Van Laar Equation Research Articles

Density, Refractive Index, and Speed of Sound at 298.15 K, and Vapor−Liquid Equilibria at 101.3 kPa for Binary Mixtures of Methanol + Ethyl Butyrate and Vinyl Acetate + Ethyl Butyrate

Densities, refractive indices, and speeds of sounds at 298.15 K, and isobaric vapor−liquid equilibria data at 101.3 kPa were reported for the binary mixtures containing methanol + ethyl butyrate and vinyl acetate + ethyl butyrate. Excess molar volumes, refractive index deviations, and changes of speed sound on mixing were calculated from the measurement results and fitted with Redlich−Kister polynomials. VLE experimental data were satisfactorily tested for thermodynamic consistency by means of a modified Dechema test. The activity coefficients were correlated with the Margules, van Laar, UNIQUAC, NRTL, and Wilson equations. The ASOG model was also used for prediction.

Density, Refractive Index, Speed of Sound, and Vapor−Liquid Equilibria for Binary Mixtures of Methanol + Ethyl Propionate and Vinyl Acetate + Ethyl Propionate

Densities, refractive indices, and speeds of sound at 298.15 K, and isobaric vapor−liquid equilibria data at 101.3 kPa were reported for binary mixtures containing methanol + ethyl propionate and vinyl acetate + ethyl propionate. Excess molar volumes, refractive index deviations, and changes of speed of sound on mixing were calculated from the measured results and fitted to Redlich−Kister polynomials. VLE experimental data were tested for thermodynamic consistency by means of a modified Dechema test and were demonstrated to be consistent. The activity coefficients were correlated with the Margules, van Laar, UNIQUAC, NRTL, and Wilson equations with two suffixes and the Wilson model with three suffix equations. The ASOG model also was used for prediction. The methanol (1) + ethyl propionate (2) system shows an azeotrope at x1 = 0.984.

Isobaric Vapor−Liquid Equilibrium for the Binary Mixtures (2-Butanol + n-Hexane) and (2-Butanol + 1-Butylamine) and for the Ternary System (2-Butanol + n-Hexane + 1-Butylamine) at 101.3 kPa

Isobaric vapor−liquid equilibrium has been experimentally studied for the binary mixtures 2-butanol + n-hexane and 2-butanol + 1-butylamine and for the ternary mixture 2-butanol + n-hexane + 1-butylamine at 101.3 kPa. The activity coefficients were found to be thermodynamically consistent, and they were satisfactorily correlated with the Margules, van Laar, Wilson, NRTL, and UNIQUAC equations. The activity coefficients were also compared with the results obtained from the application of the ASOG and modified UNIFAC group contribution methods. The boiling points of the solutions were correlated with compositions by the Wisniak−Tamir equations. The results obtained indicate that the binary system 2-butanol + n-hexane deviates positively from ideality, whereas 2-butanol + 1-butylamine deviates negatively from ideality. The ternary system deviates positively or negatively depending on the composition. Only the binary systems present azeotropy. Azeotropic behavior was not found in the ternary mixture.

Arrangement and process for transport, storage and processing of hydrocarbons

Solid–liquid equilibria (SLE) for solvent–triacylglyceride (TAG) systems are studied with activity coefficient models. Systems consisted of 29 data sets of C10:0 to C18:0 saturated triglycerides in nine solvents, benzene, acetone, carbon disulfide, carbon tetrachloride, chloroform, diethyl ether, ethanol, ethyl acetate, and n-hexane making up 562 data points. Eighteen activity coefficient models containing 0–2 fitting parameters were evaluated including a number of Flory Free Volume (FFV) and Entropic Free Volume (FEFV) models evaluated by Coutinho et al. [J.A.P. Coutinho, S.I. Andersen, E.H. Stenby, Evaluation of activity coefficient models in prediction of alkane solid–liquid equilibria, Fluid Phase Equilibria 103 (1995) 23–39], the UNIFAC model and its variations, the Wilson, UNIQUAC, and van Laar equations and some proposed modifications of the FEFV and UNIFAC models. The modifications were as follows: (i) a Flory type χ parameter was added to the FEFV model (FEFV-X) and (ii) the exponent in the UNIFAC combinatorial term was treated as a fitting parameter (UNIFAC-C). Models were compared in terms of absolute average percent deviation (AAPD) in temperature. The best predictive model for TAG–solvent systems was found to be the Dortmund version of UNIFAC. Addition of a fitting parameter to the UNIFAC models provided significant improvement. For the UNIFAC-1977, UNIFAC (Lyngby) and UNIFAC (Dortmund), these exponents were found to be 0.897, 0.858, and 0.749, respectively. The best single parameter correlative model was found to be the FEFV-X model, which gave an AAPD of 0.305%. The Wilson equation was the best two parameter correlation equation and provided an AAPD of 0.154%.

Isobaric vapour–liquid equilibrium for the binary mixtures of 2-methyl-2-propanol with some halohydrocarbons at 40.0 and 101.3 kPa

Vapour–liquid equilibria of the binary systems 2-methyl-2-propanol+chlorocyclohexane, chlorobenzene, bromocyclohexane or bromobenzene have been determined at two constant pressures, 40.0 and 101.3 kPa. The equipment used was a dynamic recirculating still. The isobaric VLE data have been found to be thermodynamically consistent according to the point-to-point test of Van Ness. The activity coefficients have been correlated with the mole fraction through Margules, van Laar, Wilson, NRTL and UNIQUAC equations, and they have been compared also to the predictions obtained using ASOG and UNIFAC group contribution methods.

Vapor–liquid equilibria for 1,1,2,2-tetrafluoroethyl, 2,2,2-trifluoroethyl ether with several organic compounds containing oxygen

Isobaric vapor–liquid equilibria for 1,1,2,2-tetrafluoroethyl, 2,2,2-trifluoroethyl ether (CHF 2CF 2OCH 2CF 3)+alcohols, ketones, or esters systems were measured at 101.3 kPa. The alcohols used were ethanol and 1-propanol. The ketone and ester components were 2-butanone and ethyl acetate, respectively. The measurements were made in an equilibrium still with circulation of both the vapor and liquid phase. The two binary isobaric systems composing of CHF 2CF 2OCH 2CF 3 and the alcohols exhibit minimum boiling azeotropes. The azeotropic points are found at x 1(az)=0.800 mole fraction and T(az)=326.67 K for CHF 2CF 2OCH 2CF 3 (1)+ethanol (2) and x 1(az)=0.965 mole fraction and T(az)=329.23 K for CHF 2CF 2OCH 2CF 3 (1)+1-propanol (2), respectively. The two binary systems of CHF 2CF 2OCH 2CF 3 (1)+2-butanone (2) and CHF 2CF 2OCH 2CF 3 (1)+ethyl acetate (2) are both non-azeotropic. The experimental data for the binary systems investigated were correlated with activity coefficient equations. The nonrandom two-liquid (NRTL) equation yielded a good correlation of activity coefficients for the two systems of CHF 2CF 2OCH 2CF 3 with alcohols. The CHF 2CF 2OCH 2CF 3 (1)+2-butanone (2) system is best correlated with the van Laar equation and CHF 2CF 2OCH 2CF 3 (1)+ethyl acetate (2) system best with the three-suffix Margules equation. The thermodynamic consistency of data was good according to the Van Ness and the Herington test.

Vapor–liquid equilibria for methanol+pentyl acetate, vinyl acetate+pentyl acetate, and methanol+isopentyl acetate

Isobaric vapor–liquid equilibria were determined at 101.3 kPa for methanol+pentyl acetate, methanol+isopentyl acetate, and vinyl acetate+pentyl acetate. The thermodynamic consistency of the experimental data was checked by using a modified Dechema test. The activity coefficients were correlated with Margules, van Laar, Wilson, NRTL, and Wilson equations. None of the systems shows azeotropy. Pentyl acetate is a potential extractive distillation entrainer of the azeotropic mixture methanol+vinyl acetate.

Vapor−Liquid Equilibrium of Binary Mixtures Containing Diethylamine + Diisopropylamine, Diethylamine + Dipropylamine, and Chloroform + Diisopropylamine at 101.3 kPa, and Vapor Pressures of Dipropylamine

Isobaric vapor−liquid equilibria have been measured with a dynamic still for the systems diethylamine + diisopropylamine, diethylamine + dipropylamine, and chloroform + diisopropylamine. The chloroform + diisopropylamine system shows an azeotrope in the range 0−0.040 mole fraction of chloroform. The thermodynamic consistency of the experimental data was checked by means of modified Dechema test. The activity coefficients were correlated by means of the Margules, van Laar, Wilson, NRTL, and UNIQUAC equations. UNIFAC and ASOG predictions have been also used. Experimental vapor pressures of dipropylamine are also included and the Antoine constants were determined.

Isobaric VLE data of the binary mixture ( n-hexane+1-chlorobutane) and the ternary system (1-butanol+ n-hexane+1-chlorobutane) at 101.3 kPa

Isobaric vapour–liquid equilibrium (VLE) for the ternary mixture, 1-butanol (1)+ n-hexane (2)+1-chlorobutane (3) and for the binary mixture, n-hexane (1)+1-chlorobutane (2) at 101.3 kPa has been experimentally studied. The activity coefficients were found to be thermodynamically consistent and were satisfactorily correlated with the Margules, van Laar, Wilson, NRTL and UNIQUAC equations. They have been also compared with the results obtained from the application of ASOG and the modified UNIFAC group contribution methods.

99/02435 Phase behavior prediction of petroleum fluids with minimum characterization data

Isobaric vapour-liquid equilibrium data at 40.0 and 101.3 kPa for the binary systems dibromomethane with 1-butanol, 2-butanol, 2-methyl-1-propanol and 2-methyl-2-propanol are reported. All the systems show minimum temperature azeotropes. The experimental data were tested for thermodynamic consistency and correlated with the Margules, Van Laar, Wilson, NRTL and UNIQUAC equations. Predictions with the UNIFAC method were also obtained.

Behaviour of butyl ether as entrainer for the extractive distillation of the azeotropic mixture propanone+diisopropyl ether. Isobaric VLE data of the azeotropic components with the entrainer

The behaviour of butyl ether as entrainer in extractive distillation for the rupture of the propanone+diisopropyl ether azeotropic mixture is investigated. The vapor–liquid equilibrium of each component with butyl ether has been carried out at 101.3 kPa in order to check the absence of azeotropes. Neither system showed an azeotrope. Thermodynamic consistency of the experimental data was good. The activity coefficients were correlated by means of the van Laar, Wilson, NRTL and UNIQUAC equations. UNIFAC prediction has been also used. As a final part, an experiment of extractive distillation was carried out and a composition of 0.990 in mole fraction of acetone, 0.001 of diisopropyl ether and 0.009 of butyl ether resulted in the head of the column. In conclusion, butyl ether is an excellent solvent for the rupture of the studied azeotropic mixture.

Isothermal Vapor−Liquid Equilibria for Methyl-2,2-dimethylethyl Ether + 2-Methylpropan-2-ol, Diethyl Ether + Ethyl-2,2-dimethylethyl Ether, 2-Methyl-2-butene + (2-Methylbutan-2-ol), and Diisopropyl Ether + Octane

Isothermal vapor−liquid equilibrium data for four binary systems methyl-2,2-dimethylethyl ether + 2-methylpropan-2-ol, diethyl ether + ethyl-2,2-dimethylethyl ether, 2-methyl-2-butene + 2-methylbutan-2-ol, and diisopropyl ether + octane were collected at two temperatures using a modified Malanowski still. The virial equation truncated at the second virial coefficient was used to calculate the vapor-phase fugacity coefficients. The liquid-phase activity coefficient data were fitted to the van Laar, Wilson, and NRTL equations.

Vapor–liquid equilibrium of binary mixtures of trichloroethylene with 1-pentanol, 2-methyl-1-butanol and 3-methyl-1-butanol at 100 kPa

Isobaric vapor–liquid equilibria (VLE) have been obtained for the systems trichloroethylene+1-pentanol, trichloroethylene+2-methyl-1-butanol and trichloroethylene+3-methyl-1-butanol at 100 kPa using a dynamic still. The experimental error in temperature is ±0.1 K, in pressure ±0.1 kPa, and in the liquid and vapor mole fraction ±0.001. The three systems satisfy the point-to-point thermodynamic consistency test. All the systems show positive deviations from ideality. The data have been correlated with the Margules, van Laar, Wilson, NRTL and UNIQUAC equations.

Vapor–liquid equilibrium of binary mixtures of chlorobenzene with 3-methyl-1-butanol, 3-methyl-2-butanol and 2-methyl-2-butanol, at 100 kPa

Isobaric vapor–liquid equilibria have been obtained for the systems 3-methyl-1-butanol+chlorobenzene, 3-methyl-2-butanol+chlorobenzene and 2-methyl-2-butanol+chlorobenzene at 100 kPa, using a dynamic still. The experimental error in temperature is ±0.1 K, in pressure ±0.1 kPa, and in the liquid and vapor mole fraction ±0.001. The three systems satisfy the point-to-point thermodynamic consistency test. All the systems show positive deviations from ideality. The data have been correlated with the Margules, Van Laar, Wilson, NRTL and UNIQUAC equations.

(Vapour + liquid) equilibria for (methanol + butyl acetate), (vinyl acetate + butyl acetate), (methanol + isobutyl acetate), and (vinyl acetate + isobutyl acetate)

Isobaric (vapour+liquid) equilibria were determined atp=101.3kPa for (methanol+butyl acetate), (methanol+isobutyl acetate), (vinyl acetate+butyl acetate), and (vinyl acetate+isobutyl acetate). The thermodynamic consistency of the experimental data was checked by using a modified Dechema test. The activity coefficients were correlated with Margules, van Laar, Wilson, NRTL, and Wilson equations. Among the solvents chosen as potential extractive distillation entrainers, none shows azeotropy. It was found more appropriate to use butyl acetate as solvent for the extractive distillation from an economical perspective.

Calculation of the efficiency of purification by crystallization of ideal multicomponent stereoisomeric mixtures

A method for evaluating the maximum theoretical recovery of pure component from a stereoisomeric mixture by crystallization is discussed. The approach is based on the approximation of ideal behaviour as exemplified by the Schroeder–van Laar equation for conglomerates, and the Prigogine–Defay equation for racemic compounds. These equations are used to calculate the n-dimensional eutectic. It is shown that the n-dimensional eutectic is more soluble than the ( n−1)-dimensional eutectic. A calculation is performed which removes only the n-dimensional eutectic from the sample and calculation of recovery through this discrete purification step is possible. After this, a system of n−1 components is obtained. The calculation may be repeated until only one component remains. The overall recovery of pure isomer is the product of the recoveries at each discrete purification step. The procedure is well suited to computer algorithm and a summary listing is presented. A series of example calculations are included for reference purposes. The methodology is intended to be useful in guiding efforts to improve process economics.

Studies of Thermotropic Properties and the Mesophase of Mixtures of n-Alkanoates and Perfluoro-n-alkanoates of Dimolybdenum (MM)

Mixtures of Mo2(O2C(CH2)nCH3)4, where n = 6 (=Oct) and 7 (=Non), form a columnar mesophase upon heating and the crystal-to-liquid crystal phase transition temperatures differ little from those predicted by the Shroder−van Laar equation for an ideal mixture. The XRD of the solid sample obtained from cooling a 1:1 mixture of Mo2(Oct)4 and Mo2(Non)4 conformed to a triclinic cell with lattice parameters intermediate between those of the pure compounds. Similarly in the mesophase the intercolumnar separation (d) was an intermediate distance. The phase behavior of mixtures of Mo2(non)4 and Mo2(O2C(CH2)10CH3)4 [Mo2(Dod)4] were more complex, but in all instances a mesophase was observed whereas that of the pure Mo2(Dod)4 shows only a crystalline solid to isotropic phase transition. Mixtures of Mo2(Oct)4 and Mo2(O2C(CF2)6CF3)4 [Mo2(Octf)4] were also shown to form a columnar mesophase with an intercolumnar separation intermediate between that of the pure compounds. The mesophase is an optically positive material with the largest component of the index of refraction coincident with the columnar axis. The solid to mesophase transition temperatures varied significantly from that predicted for an ideal mixture. These results are discussed on the basis of facile carboxylate scrambling to produce Mo2(O2CR)4-n(O2CR‘)n, where n = 0−4 in both the mesophase and the resultant solid solution.

Prediction and correlation of triglyceride–solvent solid–liquid equilibria with activity coefficient models

Solid–liquid equilibria (SLE) for solvent–triacylglyceride (TAG) systems are studied with activity coefficient models. Systems consisted of 29 data sets of C10:0 to C18:0 saturated triglycerides in nine solvents, benzene, acetone, carbon disulfide, carbon tetrachloride, chloroform, diethyl ether, ethanol, ethyl acetate, and n-hexane making up 562 data points. Eighteen activity coefficient models containing 0–2 fitting parameters were evaluated including a number of Flory Free Volume (FFV) and Entropic Free Volume (FEFV) models evaluated by Coutinho et al. [J.A.P. Coutinho, S.I. Andersen, E.H. Stenby, Evaluation of activity coefficient models in prediction of alkane solid–liquid equilibria, Fluid Phase Equilibria 103 (1995) 23–39], the UNIFAC model and its variations, the Wilson, UNIQUAC, and van Laar equations and some proposed modifications of the FEFV and UNIFAC models. The modifications were as follows: (i) a Flory type χ parameter was added to the FEFV model (FEFV-X) and (ii) the exponent in the UNIFAC combinatorial term was treated as a fitting parameter (UNIFAC- C). Models were compared in terms of absolute average percent deviation (AAPD) in temperature. The best predictive model for TAG–solvent systems was found to be the Dortmund version of UNIFAC. Addition of a fitting parameter to the UNIFAC models provided significant improvement. For the UNIFAC-1977, UNIFAC (Lyngby) and UNIFAC (Dortmund), these exponents were found to be 0.897, 0.858, and 0.749, respectively. The best single parameter correlative model was found to be the FEFV-X model, which gave an AAPD of 0.305%. The Wilson equation was the best two parameter correlation equation and provided an AAPD of 0.154%.

Crystal Forms of Piroxicam Pivalate: Preparation and Characterization of Two Polymorphs

□ This study investigates the polymorphism of piroxicam ester with pivalic acid. Two crystal modifications were prepared by recrystallization from toluene (form 1) and ethyl acetate (form 2). Data regarding preparation conditions, solid state properties, and physico-chemical characterization of two polymorphs by means of FT/IR spectroscopy, X-ray diffractometry on powder, and thermal analysis are reported. Heat of fusion rule and thermodynamic formulas consistently indicate an enantiotropic stability relationship of forms 1 and 2 with a calculated transition point (32°C) near the ambient temperature. The phase diagrams of each polymorph with piroxicam were also investigated in order to gain information about the thermal behavior of their solid mixtures. Liquidus curves calculated by the Schro¨der-Van Laar equation from fusion enthalpies and temperatures were found to agree satisfactorily with experimental results obtained by first heating runs with differential scanning calorimetry.

VAPOR-LIQUID EQUILIBRIUM MEASUREMENT AND DATA TREATMENT OF n-PROPANOL AND ISOBUTANOL MIXTURE AT ATMOSPHERIC PRESSURE

The measurement of vapor-liquid equilibrium of n-propanol and isobutanol binary mixture was carried out in a condensed vapor phase recirculating still at atmospheric pressure. The experimental data were checked by Herington consistency test and chi-square distribution of statistics. The correlation results showed that van Laar equation was the most suitable model to describe the VLE behavior of this mixture and that the absolute correlation coefficient of the pair parameters of model is near to unity. This says that the model parameters are linearly related to each other and this mixture behaves like a regular solution. The experimental points with large residuals were deleted from the data set. The F-distribution test of statistics was then applied to judge whether the new data-set could better describe phase behavior of mixture than the previous set. The statistical chi-square analysis was also applied to determine whether the estimated variance of fit used for objective function was reasonable. The data treatment applied in this study was different from that applied to isoprene and n-pentane mixture in our previous paper (Lee et al., 1994) where the T-x diagram was used to delete the experimental points with systematic error.