Redlich-Kister Coefficients Research Articles

Thermodynamic Properties of Ethanol + Pyridine, Ethanol + Benzene, and Pyridine + Benzene Mixtures at Temperature 298.15 K and Under Atmospheric Pressure

Experimental densities, viscosities, refractive indices, and sound speeds at temperature 298.15 K and atmospheric pressure are reported for the binary liquid mixtures of ethanol + benzene, ethanol + pyridine, and benzene + pyridine. From these experimental data, various thermodynamic excess and deviation properties were calculated and fitted by the Redlich-Kister polynomial to determine the adjustable coefficients and the standard deviations. The number of Redlich-Kister coefficients for significantly representing each thermodynamic property was optimized by applying the F-test. The variation of thermodynamic excess and deviation properties with composition has been interpreted in terms of molecular interactions between components of the mixture and structural effects. Furthermore, several theoretical and semi-empirical models were used to predict the refractive indices and sound speeds of the investigated mixtures. The predicting ability of each model was ascertained in terms of mean absolute percentage deviation between experimental and calculated data.

Evaluation of molecular interactions in binary mixtures comprising ethylene and di-ethylene glycol with ethyl lactate through thermophysical and spectroscopic studies

In this article, the study of molecular interactions in liquid systems containing industrially and biologically important solvents with minimal environmental damage has been done. Density (ρ) and refractive index (nD) of binary systems comprising ethyl lactate (EL) + ethylene glycol (EG) and di-ethylene glycol (DEG) at various mole fractions and T = (298.15 to 313.15) K along with pure components have been measured. The observed parameters were further used for determination of excess molar volumes (VmE), partial molar volumes (V¯m), excess partial molar volumes (V¯mE), deviations in refractive index (ΔϕnD) and deviations in molar refraction (ΔϕRM). Redlich-Kister coefficients along with standard deviations have been obtained by approximation of data to polynomial equation. The obtained VmE results have been investigated theoretically by means of Prigogine-Flory-Patterson (PFP) and Graph theories to estimate type and nature of interactions among constituent molecules which can be used to explain the changes in physicochemical properties of the mixtures. By analysing experimental data in light of PFP Theory, Interactional and characteristic pressure contributions have been found negative values for both the binary systems whereas free volume contribution possess positive sign. The structural variation of the components in the mixtures due to change in molecular interactions has been discussed by Graph theory. Fourier Transform InfraRed (FT-IR) studies have also been performed for pure and equimolar mixtures to enlighten the experimental outcomes. It confirmed the rupture of pre-existing bonding in lactate and the formation of new hydrogen bonds with glycols.

Computational analytical study in (O-Anisidine + Propyl Acetate) mixture through thermo-acoustical excess parameters and redlich-kister coefficients

The analysis involved in the present study of excess acoustical parameters and their Redlich-Kister Coefficients at different temperatures range from 303.15 K to 318.15 K with variation of 5 K temperature interval for each study and all these are explained in liquid mixtures containing functional materials namely (O-Anisidine mixed with Propyl Acetate). The obtained excess values of acoustical parameters namely Gibb’s free energy (G*E), enthalpy (HE) and internal pressure (πE) have been computed from measured experimental data. The results have also been helpful to obtain Redlich-Kister coefficients from polynomial equation and also to obtain their deviations.

Study of acoustical excess parameters and Redlich-Kister coefficients analysis in functional materials

The present research work is related to the analysis involved in the study of excess acoustical parameters and their Redlich-Kister Coefficients at different temperatures range from 303.15 K to 318.15 K with variation of 5 K temperature interval for each study and all these are explained in liquid mixtures containing functional materials namely (Benzene mixed with 1-Propanol). The obtained excess values of acoustical parameters namely Gibb’s free energy (G*E), enthalpy (HE) and internal pressure (πE) have been computed from measured experimental data. The results have also been helpful to obtain Redlich-Kister coefficients from polynomial equation and also to obtain their deviations. Excess thermo-acoustical parameters are discussed along with Redlich-Kister coefficients generally for the study of interactions among the molecules of liquid species.

Analytical study of thermo acoustical excess parameters and Redlich-Kister coefficients in functional materials at known four temperatures range from 303.15 K to 318.15 K

The Analysis of the present work is related to study involved in investigation of excess thermal acoustic parameters and their Redlich Kister Coefficients at different temperatures and all these are analyzed in liquid mixtures containing three functional material combinations namely (Aniline mixed with Toluene), (Aniline mixed with o-Xylene) and (Aniline mixed with Mesitylene). The obtained excess values of acoustical parameters namely Gibb’s free energy (G*E) , enthalpy (HE) and internal pressure (πE) have been computed from measured experimental data . The results have also been helpful to obtain Redlich-Kister coefficients from polynomial equation and also to obtain their deviations. Excess thermo-acoustical parameters are discussed along with Redlich-Kister coefficients generally for the study of interactions among the molecules of liquid species and they are analyzed at known temperatures range from 303.15 K to 318.15 K with variation of 5 K temperature interval for each study.

Geometric investigation of the three-coefficient Redlich-Kister expansion global phase diagram for binary mixtures

The Redlich-Kister (RK) three-coefficient expansion for gE is investigated geometrically and its global phase diagram is presented. The azeotropy and stability conditions yield surfaces (envelopes) in the three-dimensional azeotropy space and stability space respectively, whose axes represent variables determined from Henry's constants, pure substance vapor pressures and the highest-order RK coefficient. Zeotropy, single, double, triple, and tangent azeotropy (or saddle-point azeotropy), as well as stability, are identified in regions of the azeotropy and stability spaces. The connection between the two spaces is established. Envelopes for gE = 0 and dgE/dx=0 are also constructed in the azeotropy or stability spaces, to indicate the gE shape. Some results regarding the shape of gE are transferable to hE and vE when these are described independently by three-coefficient Redlich-Kister expansions. The analysis is applied to eleven actual mixtures, whose state is represented in the azeotropy and stability space. Fitting temperature-dependent RK coefficients allows to estimate the continuous path the mixture follows in both spaces at varying temperature, revealing possible intermediate states and the mixture tendency at the extreme temperatures.

VOLUMETRIC PROPERTIES OF ACRYLONITRILE+ETHANOL MIXTURE OVER TEMPERATURE RANGE FROM (293.15 TO 323.15) K AT AMBIENT PRESSURE

Densities of binary mixture of acrylonitrile in ethanol have been measured over the full range of compositions at temperatures from 293.15K to 323.15 K at the ambient pressure (87.9 kPa). The volumetric properties such as excess molar volumes, apparent molar volumes, partial molar volumes, excess partial molar volumes, standard partial molar volumes for binary mixture were calculated. Excess molar volumes were described by the Redlich–Kister polynomial equation. The Redlich–Kister coefficients and the standard deviations were calculated as well. The excess molar volumes exhibit mainly negative deviations from the ideal behavior over the whole range of composition for acrylonitrile+ethanol binary mixtures at low temperatures and become less negative with increasing temperature from 293.15 to 323.15 K. The results are interpreted on the basis of strong interaction between group of acrylonitrile and OH group of ethanol by hydrogen bonding. However, the sigmoid shape of plots of excess molar volumes versus molar fraction of ethanol from positive to negative values indicates to the varying interactions depending upon the composition of binary mixtures. Moreover, it is also attributed to the self-associating effect of ethanol therefore the self-associates of acrylonitrile by dipole-dipole interactions and the self-associates of ethanol by hydrogen bonding between same molecules at low concentrations predominate too.

Volumetric properties of binary mixtures of o-cresol + poly(ethylene glycols) in the temperature range 288.15–308.15 K and atmospheric pressure

ABSTRACTThe density of binary mixtures of (o-cresol + poly(ethylene) glycol (PEG)-200, + PEG-300 and + PEG-400) has been measured over the entire range of composition at temperatures (288.15, 293.15, 298.15, 303.15 and 308.15 K) and atmospheric pressure. Excess molar volumes () of the mixtures were calculated and correlated by the Redlich–Kister equation. Temperature dependences of the Redlich–Kister coefficients are also presented.From the experimental density data, apparent molar volumes Vϕ1 and Vϕ2, partial molar volumes () and () and excess partial molar volumes () and () were calculated for all binary systems. The variation of these parameters with composition and temperature is discussed in terms of molecular interactions in these binary mixtures.

Density and excess molar volume of binary mixture of thiocyanate-based ionic liquids and methanol at temperatures 293.15–323.15 K

Densities of binary mixture of three ionic liquids, 1-butyl-3-methylimidazolium thiocyanate ([C4C1im][SCN]), 1-allyl-3-methylimidazolium thiocyanate ([C1=C2)C1im][SCN]) and 3-(3-butyl-1H-imidazol-3-ium-1-yl)propanenitrile thiocyanate ([(NC)2C2C4im][SCN]), with methanol were measured over a temperature range of 293.15 to 323.15K and at atmospheric pressure. Excess molar volumes (VmE) were calculated from density values and correlated with Redlich–Kister polynomial equation.Partial molar volumes at infinite dilutions (Vm,i∞) of the ILs and methanol were determined from the Redlich–Kister coefficients. For all the studied systems, the VmE is negative over the entire composition range. The VmE and Vm,i∞ are interpreted in terms of intermolecular interactions in the binary mixture. Density functional theory has been used to investigate the interactions between methanol and the studied ILs.

Molar excess enthalpy (HmE) for systems of aqueous piperazine derivatives

Molar excess enthalpies (HmE) of aqueous1-methyl piperazine (1-MPZ), 4-(2-hydroxy ethyl) morpholine (4,2-HEMO), 1,4-dimethyl piperazine (1,4-DMPZ), 1-(2-hydroxyethyl) piperazine (1,2-HEPZ), 3-morpholinopropyl amine (3-MOPA), morpholine (MO) were reported at three different temperatures T=(298.15, 313.15, and 323.15)K and over the entire range of mole fractions. The Redlich–Kister (RK) equation was used to correlate the experimentally measured HmE values as a function of mole fractions. The molar enthalpies of amines and water at infinite dilutions were determined from the RK coefficients. Among the studied solution theory models to correlate the experimental data, the modified UNIFAC (UNIversal Functional groups Activity Coefficient, Dortmund) model exhibited the lowest percentage of average absolute deviations from the experimental data, followed by the NRTL (Non-Random Two Liquid) model and the UNIQUAC (UNIversal QUAsi Chemical) model. Among the six amines studied, the {1-MPZ+water} system exhibited the highest values of molar excess negative enthalpies followed by {3-MOPA+H2O}, {1,2-HEPZ+H2O}, {MO+H2O}, {1,4-DMPZ+H2O} and {4,2-HEMO+H2O} systems.

Solute–Solvent Interaction of Benzene with Acetic Acid at Different Temperatures

The present paper reports a study of binary mixtures of benzene and acetic acid over the entire range of composition at temperatures of 288, 298, 308 and 318 K. The measured values of static dielectric constant, density, and refractive index of the binary mixtures are further used to evaluate the excess dielectric constant, excess molar volume, excess refractive index, molar and excess molar refraction at these temperatures. The values of excess dielectric constant and excess refractive index are positive whereas the excess molar volume is negative over the entire range of mole fractions of acetic acid. The results are discussed in light of the intermolecular interactions occurring between the benzene and acetic acid molecules. The excess parameters were fitted with the Redlich–Kister equation and the resulting estimated Redlich–Kister coefficients (a j ) and standard deviations are reported.

Densities, Excess Molar Volumes, and Thermal Expansion Coefficients of Aqueous Aminoethylethanolamine Solutions at Temperatures from 283.15 to 343.15K.

The densities of aqueous mixtures of aminoethylethanolamine (CAS #000111-41-1) were measured over the entire compositional range at temperatures of 283.15–343.15 K. The results of these measurements were used to calculate excess molar volumes and isobaric thermal expansion coefficients, and partial molar and apparent molar volumes and excess isobaric thermal expansion coefficients were subsequently derived. The excess molar volumes were correlated as a function of the mole fraction using the Redlich–Kister equation. Temperature dependences of the Redlich–Kister coefficients are also presented. The partial molar volumes at infinite dilution of AEEA in water were determined using two different methods. In addition, the solution density was correlated using a Joubian–Acree model. Aqueous solutions of AEEA exhibit similar properties to the aqueous solutions of other alkanolamines (like monoethanolamine) used in acid gas sweetening.

Dielectric relaxation study of hydrogen bonded structures in ethanolamine with diethanolamine using TDR technique

The complex permittivity spectra for ethanolamine-diethanolamine binary mixture have been determined over the frequency range of 10MHz to 20GHz using time domain reflectometry (TDR) method in the temperature rang 35°C to 50°C for 11 different concentrations of the system. The present work reveals molecular interaction between same multi-functional groups [−OH and −NH2] of the alkanolamines (ethanolamine and diethanolamine) with different molecular size (carbon chain), on the basis of evaluation the static dielectric constants, relaxation time, the corresponding excess properties, the Redlich-Kister coefficients up to their order and Kirkwood correlation factor of the mixture have been determined. The value of static dielectric constant decreases and relaxation time increases with increasing concentrations of DEA in ETA for all temperatures. The static dielectric constants for the mixture have been fitted with the modified Bruggeman model.

Application of the PFV EoS correlation to excess molar volumes of (1-ethyl-3-methylimidazolium ethylsulfate + alkanols) at different temperatures

The experimental densities for the binary systems of an ionic liquid and an alkanol {1-ethyl-3-methylimidazolium ethylsulfate [EMIM] + [EtSO 4] − + methanol or 1-propanol or 2-propanol} were determined at T = (298.15, 303.15, and 313.15) K. The excess molar volumes for the above systems were then calculated from the experimental density values for each temperature. The Redlich–Kister smoothing polynomial was used to fit the experimental results and the partial molar volumes were determined from the Redlich–Kister coefficients. For all the systems studied, the excess molar volume results were negative over the entire composition range for all the temperatures. The excess molar volumes were correlated with the pentic four parameter virial (PFV) equation of state (EoS) model.

Excess molar volumes and isentropic compressibility of binary systems {trioctylmethylammonium bis(trifluoromethysulfonyl)imide + methanol or ethanol or 1-propanol} at different temperatures

This paper reports measurements of densities for the binary systems of an ionic liquid and an alkanol at T = (298.15, 303.15, and 313.15) K. The IL is trioctylmethylammonium bis(trifluoromethylsulfonyl)imide [OMA] +[Tf 2N] − and the alkanols are methanol, or ethanol, or 1-propanol. The speed of sound at T = 298.15 K for the same binary systems was also measured. The excess molar volumes and the isentropic compressibilities for the above systems were then calculated from the experimental densities and the speed of sound, respectively. Redlich–Kister smoothing polynomial equation was used to fit the excess molar volume and the deviation in isentropic compressibility data. The partial molar volumes were determined from the Redlich–Kister coefficients. For all the systems studied, the excess molar volumes have both negative and positive values, while the deviations in isentropic compressibility are negative over the entire composition range.

The two faces of the Redlich–Kister equation and the limiting partial molar volume of water in 1-aminopropan-2-ol

The properties of the Redlich–Kister equation when expressed in power series of x 1 − x 2 are related to its alternative expression in terms of power series of x 2 − x 1, where x 1 and x 2 are mole fractions of the components 1 and 2 of a binary liquid mixture. The simple relationship between both sets of coefficients is derived and shown to conceal pitfalls while using Redlich–Kister coefficients to estimate partial molar properties of the components. The zero-powered terms, which are the same for the alternative expansions, are shown to yield four-fold the excess molar property for the equimolar mixture. Literature data for the partial molar volume of water at infinite dilution in 15 neat aminoalkanols at different temperatures are collected and tabulated. These data generally show a positive dependence of that limiting value on the temperature, the only apparent exception being in the case of 1-aminopropan-2-ol. It is demonstrated that the recently published data for this aminoalkanol [S. Mokraoui, A. Valtz, C. Coquelet, D. Richon, Thermochim. Acta 440 (2006) 122–128] were ill-treated and recalculated limiting values are given, which increase with increasing temperature.

Molar excess enthalpy [formula omitted] for various {alkanolamine (1) + water (2)} systems at T = (298.15, 313.15, and 323.15) K

The molar excess enthalpies ( H m E ) for 2-{(2 aminoethyl)amino}ethanol (AEEA), 3-amino-1-propanol (AP), 2-(methylamino)ethanol (MAE), 1-amino-2-propanol (MIPA), and N- N-dimethylethanolamine (DMEA) in water are reported at three different T = (298.15, 313.15, and 323.15) K and over the entire range of mole fractions. The experimentally measured H m E values are correlated as a function of mole fractions using the Redlich–Kister (RK) equation. The molar enthalpies of alkanolamines and water at infinite dilutions are determined from the RK coefficients. The experimentally measured H m E values are modeled using the following solution theory models: NRTL (non-random two liquid), UNIQUAC (UNIversal QUAsi Chemical), and the modified UNIFAC (UNIversal Functional groups Activity Coefficient, (Dortmund)) model.

Single crystal growth of Bi 1− xSr xMnO 3—Thermodynamics and experiment

The primary crystallization field of a perovskite solid solution Bi 1− x Sr x MnO 3− δ was delimited by calculating the respective phase equilibria in the quaternary Bi–Sr–Mn–O system. The calculations are based on the recent assessment involving all three ternary subsystems, a quaternary liquid approximated as a mixture of Mn, MnO, Mn 2O 3, SrO and Bi 2O 3 species with binary Redlich–Kister coefficients and the perovskite phase described in terms of a point defect model allowing Sr 2+ for Bi 3+ substitution, oxygen vacancy formation and the related Mn 3+/Mn 4+ mixing on Mn-sublattice. The crystallization path and the composition of the crystallized solid solution are compared with single crystal growth experiments performed by self-flux method from a Bi-rich melt. The crystallization path obtained for a selected feed composition for which the largest and high quality single crystal have been grown, turns out to end very close to the global eutectic point.

Phase equilibria modeling in Bi 2O 3–SrO–MnO x system

The selected pseudobinary, isothermal and isoactivity sections of the Bi 2O 3–SrO–MnO x phase diagram are constructed from the calculated phase equilibria. The starting point for the thermodynamic analysis were the assessments of the respective pseudobinary systems Bi 2O 3–SrO, Bi 2O 3–MnO x and SrO–MnO x . The only quaternary solid phase–the perovskite solid solution–is described in terms of the point defect model [ Bi 3+ 1− x Sr 2+ x ] [ Mn 3+ 1− x+2δ Mn 4+ x−2δ ] [O 2− 1−δ/3 V a δ/3] 3. The quaternary liquid is approximated by a phenomenological model using the liquid species Mn, MnO, MnO 1.5, SrO, and BiO 1.5 with only binary Redlich–Kister coefficients. The ab initio electronic structure calculations of cohesive energies are employed to evaluate the enthalpies of formation of some stoichiometric phases.

Excess molar volumes and partial molar volumes for (propionitrile+an alkanol) at T=298.15 K and p=0.1 MPa

Abstract The excess molar volumes and the partial molar volumes for (propionitrile + an alkanol) at T = 298.15 K and at atmospheric pressure are reported. The hydrogen bonding between the OH⋯NC groups are discussed in terms of the chain length of the alkanol. The alkanols studied are (methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, and 1-pentanol). The excess molar volume data was fitted to the Redlich–Kister equation The partial molar volumes were calculated from the Redlich–Kister coefficients.