated by general solution model, as well as measurements performed by DTA and optic microscopy in order to investigate phase diagram of the given section, are presented in this paper. Thermodynamic properties, such as integral molar enthalpies of mixing, activities, activity coefficients, partial and integral excess Gibbs energies at 600 and 650 K were determined and comparison between obtained experimental and calculated values were done. Also, based on cooling curves, DTA recordings and optic microscopy results phase diagram was constructed and compared with literature data.

On the constitution and thermodynamics of Ni–Tb alloys

The thermodynamic properties of the Ni–Tb system were determined between 873 and 1073 K from electromotive force measurements using CaF 2 single crystals as solid electrolytes. The results yield a complete set of thermodynamic functions for the intermetallic phases (Ni), Ni 17Tb 2, Ni 5Tb, Ni 7Tb 2, Ni 3Tb, Ni 2Tb, NiTb, Ni 2Tb 3, and NiTb 3 as well as information on the phase relations. The system is characterized by pronounced negative deviations from ideality. The relative partial excess Gibbs energy of Tb at infinite dilution was determined to be −(99±2) kJ/mol. This value is interpreted by taking electronic and elastic effects into account. The liquidus line was fixed over the entire range of composition by differential thermal analysis. The present results were used as basis for a thermodynamic optimization of the Ni–Tb system using a computer program based on the least squares method. The optimized thermodynamic functions which turned out to be in excellent accordance with the experimental results were subsequently used to calculate the phase diagram.

Thermodynamic study of liquid lithium–lead alloys using the EMF method

Liquid Li–Pb alloys were investigated by the electromotive force (emf) method at Li concentrations of 0.025⩽ X Li⩽0.965 mole fraction and at temperatures from 775 to 975 K. The experiments were conducted at constant temperature, and the Li concentration was changed by the coulometric-titration technique. The two-phase Li–Bi alloys and liquid lithium were used as the reference electrodes. The dependence of emfs on temperature for each investigated alloy was linear, and from the linear equations ( E= a+ bT), partial Li excess Gibbs energies, partial enthalpies and entropies of lithium were calculated, and compared with previously published data. The excess stability function ES and the concentration–concentration partial structure factor S cc(0) were calculated and discussed in relation to the neutron diffraction data and other properties. A change in the type of chemical bonding near the composition Li 4Pb is indicated. This study was initiated since Pb–17Li eutectic alloy has been proposed as a breeder blanket fluid for fusion reactors.