Showing papers in "Physics and Chemistry of Liquids in 2008"

Numerical expressions for viscosity, surface tension and density of biodiesel: analysis and experimental validation

Abstract: The purpose of this work was to test the accuracy and predictive power of different numerical methods in order to compute reliable values of viscosity, surface tension and density of biodiesel in a wide range of temperature. Available formulae in literature were used to compute the mentioned properties in the temperature ranges in which they were developed. To validate the numerical expressions we have used experimental measurements of viscosity, surface tension and density performed in our laboratory and published in the literature. In this article, the results obtained by the application of different expressions are shown and possible sources of discrepancy between measured and predicted values are mentioned. The method that predicts the best results is identified for each property. In order to achieve a better fitting to the experimental data, corrections in the expression of the temperature-dependent properties were made when they were necessary.

Binary mixtures containing OMIM PF6: density, speed of sound, refractive index and LLE with hexane, heptane and 2-propanol at several temperatures

Abstract: Experimental densities, speeds of sound and refractive indices of the binary mixtures OMIM PF6 (1-methyl-3-octylimidazolium hexafluorophosphate) with hexane, heptane, and 2-propanol were determined at T = 293.15, 298.15, and 303.15 K. Excess molar volumes, changes of refractive index on mixing and deviations in isentropic compressibility for the above systems were performed. The liquid–liquid equilibrium data of these binary mixtures were carried out experimentally and the NRTL and UNIQUAC correlative equations were applied.

Thermodynamics of oxygenate fuel additives as a function of temperature

Abstract: This article reports experimental data of density and ultrasonic velocity at the range from 278.15 to 323.15 K and atmospheric pressure of ethers used as additives in fuels (methyl tert-butyl ether ethyl tert-butyl ether, tert-amyl ether and diisopropyl ether). From the experimental data, temperature dependent polynomials were fitted and theoretical models were used to correlate these properties. The MTC Lattice Gas EOS is used to correlate simultaneously vapour pressures and volumetric properties. Free Length Theory is applied to estimate the ultrasonic velocity of the chemicals as a function of temperature, satisfactory predictions were obtained. The dependence of temperature showed by these magnitudes reveals a strong interaction at low values.

Investigation of NMR shielding tensors in 1,3 dipolar cycloadditions: solvents dielectric effect

Abstract: In this article, NMR shielding is investigated in the reactions of 1,3 dipolar cycloaddition of benzonitrile oxide with acrylonitrile, which have been recently studied [E. Rajaeian, M. Monajjem, Cholami, J. Chem. Res., s, 279, (2002); E. Rajaeian, M. Monajjem, Cholami, J. Chem. Res., s, 91, (2003)]. We reported 15N and 17O tensors for benzonitrile oxide and two products in reactions in gas phase and several various solvents and compared the effect of dielectric constant on tensors of the materials mentioned above. Also diffuse and polarizable function effects in basis set are investigated.

Theoretical estimations of thermodynamic properties of liquid mixtures by Flory's statistical theory

Abstract: Flory's statistical theory has been employed for the computation of ultrasonic velocity (u), density (ρ), internal pressure (P i), thermal expansion coefficient (α), isothermal compressibility (β T), adiabatic compressibility (β S), heat capacity at constant pressure (C P), heat capacity at constant volume (C V), heat capacities ratio (γ), pseudo-Gruneisen parameter (Γ), excess volume (V E) and excess heat capacity at constant pressure ( ) at varying temperatures for 10 binary and 5 ternary systems. The binary systems under investigation are: acetonitrile + benzene, benzene + DMF, acetonitrile + DMF, cyclohexanol + cyclohexane, piperidine + tetrahydropyran, piperidine + cyclohexane, tetrahydropyran + cyclohexane, benzene + p-xylene, benzene + p-dioxan, acetone + methyliodide, and the ternary systems are: benzene + chloroform + cyclohexane, toluene + chloroform + cyclohexane, chlorobenzene + chloroform + cyclohexane, dioxane + chloroform + cyclohexane and chlorobenzene + cyclohexane + n-heptane. The result...

Effect of temperature on partial molar volumes and viscosities of dilute aqueous solutions of 1-butanol, 1,2-butanediol, 1,4-butanediol, 1,2,4-butanetriol, and butanetetrol

Abstract: Experimental densities and viscosities of dilute aqueous binary mixtures of 1-butanol, 1,2-butanediol, 1,4-butanediol, 1,2,4-butanetriol, and 1,2,3,4-butanetetrol (erythritol) were measured in the temperature range from 283.15 to 323.15 K. Apparent molar volumes were determined as a function of composition from density measurements. The limiting partial molar volumes of alcohols in aqueous solution were evaluated through extrapolation. The relative viscosity values were adjusted by least-squares to a second order equation to obtain the viscosity B coefficient which has been related to the size and shape of the solute molecule. The temperature dependence of the partial molar volume at infinite dilution and the viscosity B coefficient are discussed in terms of the relationship among polar and non polar groups on water structure and the effect of the position of hydroxyl groups in the molecule.

Computation methodology for determining Abraham solute descriptors from limited experimental data by combining Abraham model and Goss-modified Abraham model correlations

Abstract: A new computation methodology is proposed for calculating the Abraham solute descriptors. The proposed method combines correlations based on both the Abraham model and the Goss-modified version of the Abraham model. The computation methodology is illustrated using published solubility and partition data for benzil in a wide range of organic solvent systems. Calculated solute descriptors back-calculate the observed experimental values to 0.119 log units. The proposed method of using both the Abraham model and the Goss-modified Abraham model correlations significantly increases the number of available equations that can be used in the solute descriptor determination.

Viscosity of glass forming Al86Ni8(La/Ce)6, Al86Ni6Co2Gd4(Y/Tb)2 melts

Abstract: The temperature and time dependences of kinematic viscosity in Al86Ni8(La/Ce)6, Al86Ni6Co2Gd4(Y/Tb)2 melts over the range of liquidus up to 1300°C have been investigated. An irreversible non-monotonic change of the melts viscosity above the temperature of melting brought about by the destruction of their microheterogeneous state inherited from the multi-phase solid sample has been found out. It is shown that for the melts transition into the quasi-equilibrium state long isothermal holding is necessary. The relaxation time decreases with the increase of the melt temperature.

Improving the prediction of liquid saturation densities from models based on the corresponding states principle

Abstract: The liquid saturation density of pure fluids is commonly predicted using models based on the corresponding states principle. Nevertheless, it is well-known that these models are not always accurate near the triple point. In this work we use simple modifications of several of those models in order obtain good accuracy at any temperature. In particular, for each model we change a fixed coefficient to a variable coefficient, which permits the model to reproduce exactly the value of the density at the triple point. The accuracy of a model based on a scale-variable-reduced-coordinate framework, and of a new simple predictive model recently proposed by us is also checked. This latter model does not contain adjustable coefficients but only two variable coefficients that depend on the temperature and density at both the critical and the triple point. We find that a simple modification of the well-known and straightforward Rackett model gives excellent accuracy (mean average absolute deviation 0.9%) in the whole t...

Ultrasonic method of determination of stability constants of charge transfer complexes of certain carbonyl compounds and diethylamine in n -hexane

Abstract: The ultrasonic velocities (U), densities (ρ) and viscosities (η) were measured for solutions containing equimolar concentrations of diethylamine (donor), nine aldehydes and nine ketones (acceptors) in n-hexane at 303 K. Acoustical parameters such as adiabatic compressibility (β), free length (L f), viscous relaxation time (τ), and molecular interaction parameter (χU) have been computed. These values indicate the formation of charge transfer complexes between carbonyl compounds and amine. Formation constant (K) values of the complexes have been evaluated using the equation proposed by Kannappan. The constant values of free energy of activation (ΔG ) and relaxation time indicate the formation of similar charge transfer complexes in these systems. However, the variation in free energy of formation (ΔG°F) values suggests that their thermodynamic stability depends on the structure of donor and acceptor.

LFER correlations for the solubilising characterisation of room temperature ionic liquids containing trifluoromethanesulfonate and trifluoroacetate anions

Abstract: Gas-to-RTIL (room temperature ionic liquid) partition coefficients have been compiled from the published literature for solutes dissolved in 1-methyl-3-butylimidazolium trifluoromethylsulfonate, {[MBIm]+[Trif]−}, and in 1-methyl-3-ethylimidazolium trifluoroacetate, {[MEIm]+[F3Ac]−}. These partition coefficients were converted into water-to-RTIL partition coefficients using the corresponding gas-to-water partition coefficients. Both sets of partition coefficients were analysed using the Abraham model and Goss modified Abraham models with cation-specific and anion-specific equation coefficients. Equation coefficients are reported for the trifluoromethylsulfonate and trifluoroacetate anions. The calculated anion coefficients can be combined with our previously determined eight sets of cation-specific equation coefficients to yield expressions capable of predicting the partition coefficients of solutes in 16 different RTILs.

Ionic interaction of electrolyte with dilute solution of poly(vinyl alcohol) at different temperatures

Abstract: The ionic interactions of ZnSO4 · 7H2O were studied, using dilute solution of polymer as a solvent. The ionic conductance of ZnSO4 · 7H2O in aqueous and mixed solvent systems of aqueous poly(vinyl alcohol) (0–0.9%) was measured in concentration range (2 × 10−3 to 10 × 10−2 m dm−3) at different temperatures (25–45°C), respectively. Conductance data were analyzed by Ostwald dilution law to get the limiting molar conductance (λm°). The limiting molar conductance ( ) decreased with the increase in the composition of polymer showing decreased ion–solvent interaction. Walden product, degree of dissociation and dissociation constant were also calculated using conductance data. Thermodynamic parameters such as free energy change of activation (ΔG*), enthalpy change of activation (ΔH*) and entropy change of activation (ΔS*) were also calculated at various temperatures as function of concentration of electrolyte in aqueous and mixed solvent systems.

Volumetric, viscometric and acoustic properties of binary mixtures of 2-propanol with n -alkanes (C6, C8, C10) at 298.15 and 308.15 K

Abstract: Densities (ρ), viscosities (η), and speeds of sound, (u) of the binary mixtures of 2-propanol with n-alkanes (n-hexane, n-octane, and n-decane) were measured over the entire composition range at 298.15 and 308.15 K and at atmospheric pressure. Using the experimental values of density, viscosity and speed of sound, the excess molar volumes (V E), viscosity deviations (Δη), deviations in speed of sound (Δu), isentropic compressibility (κ s), deviations in isentropic compressibility (Δκ s), and excess Gibbs energies of activation of viscous flow (ΔG* E) were calculated. These results were fitted to the Redlich–Kister type polynomial equation. The variations of these excess parameters with composition were discussed from the viewpoint of intermolecular interactions in these mixtures. The excess properties are found to be either positive or negative depending on the molecular interactions and the nature of liquid mixtures.

Electrical transport properties of some liquid metals

Abstract: In the present article, we report the electrical transport properties viz. the electrical resistivity (ρ), the thermoelectric power and thermal conductivity (σ) of several monovalent, divalent and polyvalent liquid metals of the different groups of the periodic table on the basis of model potential formalism. The well-known empty core model potential of Ashcroft is used for the first time with seven local field correction functions proposed by Hartree, Hubbard–Sham, Vashishta–Singwi, Taylor, Ichimaru–Utsumi, Farid et al. and Sarkar et al. in the present computation and found suitable for such study. In the calculation of these properties we have used the values of the theoretical structure factors due to hard core fluid theory. It is concluded that the comparisons of present and theoretical or experimental findings wherever exists are highly encouraging.

Volumetric properties of dimethyl sulfoxide with some alcohols at 298.15 K

Abstract: Densities ρ, of the binary systems of dimethyl sulfoxide (DMSO) with methanol, ethanol, propan-1-ol, propan-2-ol, butan-1-ol, and butan-2-ol have been measured as a function of the composition of DMSO at 298.15 K and atmospheric pressure, using an Anton Paar model DMA 4500 oscillating U-tube densitometer. From the experimental results, excess molar volumes , and excess partial molar volumes , were calculated. Limiting excess partial molar volumes , are also calculated by extrapolation of partial excess molar volumes to infinite dilution. The excess molar volumes are negative for methanol, ethanol, propan-1-ol and positive for propan-2-ol, butan-1-ol, and butan-2-ol in the entire composition range. The results are explained in terms of aggregates between unlike molecules through O ··· HO hydrogen bonding.

Thermodynamic studies of inclusion complex between cetyltrimethylammonium bromide (CTAB) and β -cyclodextrin ( β -CD) in water/n-butanol mixture, using potentiometric technique

Abstract: The behaviour of the inclusion complex consisting of cetyltrimethylammonium bromide (CTAB) and β-cyclodextrin (β-CD) in water/n-butanol mixture was studied using ion selective electrodes sensitive to surfactant ions. The experiments were carried out at different temperatures and different composition of water/alcohol. The data obtained indicate that the inclusion complexes S(CD) and S(CD)2 had formed between CTAB and β-CD in water/alcohol mixture environment. In addition to the 1 : 1 complex, CTAB formed 1 : 2 complexes with β-CD. Further investigation showed that K 1 for S(CD) was greater than K 2 for S(CD)2, and the values of Ki were reduced with increasing butanol concentration. Finally, thermodynamic parameters of the complexation, i.e. ΔH°, ΔG° and ΔS° were also calculated. The obtained thermodynamic data showed that the hydrophobic interaction is the main factor for inclusion complex formation and tendency of complex formation has been reduced with increasing of medium hydrophobicity.

Effect of toluene in the dipolar interaction of some aliphatic alcohols

Abstract: Sound velocity, density and viscosity values have been measured at 303 K in the three binary systems of toluene + methanol, ethanol, 1-propanol. From these data, acoustical parameters such as adiabatic compressibility, free length, free volume and internal pressure have been estimated using the standard relations. The results are interpreted in terms of molecular interaction between the components of the mixtures. Observed excess value in all the mixture indicates that the molecular symmetry existing in the system is highly disturbed by the non-polar toluene molecules and dipole–dipole type interactions exist in the systems.

Densities and viscosities of propylene carbonate with aromatic hydrocarbons (benzene, 1,4-dimethylbenzene and ethylbenzene) at 288.15, 298.15 and 308.15 K

Abstract: Densities and viscosities of the binary mixtures of propylene carbonate with benzene, 1,4-dimethylbenzene and ethylbenzene were measured over the entire mole fraction range at 288.15, 298.15 and 308.15 K. Using the experimental values of densities and viscosities the excess molar volumes and viscosity deviations were calculated. The results were fitted by Redlich–Kister equation. The results were discussed in terms of intermolecular interactions.

Non-monotonic behaviour with concentration of the surface tension of certain binary liquid alloys

Abstract: The surface tension σ(c) of most liquid binary alloys usually varies with concentration c in a monotonic way between the values σ1 and σ2 of the two pure metals, and this behaviour is well explained by current models. Some alloys show deviations from this ideal behaviour. One of those is Fe–B. The surface tension of this liquid alloy shows a minimum at 17 atomic % B, which corresponds well with the composition of the eutectic point in the phase diagram, followed by a maximum at a concentration of 24 atomic % B or higher. The usual models for the surface tension of liquid binary alloys do not explain those exceptional features, and we propose that a model involving the concentration fluctuations in the liquid alloy has the proper ingredients to account for the features in Fe–B and similar alloys.

Experimental results of and for binary mixtures (propylbenzene + an alkane or + an alkyl ethanoate)

Abstract: This article presents an experimental and theoretical contribution on binary mixtures alkylbenzene + alkanes or + alkylethanoates as a continuation of an investigation project on liquid mixtures containing aromatic compounds and a second component. So, excess molar enthalpies at T = 298.15 K and excess molar volumes at T = 298.15 and 318.15 K for a set of 11 binary mixtures formed by propylbenzene and alkanes (C7 to C16) and alkyl ethanoates (methyl to butyl) are presented. All systems studied showed endothermic effects increasing regularly the in mixtures with alkanes as the aliphatic hydrocarbon chain-length increases, however, in mixtures with ethanoates both excess properties decrease with the increase of the ester molecular weight. The s result positive in mixtures with all alkanes except with heptane and also with all alkylethanotes except with butyl ethanoate which present a sigmoidal representation. An increase in temperature produces in mixtures containing heptane and hexadecane and a almost null...

Surface thermodynamic behaviour of binary liquid mixtures of benzene+1,1,2,2-tetrachloroethane at different temperatures: an experimental and theoretical study

Abstract: Surface tensions, σ, of pure benzene, 1,1,2,2-tetrachloroethane and those of their binary liquid mixtures over the whole composition range at 298.15, 308.15 and 313.15 K have been measured. The experimental σ data have been correlated against temperature and concentration using standard relations. The measured values have been used to calculate various useful thermodynamic parameters, viz., deviation in surface tension, Δσ, surface entropy, S s, and surface enthalpy, H s. The sign and magnitude of these parameters were discussed in terms of molecular interactions between the component molecules of the liquid mixtures. A number of empirical, semi-empirical and statistical models and theories such as Aurebach, Sanchez, Goldsach–Sarvas volume fraction statistics, Brock and Bird relation, Sudgen's relation and Flory–Patterson–Rastogi model have been used to compute theoretically the values of surface tension. Moreover, deviation in surface tension, Δσ has also been calculated using HSIS and HSEG theories and ...

Infrared studies on hydrogen bonding interaction between acrylic esters with 1-dodeconal and phenol in carbon tetrachloride

Abstract: The influence of the hydroxyl group in 1-dodeconal and phenol on the carbonyl vibration of representative compounds belonging to methyl methacrylate, ethyl methacrylate and butyl methacrylate in carbon tetrachloride has been studied by Fourier transform infrared spectroscopic method. The integrated intensities and change in dipole moments for O–H and C=O bonds were calculated. The formation constants of the 1 : 1 complexes have been calculated using Nash's method. The values of the formation constant and Gibbs energy vary with the ester chain length, which suggests that the strengths of the intermolecular hydrogen bonds (O–H ··· O=C) are dependent on the alkyl group of the acrylic ester and the results show that the proton accepting ability of acrylic esters is in the order methyl methacrylate < ethyl methacrylate < butyl methacrylate. The strength of the intermolecular C=O: HO bonds is also shown to be dependent on the basicity of the C=O group of acrylic esters and the acidity of the proton donor.

Physics of glycine interactions with halide salts of alkali metals (group I) determined with density, viscosity, and activation energy in aqueous solutions at 310.15 K

Abstract: Density, ρ (103 kg m−3) and viscosity, η (10−1 kg m−1 s−1) for 0.01–0.33 mol kg−1 aqueous lithium to cesium chloride and iodide salts, and of 0.01–0.10 mol kg−1 glycine (Gly) in 0.01 mol kg−1 aqueous salts have been measured at pH 7. The apparent molal volume (V φ/10−6 m3 mol−1) was calculated from the ρ values, and the η values were fitted in the extended Jones–Dole equation for B (kg mol−1) and D (kg mol−1)2, and Jones–Dole coefficients at infinite dilution (m → 0). The limiting apparent molal volume V φ^ 0, referred to as the partial molal volume ( , binary) of the solute at m → 0, was obtained from the regression of the V φ values, illustrates the solute–solvent and solute–solute interactions. The of water was calculated from ρ, and for Gly in aqueous salts from ρ values for Gly systems. The free energy of activation of the viscous flow ( (kJ mol−1)) per mol of water was calculated from and η0; and (for aqueous salts) from their B coefficients, , and ; while (for Gly in aqueous salts) from their B coe...

Density oscillations in a model of water and other similar liquids

Abstract: It is suggested that the dynamics of liquid water have a component consisting of O−2z (oxygen) anions and H+z (hydrogen) cations, where z is a (small) reduced effective electron charge. Such a model may apply to other similar liquids. The eigenmodes of density oscillations are derived for such a two-species ionic plasma, included the sound waves, and the dielectric function is calculated. The plasmons may contribute to the elementary excitations in a model introduced recently for the thermodynamics of liquids. It is shown that the sound anomaly in water can be understood on the basis of this model. The results are generalised to an asymmetric short-range interaction between the ionic species as well as to a multi-component plasma, and the structure factor is calculated.

Density, viscosity and thermodynamics for viscous flow of water + 1,2-dimethoxyethane

Abstract: Densities and viscosities for the system, water (W) + 1,2-dimethoxyethane (DME), have been determined for the entire range of composition at temperatures, ranging from 303.15 to 323.15 K. Density, viscosity, enthalpy, entropy and free energy of activation for viscous flow have been plotted against the mole fraction of DME. Excess molar volume, , excess viscosity, η E, and excess free energy of activation, ΔG ≠E, have also been plotted against the mole fraction of DME. Most of these properties have been fitted to appropriate polynomial equations. Results have been explained in terms of such factors as, size difference of component molecules, hydrophilic effect, hydrophobic hydration and dipole–dipole interaction.

Vibrational analysis of p - tert -butyl-calix[4]arene conformers by ab initio calculations

Abstract: Band frequencies and intensities in the IR spectra of calix[4]arene have been calculated. Ab initio calculations at HF/6-311G (d, p) level gave vibrational frequencies and infrared intensities for four conformers: cone, partial cone, 1,2- and 1,3-alternate. The geometry optimization has been performed in the basis of C2 symmetry frame of p-tert-butyl-calix[4]arene as a calculation input because it contains no imaginary vibrational frequencies. Additionally the experimental IR spectra of the p-tert-butyl-calix[4]arene were measured and related to the theoretical geometric parameters and force constants. The bands characteristic for each conformation and its reference with respect to specially the OH stretching were defined. Finally we discuss the possibility of hydrogen bonding stability of conformers were discussed.

Thermodynamics of mixtures containing alkoxyethanols. Part xxiii. Speed of sound predictions and ultrasonic studies of hydroxyether + organic solvent mixtures

Abstract: The ability of different models to predict speeds of sound, u, of binary mixtures formed by alkoxyethanol and octane, oxaalkane or propylamine has been examined. The models applied are: the free length theory (LFT), the collision factor theory (CFT), and equations such as those proposed by Nomoto, Junjie or Van Dael. Collision factor theory, Nomoto's and Junjie's equations provide similar deviations between experimental and calculated u, which is represented quite accurately by these three models. Poorer predictions are obtained when applying the Junjie's equation to propylamine systems, probably due to the existence of strong interactions between unlike molecules in such mixtures. In contrast, slightly better u predictions from CFT are obtained for the systems 2-methoxyethanol + polyether, or hydroxyether + propylamine. The good u predictions obtained using Nomoto's equation remark the validity of Rao's assumption on additivity of molar sound velocity contributions from atoms, atom groups and chemical bo...

Analytic inhomogeneous electron liquid and its density for model spin-compensated two-electron atomic ions with Coulomb confinement: an exact nonrelativistic Hamiltonian

Abstract: In earlier work, Howard and March (HM) proposed an analytic ground-state electron density ρ( r ) starting from the s-wave model of the He atom. Subsequently Ancarani has constructed by numerical methods a variational approach for this s-wave model with a lower energy than the HM result. This clearly means that the HM ρ( r ) is not the ground-state electron density of the He s-wave model. Therefore, we derive here an exact nonrelativistic Hamiltonian, with strong radial correlation plus Coulomb confinement, for which the HM ρ( r ) is indeed the ground-state electron density.

Micellar catalysis in reactions of some β-lactam antibiotics with p -dimethylaminobenzaldehyde

Abstract: Kinetic study of the reactions of amoxicillin (I), ampicillin (II) and cephlaxin (III) with p-dimethylaminobenzaldehyde (DAB) in weakly acidic EtOH/H2O solution has been investigated using spectrophotometric method. Relatively slow reversible reactions of first order with respect to the antibiotic have been found. A derived equation for detecting the existence of reversibility from the linearity has been introduced. The effect of anionic surfactants (sodium dodecyl sulfate, SDS) on the kinetic of these reactions in aqueous solution has been studied. The presence of 0.005 M of SDS increases the rate constants by 4.3, 2 and 3.3 times for I, II and III, respectively. The consequence of the rate constants have a similar order in absence and presence of SDS; III > II > I. The rate constants pass through maxima with increasing SDS concentration followed by a gradual but steady decrease in the rate as the surfactant concentration increases further. Multiple linear regression method has been performed to evaluate...

Vapor–liquid equilibrium, densities, and interfacial tensions for the system benzene + propan-1-ol

Abstract: Isobaric vapor–liquid equilibrium data at 50, 75, and 94 kPa have been determined for the binary system benzene + propan-1-ol, in the temperature range 320–370 K. The measurements were made in a vapor–liquid equilibrium still with circulation of both phases. Mixing volumes have been also determined from density measurements at 298.15 K and 101.3 kPa and, at the same temperature and pressure; the dependence of interfacial tension on concentration has been measured using the maximum bubble pressure technique. According to experimental results, the mixture presents positive deviation from ideal behaviour and azeotropy is present at 50, 75, and 94 kPa. The mixing volumes of the system change from negative to positive as the concentration of benzene increases, and the interfacial tensions exhibit negative deviation from the linear behaviour. The activity coefficients and boiling points of the solutions were well-correlated with the mole fraction using the Wohl, Wilson, UNIQUAC, NRTL equations and predicted by ...