Kister Equation Research Articles

Investigation of the Thermodynamic Properties, Phase Relations, and Stability of the Cd–Gd System via Thermodynamic Remodeling

The CAlculation of PHAse Diagram (CALPHAD) technique is used in the critical remodeling of the Cd–Gd system. On the basis of a new experiment in literature, the excess Gibbs energies of the solution phase expression (liquid, bcc, and hcp_A3) are described using the Redlich–Kister equation. Intermetallic compounds (α-Cd2Gd, β-Cd2Gd, and Cd45Gd11), which exhibit a homogeneity range, are treated as a two-sublattice model. Four compounds (Cd3Gd, Cd58Gd13, Cd6Gd, and Cd8Gd) are treated as stoichiometric compounds. Two Calphad-type thermodynamic descriptions are developed for the CdGd and bcc. Model I is to model the compound CdGd and bcc-Gd separately. Model II is to use the formula (Cd,Gd)0.5(Cd,Gd)0.5(Va)3 to describe the compound CdGd with a CsCl-type structure (B2) and cope with the disorder–order transition from bcc-A2 to bcc-B2. The present work displays that two eutectic reactions, five peritectic reactions, one peritectoid reaction, one eutectoid reaction, one polymorphic transformation, and one congruent reaction are observed in the Cd–Gd system.

Volumetric properties of binary mixtures of 1-ethyl-3-methylimidazolium ethyl phosphonate + methanol or 2-propanol

The present study aimed to determine the refractive indices at 293.15 K and density data at T= (283.15, 293.15, 303.15 and 313.15) K of the binary mixtures of 1-ethyl-3-methylimidazolium ethylphosphonate + methanol or 2-propanol under the atmospheric pressure. The excess molar volume, the apparent molar volume, the partial molar and excess partial molar volumes of the components at infinite dilution were calculated from the experimental values. The results of excess molar volumes were fitted to a Redlich– Kister equation, leading thus to obtain the coefficients and to estimate the standard deviations between the experimental and the calculated quantities. Also, the results of excess molar volumes of the two investigated binary mixtures showed negative deviations from ideal behavior of the investigated binary systems which can be then discussed in terms of ion-dipole interactions, formation of hydrogen bonds and structural factors. Additionally, the refractive indices measurements and the deviations of refractive index were determined.

Physicochemical Properties and Spectral Studies for Binary Systems of 2-Ethoxyethanol (1) + Water (2) and + Dimethyl Sulfoxide (2)

In the development of CO2 capture and utilization, the physical and transport properties of the binary systems are significant, because these can affect the gas absorption and desorption processes. Thus, we report the densities and viscosities of two binary systems: 2-ethoxyethanol (ECS) + water (H2O) and ECS + dimethyl sulfoxide (DMSO), with various compositions at temperatures from (298.15 to 318.15) K. On the basis of these data, excess molar volumes ( $$V_{\text{m}}^{\text{E}}$$ ) and viscosity deviations (Δη) were calculated. The $$V_{\text{m}}^{\text{E}}$$ values of the two binary mixtures are negative and decrease with increasing temperatures; Δη values are positive at all compositions and decrease with increasing temperatures. The $$V_{\text{m}}^{\text{E}}$$ and Δη values were fitted with the Redlich–Kister equation. The physico-chemical properties of the two binary systems, including activation enthalpy and entropy, were calculated from the kinematic viscosity. In addition, various spectral results offer evidence for the formation of weak interactions between ECS and DMSO or H2O.

Physico-chemical properties of ionic liquids: Density, viscosity, density at high pressure, surface tension, octan-1-ol/water partition coefficients and thermodynamic models

Ionic liquids (ILs) are an important new media and one of the most attractive solvents used in extraction and separation processes. This work presents some important physico-chemical properties and topics related to ILs, which were found by us as good extractive solvents for the desulfurization of fuels and for the separation of water/biobutan-1-ol. It consists of the most important series of experimental measurements of density and viscosity of pure ILs and in binary systems with thiophene and butan-1-ol: (N-hydroxyethylpyridinium tricyanomethanide, [C2OHPy][TCM] + thiophene), or (N-hydroxypropylpyridinium tricyanomethanide, [C3OHPy][TCM] + thiophene) or (N-benzyl-N-dodecyl-N,N-dimethylammonium bis(trifluoromethyl-sulfonyl)imide, [N1,1,12,Bz][NTf2] + butan-1-ol). These systems exhibit mainly negative molar excess volumes, VE in systems with thiophene and slightly positive and negative in the system with butan-1-ol. The Redlich – Kister equation was used for correlation of the liquid density, excess molar volumes and dynamic viscosity deviations as a function of temperature and composition, whereas Vogel-Fulcher-Tammann, VFT was used for describing the temperature dependence of dynamic viscosities. Very often, the high pressure is proposed for new technologies of separation and that is why we present the influence of pressure on the density of [C2OHPy][TCM], [C3OHPy][TCM] and [N1,1,12,Bz][NTf2] in a wide range of temperature from T = (298.15–348.15) K and pressure from p = (0.1–40) MPa. The Tait equation was used for the correlation of density as a function of mole fraction, temperature, and pressure. The influence of pressure for ILs, is as usual, not significant. The thermal expansion coefficient α and isothermal compressibility coefficient κ as a function of temperature T, and pressure p are presented. Herein, surface tension of new ILs was measured for the collection of physico-chemical properties of the ILs used in this work. Also, the octan-1-ol/water, Kow partition coefficients in ternary liquid-liquid phase equilibrium were determined for the systems {[C2OHPy][TCM], or [C3OHPy][TCM] (1) + octan-1-ol (2) + water (3)} at temperature T = 298.15 K and the discussion of the biocompatibility of the used ILs is presented.

Densities and Viscosities of N,N-Dimethylaniline and Mixtures with Methanol, Ethanol, 1-Propanol, and 1-Butanol at 298.15–313.15 K

Densities and viscosities of N,N-dimethylaniline mixtures with methanol, ethanol, 1-propanol, 1‑butanol were measured over the entire composition range at 298.15, 303.15, 308.15, and 313.15 K and atmospheric pressure. There was calculated excess molar volumes, viscosity deviation and excess Gibbs energies of activation of viscous flows. The excess properties were fitted to the Redlich–Kister equation.

Density and viscosity for binary mixtures of methyl decanoate with 1-propanol, 1-butanol, and 1-pentanol

In this work, the volumetric and viscometric properties of the mixtures of methyl decanoate with 1-propanol, 1-butanol, and 1-pentanol were investigated from 298.15 K to 333.15 K. The density data of the mixtures were obtained based on the vibrating-tube densimeter, and the kinematic viscosities of the mixtures were measured using the Ubbelohde capillary viscometer. Based on the experimental data, the excess molar volumes and viscosity deviations were calculated and correlated with the Redlich–Kister equation. In addition, the McAllister four-body model, Frenkel model, Grunberg-Nissan model, and Heric's model were used to correlate the viscosities of the mixtures.

Critical properties for the mixtures of ethanol and some biodiesel surrogates

Critical temperature Tc and critical pressure pc of the mixtures of ethanol and biodiesel surrogates (ethanol + methyl butanoate, ethanol + ethyl propanoate, ethanol + methyl hexanoate, methyl butanoate+ ethyl propanoate and ethanol + methyl butanoate + ethyl propanoate) were measured via a flow method. A linear decrease in Tc and an increase in pc of three binary mixtures can be observed with the increasing mole fraction of ethanol. Despite the mole fraction of ethyl propanoate increases, critical curves of the ternary mixture change almost linearly with the mole fraction of ethanol. Critical properties of the binary mixtures were interrelated with Redlich–Kister equations and PR-WS equations and predicted by He equations. Maximum AADs for Tc and pc using Redlich–Kister equations are 0.08% and 0.65%. There is a great agreement between our experimental data and calculated values from two correlations for the critical parameters of ternary mixture.

Volumetric and viscometric properties of binary and ternary mixtures of monoethanolamine, 2-(diethylamino) ethanol and water from (293.15 to 333.15) K

The densities and viscosities of binary mixtures monoethanolamine (MEA) + H2O, 2-(Diethylamino)ethanol (DEEA) + H2O, MEA + DEEA and ternary mixtures MEA + DEEA + H2O were measured over the entire composition at temperatures ranging from (293.15 to 333.15) K and atmospheric pressure. The volumetric and viscometric properties such as excess molar volume, partial molar volume, partial molar volume at infinite dilution, apparent molar volume, viscosity deviation, molar enthalpy, molar entropy and the molar Gibbs energy of activation for viscous flow of mixtures were calculated in terms of experimental data, respectively. Furthermore, excess molar volumes were fitted by the Redlich–Kister equation for binary mixture and by Cibulka equation for ternary solution. The volumetric and viscometric properties were analyzed through the molecular structure and intermolecular interactions.

Excess enthalpies and heat of esterification reaction in ethanol + acetic acid + ethyl acetate + water system at 313.15 K

The excess enthalpies for ethanol + acetic acid + ethyl acetate + water system in the chemically equilibrium states are determined with the C80 calorimeter (Setaram) equipped with membrane mixing cells at 313.15 K and atmospheric pressure. The quaternary system exhibited positive values of the excess enthalpies over the entire range of mole fractions. The heat of esterification reaction is calculated on the base of data obtained for heat effects in the mixture, and it was found to be − 3.6 ± 0.2 kJ mol−1. The correlation of the data was carried out using NRTL model and Redlich–Kister equation.

Thermodynamic description of the Ce–Ga and Ga–Gd systems

The Ce–Ga and Ga–Gd systems are critically assessed by means of the calculation of phase diagram (CALPHAD) technique. The excess Gibbs energy of the solution phases [liquid, orthorhombic (Ga), fcc (Ce), bcc (Ce or Gd), and hcp (Gd)] is modeled with the Redlich–Kister equation. In the Ce–Ga and Ga–Gd systems, the intermetallic compounds, CeGa, Ce3Ga2, Ce3Ga, α-CeGa6, β-CeGa6, GaGd, Ga6Gd, Ga2Gd3, and Ga3Gd5 are treated as stoichiometric compounds. The intermetallic compounds CeGa2 and Ga2Gd with a homogeneity range, are treated using a two-sublattice model as the formula (Ce,Ga)0.333333(Ce,Ga)0.666667, and (Ga,Gd)0.666667(Ga,Gd)0.333333, respectively. In the Ce–Ga system, there are nine invariant reactions, and five stoichiometric intermetallic compounds and the compound CeGa2 with a homogeneity domain ranging from about 66.67 to 77.94 at.% Ga. Some improvements are obtained based on the experimental data in the present work, the liquidus line is more close to the most experimental points, and the homogeneity range of the compound CeGa2 seems more reasonable at full temperature range. In the Ga–Gd system, there are eight invariant reactions, and four stoichiometric intermetallic compounds and the compound Ga2Gd with a homogeneity domain ranging from about 19.64 to 33.33 at.% Gd. The present phase diagram and thermodynamic properties of the system are well reproduced with the experimental data.

The molar surface quasi-Gibbs energy and its application to the binary mixtures of 1-(2-methoxyethyl)-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide [MOEMIM][NTf2] with methanol and ethanol

The IL (ionic liquid) 1-(2-methoxyethyl)-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide [MOEMIM][NTf2] was prepared and confirmed by 1H NMR (1H nuclear magnetic resonance) spectroscopy and 13C NMR (13C nuclear magnetic resonance) spectroscopy. The density and surface tension for the binary mixtures of [MOEMIM][NTf2] with methanol and ethanol were measured across the entire range of mole fraction (x1 = 0.0000–1.0000) at T = (288.15–318.15) K. The average molar volumes of the binary mixtures were calculated from the experimental density, which increased with the increase of mole fraction and temperature. The excess molar volumes, VmE, were obtained and fitted by Redlich–Kister equation. The interaction between ionic liquid and alcohol is the strongest efficient packing and/or attractive interaction at the minimum point. The lower the temperature was, the smaller the absolute value of excess molar volume was. The new function – the molar surface quasi-Gibbs energy of mixtures was obtained by us in this work. On a basis of molar surface quasi-Gibbs energy of mixtures, a new Eӧtvӧs equation was obtained of mixtures and applied to binary mixtures of [MOEMIM][NTf2] with alcohols. The absolute value of the slope of the new Eötvös equation is the mole surface entropy, s, and the intercept is the molar surface enthalpy, h, which is temperature-independent. The deviation of molar surface quasi-Gibbs energy, Δgs, of mixtures for [MOEMIM][NTf2] with methanol and ethanol were calculated. Δgs was well fitted by Redlich–Kister equation. In terms of Redlich–Kister’s parameters, Ai, a new method for estimating the surface tension, γ, with any component of the mixtures is proposed and the estimated values, γ (est.), are in good agreement with the corresponding experimental ones, γ(exp.).

Volumetric and acoustic properties of ionic liquid, 1-hexyl-3-methylimidazolium bromide in 1-hexanol, 1-heptanol and 1-octanol at T = (298.15–328.15) K

ABSTRACT The density ρ and speed of sound u of the binary mixtures (1-hexyl-3-methylimidazolium bromide ([HMIm][Br]) + 1-hexanol or 1-heptanol or 1-octanol) were reported at T= (298.15, 308.15, 318.15 and 328.15) K and atmospheric pressure. Using the experimental-measured data, the molar volume Vm , excess molar volume , isentropic compressibility κ s and isentropic compressibility deviation Δκ s were calculated. Also, the Jouyban–Acree and Redlich–Kister polynomial equations were used for correlation of (ρ, V m, u and κ s) and ( and Δκ s), respectively. The obtained percent average relative deviation %ARD and standard deviation σ show that the studied mixtures can be described well by Jouyban–Acree and Redlich–Kister equations, respectively.

Spectral Study of Intermolecular Interactions in Some Sulfolane/Alcoholic Binary Mixtures Using Solvatochromic Measurements

Solvatochromic parameters including the Kamlet–Abboud–Taft parameters (α, β, and π*: KAT parameters) and Reichardt’s polarity scale (ET(30)) were measured spectroscopically over the whole mole fraction range of binary mixtures of sulfolane and some alcohols (methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, 2-butanol, iso-butanol, tert-butanol) at 303.15 K. These parameters were obtained based on UV–Vis absorbance of some solvatochromic probes. The spectral changes of these indicators were interpreted in terms of specific and nonspecific dye–solvent interactions. The parameter ET(30) was obtained from electronic absorbance of the betaine dye within the mixtures. Absorbance band shifts of N,N-dimethyl-4-nitroaniline and 4-nitroaniline in concert with absorbance changes of Reichardt’s betaine dye were used to obtain dipolarity/polarizability (π*), hydrogen-bond donating (HBD) acidity (α) and hydrogen-bond accepting (HBA) basicity (β) of the mixtures. The Redlich–Kister equation was applied to the experimental data for different empirical solvatochromic parameters to demonstrate the effect of solvent composition on these parameters in the mixtures.

Density and Viscosity of Ternary Mixture of Cyclopentanol + exo-Tetrahydrodicyclopentadiene + 1,3-Dimethyladamantane

Oxygenated additives have been proved to improve the property of an aviation fuel, such as reducing pernicious emissions and adjusting physical properties, and an appropriate alcohol is usually a typical candidate. To understand the properties of high-energy-density hydrocarbon fuels with alcohol, densities (ρ) and viscosities (η) of ternary system, cyclopentanol + exo-tetrahydrodicyclopentadiene (JP-10) + 1,3-dimethyladamantane (1,3-DMA), and their corresponding binary systems, have been determined over the whole composition range at different temperatures, T = (293.15–333.15) K, and atmospheric pressure, p = 0.1 MPa. The excess molar volumes (VmE) and the viscosity deviations (Δη) of the binary systems mixtures were calculated and fitted to the Redlich–Kister equation, while those of the ternary systems were calculated and fitted to four different semiempirical equations. The results show that the addition of cyclopentanol can lead to a little higher density and a lower viscosity, which are beneficial t...

Density, Speed of Sound, and Dynamic Viscosity of 1-Butyl-3-methylimidazolium Bis(trifluoromethylsulfonyl)imide/1-Butyl-3-methylimidazolium Hexafluorophosphate and N-Methylaniline Binary Systems from T = 298.15 to 323.15 K at 0.1 MPa

Density, speed of sound, and viscosity values were measured for different binary mixture concentrations of 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([Bmim][NTf2]) + N-methylaniline (NMA) and 1-butyl-3-methylimidazolium hexafluorophosphate ([Bmim][Pf6]) + NMA systems at temperatures from T = 298.15 to 323.15 K under atmospheric pressure. The excess values of molar volume, molar isentropic compressibility, intermolecular free length, and viscosity were calculated. The partial molar volumes and partial molar isentropic compressibilities at infinite dilutions were also estimated. The Redlich–Kister equation was utilized to evaluate coefficients and standard deviations. The mechanism of effective packing between [Bmim][NTf2]/[Bmim][Pf6] and NMA was represented by the negative excess molar volumes. In both the studied systems, the occurrence of strong chemical interactions was represented by the negative excess intermolecular free length values. The present work clearly showed that the simu...

Densities and viscosities of binary mixtures of 2,2-diethyl-1,1,3,3-tetramethylguanidinium bis(trifluoromethylsulfonyl)imide with methanol and ethanol

The guanidinium-based ionic liquid (IL), 2,2-diethyl-1,1,3,3-tetramethylguanidinium bis(trifluoromethylsulfonyl)imide ([TMG(C2)2][NTf2]), was synthesized. Densities and viscosities of the IL and its mixtures with methanol or ethanol were reported at temperatures from 293.15 K to 323.15 K. The increment of IL concentration or the decrement of temperature significantly increases both density and viscosity. Excess molar volume (VmE) and viscosity deviation (Δη) of each binary mixture were calculated, and the Redlich–Kister equation was used to fit VmE and Δη with composition. When VmE is negative with the mole fraction of IL (x1) lower than 0.8 for two systems, Δη is negative over the whole concentration range. The positive VmE of the mixture at a high IL concentration indicates that interaction loss occurs. Moreover, structures of the equimolar mixture of IL and alcohol were obtained by DFT calculations, and alcohol–anion, alcohol–cation and cation–anion interactions were revealed. Strong H-bond interaction with the span of 1.61 Å is formed between the H atom of the OH group in alcohol and the O atom in the [NTf2]− anion, while the O atom of the OH group in alcohol interacts with the methyl groups in the [TMG(C2)2]+ cation. Significant cation–anion interactions (<2.40 Å) in the manners of H⋯F and H⋯O with spans less than 2.40 Å are found at the same time. It is the enhanced H-bond interactions that contribute to the negative VmE of the equimolar mixture at non-concentrated regions.

Density and viscosity of binary mixtures of diethyl oxalate with ethanol, ethyl acetate, tetrahydrofuran, and toluene

ABSTRACT This study presents the densities and viscosities of four binary liquid mixtures containing diethyl oxalate (DEO) with the organic solvents ethanol, ethyl acetate (EA), tetrahydrofuran (THF), and toluene at temperatures ranging from 303.15 to 323.15 K and at atmospheric pressure. DEO is widely used in the pharmaceutical industry as an intermediate or reaction reagent for synthesizing active pharmaceutical ingredients. The measured thermophysical properties are important for pharmaceutical process design and development. A vibrating tube digital density meter and a capillary viscometer were used for density and viscosity measurements, respectively. According to the measurement data, the excess molar volumes (VE ) and viscosity deviations ( ) of the binary mixtures were calculated and satisfactorily correlated with the four-parameter Redlich–Kister equation. Ethanol or THF addition to DEO led to a positive deviation of VE , whereas EA or toluene addition to DEO led to a negative deviation. These results indicated the molecular packing of DEO with EA and toluene was more efficient than that with ethanol and THF. By contrast, the values of the four binary mixtures were negative, indicating that the viscosity was markedly lower than that of an ideal mixture.

Density, Speed of Sound, and Viscosity of Diethylene Glycol Monoethyl Ether + N,N-Dimethylformamide (Ethanol, Water) at T = 288.15–318.15 K

The density (ρ), speed of sound (u), and viscosity (η) of the binary mixtures of (diethylene glycol monoethyl ether (carbitol) and water, ethanol, N,N-dimethylformamide) have been measured in full concentration range at T = 288.15, 298.15, 308.15, and 318.15 K and p = 0.0868 MPa. Using the experimental data, the molar volume (Vm), excess molar volume (VmE), isentropic compressibility (κs), excess molar isentropic compressibility (κs,mE), and viscosity deviation (Δη) were calculated. The most negative values of VmE and κs,mE and positive values of Δη obtained for the carbitol + water mixture are indicative of the strong interactions between different components relative to two other systems. The values of ρ, Vm, and κs for the studied mixtures were correlated using the Jouyban–Acree model with high accuracy. Furthermore, the obtained values of VmE, κs,mE, and Δη were described by the Redlich–Kister equation and reasonable standard deviations were obtained.

Densities and Viscosities for the Ternary System of Decalin + Methylcyclohexane + Cyclopentanol and Corresponding Binaries at T = 293.15 to 343.15 K

Densities (ρ) and viscosities (η) for the ternary system of decalin (1) + methylcyclohexane (2) + cyclopentanol (3) and three corresponding binary systems have been measured over the whole composition range at 11 temperature points from 293.15 K to 343.15 K under atmospheric pressure (0.1 MPa). The excess molar volumes (VmE) and viscosity deviations (Δη) of binary systems have been calculated and further fitted with the Redlich–Kister equation, while corresponding physical data of the ternary system have been correlated via the Clibuka, Singh, Nagata-Tamura, and Redlich–Kister equations. The VmE values are negative for the binary system of decalin (1) + methylcyclohexane (2) with a minimum when the moles of the two components are similar. For the system of decalin (1) + cyclopentanol (2), the VmE values are always positive with a maximun at about x1 = 0.6. At the same time, a sigmoid curve can be observed for the system of methylcyclohexane (1) + cyclopentanol (2). The minimum and maximum appear around x1...

Excess volumes and partial molar volumes of binary liquid mixtures of furfural or 2–methylfuran with alcohols at 298.15 K

In this work, densities, excess molar volumes, partial molar volumes and excess partial molar volumes for binary liquid mixtures of furfural and 2–methylfuran with 1–propanol or 2–propanol or 2–butanol or 1–pentanol or 2–pentanol or 1–hexanol at 298.15 K and 0.1 MPa over the entire range of composition were determined. Excess molar volumes were correlated with Redlich–Kister equation with average absolute deviations smaller than 0.0164. Excess molar volumes were negative for furfural + 1–propanol or 2–propanol and positive for all other studied binary systems. Solute partial molar volumes determined increase as alcohol carbon chain length increase, except for furfural + 2–pentanol, which presented smaller values than 2–butanol for molar fractions below 0.2. A maximum/minimum was observed from the excess partial molar volume plots. FTIR spectra data indicate bands at 3135 cm−1, for furfural systems, and 3122 cm−1 for 2–methylfuran systems, are related to the behavior found for excess molar volumes and that H–bonds are smaller for furfural systems than for 2–methylfuran.