Fluid Phase Equilibria 230 (2005) 197–203

Vapor–liquid equilibria and excess volumes of the binary systems ethanol + ethyl lactate, isopropanol + isopropyl lactate and n-butanol + n-butyl lactate at 101.325 kPa Susana Pe˜na-Tejedor, Ruth Murga, Maria Teresa Sanz, Sagrario Beltr´an ∗ Departamento de Ingenier´ıa Qu´ımica. Universidad de Burgos, Plaza Misael Ba˜nuelos s/n, 09001 Burgos, Spain Received 22 November 2004; received in revised form 16 February 2005; accepted 17 February 2005 Available online 1 April 2005

Abstract Isobaric vapor–liquid equilibrium data have been experimentally determined at 101.3 kPa for the binary systems ethanol + ethyl lactate, isopropanol + isopropyl lactate and n-butanol + n-butyl lactate. No azeotrope was found in any of the systems. All the experimental data reported were thermodynamically consistent according to the point-to-point method of Fredenslund. The activity coefficients were correlated with the NRTL and UNIQUAC liquid-phase equations and the corresponding binary interaction parameters are reported. The densities and derived excess volumes for the three mixtures are also reported at 298.15 K. © 2005 Elsevier B.V. All rights reserved. Keywords: Experimental data; Vapor–liquid equilibrium; Alcohols; Lactates; Excess volumes

1. Introduction Lactic acid esters are biodegradable and can be used as powerful high-boiling solvents for varnishes, paints, nitro and ethyl cellulose, gums, oils, dyes, etc. They are also used as food additives, in biochemicals, pharmaceuticals, cosmetics, detergents, etc. [1,2]. Production of methyl, ethyl, isopropyl and n-butyl lactates is usually carried out by conventional esterification of lactic acid with the corresponding alcohol. These esterification reactions are limited by chemical equilibrium [3–6], thus, the quaternary mixtures obtained need to be separated to obtain the purified lactates. These separations are best performed simultaneously to the reaction in hybrid processes in order to displace the chemical equilibrium to obtain high reaction yields. Some research is being carried out to selectively remove one or more species from the reaction mixture by simultaneous pervaporation [7,8] or distillation [9,10].

∗

Corresponding author. Tel.: +34 947258810; fax: +34 947258831. E-mail address: [email protected] (S. Beltr´an).

0378-3812/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2005.02.015

The design of reactive distillation columns for lactic acid esterification needs research not only on the reaction kinetics [3,4] but also on the phase equilibrium of the quaternary mixture involved in these reactions [10]. The study of the complex quaternary reactive mixtures can be implemented by studying the binary mixtures in the first place. Some of the binary mixtures are reactive and some special equipment is necessary for phase equilibria determination [11,12]. In this work, experimental vapor–liquid equilibrium (VLE) data for three non-reactive mixtures involved in the esterification of lactic acid with three different alcohols are presented, specifically, ethanol + ethyl lactate, isopropanol + isopropyl lactate and n-butanol + n-butyl lactate. The VLE of the system methanol + methyl lactate has been previously reported elsewhere [13]. No VLE data have been found in the literature for the mixtures studied in this work. Only a diagram with four experimental VLE data for the system ethanol + ethyl lactate has been reported by Benedict et al. [7], who investigated this system at atmospheric pressure just to check for azeotrope formation that is fairly common in mixtures alcohol + ester. Benedict et al. [7] studied the esterification of lactic acid with ethanol and achieved high reaction yields by stripping

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measurements given by the densimeter was within ±0.005 K and the thermostat connected to the refractometer gave an accuracy of ±0.05 K. An all-glass still of the Gillespie type with recirculation of both the liquid and vapor phases, was used to obtain VLE and vapor pressure experimental data. This apparatus has been previously described and used in our laboratory to obtain experimental vapor pressures and VLE data for the type of systems presented in this work [10,13]. The still was operated under a nitrogen atmosphere. The total pressure of the system was monitored with a digital manometer (BrandTech Scientific Inc., Vacuubrand DVR2) and controlled to the desired value (within 0.05 kPa) with an electronic pressure controller (Normag, Normastat 75) that allowed dry nitrogen to be injected into (or released from) the still in order to achieve an inert atmosphere until thermodynamic equilibrium was reached. Atmospheric pressure was measured with a Lambrecht type barometer. The boiling point temperature (±0.05 K) in the equilibrium still was measured with a digital thermometer (Ertco–Hart, Model 850).

the by-product (water) by pervaporation. On the basis of the non-existence of azeotrope in the system ethanol + ethyl lactate, they proposed a protocol for recovery of ethyl lactate from the pervaporation retentate. The VLE data obtained in this work for the system ethanol + ethyl lactate confirm the non-existence of azeotrope for this system nor for the other two alcohol + ester mixtures studied. The thermodynamic consistency according to the pointto-point method of Fredenslund was checked for the three systems studied and the activity coefficients were correlated with the NRTL and UNIQUAC equations. The densities and derived excess volumes for the three binary mixtures are also reported at 298.15 K.

2. Experimental 2.1. Chemicals Ethanol, isopropanol and n-butanol, purchased from Merck with a reported purity of 99.9%, were stored over ˚ molecular sieves in order to keep them dry. activated 3 A (−)-Ethyl l-lactate was purchased from Fluka with a reported purity of 99% and isopropyl-(S)-(−)-lactate and butyl(S)-(−)-lactate were purchased from Aldrich with a reported purity of 99% and 98%, respectively. The three lactates were purified by vacuum distillation to obtain a final purity of 99.9% as determined by gas chromatography (GC). The water content of all the components was determined with a Karl–Fisher apparatus (Mitsubishi Kasei CA-20) and was found to be below 50 ppm in all cases. As an additional purity check, some physical properties of the pure components were measured and compared with values reported in the literature. The results are presented in Table 1.

2.3. Sample analysis The liquid and vapor phases were analyzed using a Hewlett Packard GC (Model 6890) equipped with series connected thermal conductivity and flame ionization detectors (TCD and FID). The TCD was used to check for water in the samples. The GC column was a 25 m FFAP capillary column. The injector and detectors were at 473 and 573 K, respectively. The oven was operated at variable, programmed temperature, from 383 to 453 K at a rate of 40 K min−1 . Helium (99.999% purity) was used as carrier gas with a flow of 45 mL min−1 . Concentration measurements were accurate to ±0.0005 mole fraction.

3. Results and discussion 2.2. Apparatus and procedure 3.1. Saturation pressures Densities were measured with an Anton Paar (DMA5000) densimeter with an accuracy of ±0.005 kg m−3 , and refractive indexes with an Abbe type refractometer with an accuracy of ±0.0002. The accuracy of the temperature

The Antoine constants for obtaining the vapor pressures of the three alcohols and ethyl lactate at different temperatures were found in the literature. Therefore, only a few

Table 1 Physical properties of the pure compounds Compound

Ethanol Isopropanol Butanol Ethyl lactate Isopropyl lactate n-Butyl lactate a b c

Riddick et al. [14]. Clary et al. [1]. Weast et al. [15].

ρ (293.15 K) (kg m−3 )

n (D) (293.15 K)

Tb (101.33 kPa) (K)

Experimental

Literature

Experimental

Literature

Experimental

Literature

789.261 785.428 809.572 1032.939 986.942 982.178

789.20a 785.45a 809.56a 1032.8a 991b 984b

1.3614 1.3774 1.3993 1.4129 1.4105 1.4218

1.36143a 1.3772a 1.39929a 1.4124a 1.410b 1.4217c

351.44 355.36 390.88 427.65 430.21 460.75

351.443a 355.392a 390.875a 427.7a 430b 460b

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199

Table 2 Antoine equationa parameters, A, B and C Compound

Etanolb Isopropanolb Butanolb Ethyl lactateb Isopropyl lactatec n-Butyl lactatec a b c

R2

Antoine constants A

B

C

7.16879 6.86618 6.54743 7.8269 7.1153 5.3590

1552.601 1360.131 1338.769 2489.7 2109.63 1045.92

222.419 197.592 177.042 273.15 255.83 124.40

0.9997 0.9995

Antoine equation: log (P) (kPa) = A − B/[(T (◦ C) + C]. Riddick et al. [14]. From experimental data obtained in this work.

vapor pressures were experimentally determined in order to confirm that such constants could be used in the treatment of the experimental VLE data obtained in this work. In the case of isopropyl lactate and n-butyl lactate, vapor pressures were experimentally determined at several temperatures in order to correlate such data to the Antoine equation and obtain the Antoine equation parameters that were not found in the literature for these two chemicals. The temperature range in which vapor pressures were determined was between the normal boiling point of the ester and that of the corresponding alcohol. The Antoine equation parameters, A, B and C, obtained from Po versus T correlation, and used for VLE data treatment are reported in Table 2 together with the R-squared statistic. 3.2. Densities The experimental values of the density of the mixtures ethanol (1) + ethyl lactate (2), isopropanol (1) + isopropyl lactate (2), and n-butanol (1) + n-butyl lactate (2) at 298.15 K, and the values of the excess volume calculated from the density data are reported in Table 3. It may be observed that the excess volume is negative for the three systems, which may indicate the existence of some type of association between

unlike molecules, possibly hydrogen bonds between the OH groups of the lactates and the alcohols. The absolute value of the minimum excess volume decreases from the system ethanol + ethyl lactate, to the system butanol + butyl lactate and the system isopropanol + isopropyl lactate that presents the lowest value. That sequence may be explained taking into account the sterical hindrance for interaction between molecules. The excess molar volumes have been correlated by means of the Redlich–Kister equation [16]: V E = x1 x2

n


Ak (x1 − x2 )k

(1)

k=0

The parameters obtained from the correlation to a first order polynomial (n = 1) or a second order polynomial (n = 2) are reported in Table 4 together with the standard deviation as calculated by   2   E − VE Vcal  exp i σ= (2) N −m where N is the number of experimental data and m is the number of adjustable parameters.

Table 3 Experimental density data (ρ) and derived excess molar volumes (VE ) for the systems ethanol + ethyl lactate, isopropanol + isopropyl lactate and n-butanol + nbutyl lactate, at 298.15 K Ethanol (1) + ethyl lactate (2)

Isopropanol (1) + isopropyl lactate (2)

n-Butanol (1) + n-butyl lactate (2)

x1

ρ (kg m−3 )

VE (cm3 mol−1 )

x1

ρ (kg m−3 )

VE (cm3 mol−1 )

x1

ρ (kg m−3 )

VE (cm3 mol−1 )

0.0000 0.1242 0.2256 0.3120 0.3921 0.5236 0.5735 0.6735 0.7574 0.7941 0.8267 0.8559 0.9578 1.0000

1032.939 1018.422 1004.725 991.370 977.447 950.894 939.295 913.364 887.971 875.598 863.971 852.975 809.773 789.261

0.000 −0.204 −0.337 −0.414 −0.459 −0.494 −0.484 −0.453 −0.385 −0.339 −0.297 −0.255 −0.086 0.000

0.0000 0.0870 0.1970 0.2810 0.3554 0.5420 0.5652 0.6921 0.7733 0.8365 0.8675 0.9249 0.9516 1.0000

986.942 976.815 962.690 950.807 939.404 906.498 901.903 874.425 854.447 837.361 828.428 810.801 802.104 785.428

0.000 −0.037 −0.067 −0.081 −0.089 −0.096 −0.095 −0.084 −0.072 −0.059 −0.050 −0.030 −0.020 0.000

0.0000 0.0989 0.1806 0.2599 0.3973 0.5154 0.5669 0.6645 0.7069 0.7854 0.8546 0.9174 0.9728 1.0000

982.178 971.809 962.459 952.704 933.863 915.521 906.818 888.883 880.503 863.836 847.901 832.199 817.297 809.572

0.000 −0.081 −0.128 −0.167 −0.200 −0.209 −0.209 −0.187 −0.176 −0.141 −0.110 −0.068 −0.025 0.000

200

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Table 4 Parameters, Ak , obtained from the correlation of the excess molar volumes to the Redlich–Kister equation (Eq. (1)) and standard error of the estimate, σ System

n

A0 (cm3 mol−1 )

A1 (cm3 mol−1 )

A2 (cm3 mol−1 )

σ

Ethanol (1) + ethyl lactate (2) Isopropanol (1) + isopropyl lactate (2) n-Butanol (1) + n-butyl lactate (2)

1 2 1

−1.97833 −0.38430 −0.85008

−0.15473 0.00182 0.00619

−0.09126

0.004 0.001 0.003

3.3. Vapor–liquid equilibria Temperature, pressure and composition of the liquid and vapor phases have been experimentally determined for each VLE data reported. The results of these measurements for the binary systems ethanol (1) + ethyl lactate (2), isopropanol (1) + isopropyl lactate (2) and n-butanol (1) + n-butyl lactate (2) at 101.33 kPa are presented in Tables 5–7 and Fig. 1. No azeotrope was found in any of these mixtures alcohol + ester. The activity coefficients were calculated from Eq. (3):  L y i Φi P Vi 0 γi = exp (3) (P − P) RT i xi Pi0 Φ0i Table 5 Experimental VLE data for the binary system ethanol (1) + ethyl lactate (2) at 101.33 kPa T (K)

x1

y1

γ1

γ2

427.65 423.50 415.20 405.95 390.26 381.01 378.71 376.30 375.07 373.42 373.13 371.56 371.15 369.83 368.93 368.34 366.53 364.32 363.61 362.69 361.40 360.51 360.25 359.39 358.88 357.71 357.18 356.20 355.09 354.41 353.93 353.63 352.99 352.34 352.03 351.44

0.0000 0.0052 0.0354 0.0709 0.1787 0.2690 0.2938 0.3277 0.3448 0.3700 0.3789 0.4022 0.4070 0.4310 0.4529 0.4627 0.4999 0.5481 0.5738 0.5976 0.6345 0.6603 0.6730 0.6996 0.7165 0.7504 0.7725 0.8003 0.8462 0.8703 0.8892 0.8985 0.9313 0.9451 0.9688 1.0000

0.0000 0.1025 0.3185 0.5387 0.7395 0.8410 0.8675 0.8868 0.9024 0.9037 0.9082 0.9157 0.9180 0.9256 0.9365 0.9386 0.9456 0.9517 0.9552 0.9589 0.9683 0.9676 0.9693 0.9723 0.9747 0.9827 0.9844 0.9847 0.9887 0.9920 0.9935 0.9942 0.9961 0.9970 0.9984 1.0000

– 2.2388 1.2477 1.3345 1.1249 1.1245 1.1417 1.1302 1.1374 1.1203 1.1100 1.1105 1.1153 1.1100 1.1018 1.1027 1.0940 1.0843 1.0658 1.0611 1.0565 1.0474 1.0391 1.0342 1.0312 1.0360 1.0278 1.0289 1.0182 1.0188 1.0168 1.0184 1.0085 1.0195 1.0078 1.0001

1.0014 1.0265 1.0467 1.0009 1.1158 1.0860 1.0248 1.0114 0.9398 1.0303 1.0080 1.0249 1.0220 1.0200 0.9397 0.9480 0.9729 1.0490 1.0632 1.0743 0.9641 1.1016 1.0965 1.1179 1.1061 0.9041 0.9155 1.0680 1.0758 0.9309 0.9045 0.8929 0.9129 0.9048 0.8611 –

where the exponential term (Poynting correction) may be considered negligible at the low pressure at which the VLE has been determined. Vapor pressures for the pure components, Pi0 , were calculated using the Antoine equation. Vapor phase fugacity coefficients of each component in the mixture, Φi and Φ0i , were estimated by the virial equation of state [17] and second virial coefficients were calculated with the Hayden and O’Connell correlation [18]. The activity coefficients show slight deviations from Raoult’s law. The two types of molecules involved in each system are an alcohol and the corresponding lactate. Both types of molecules have an OH group that can form hydrogen bonds either with a like or an unlike molecule, preferences mostly depending on molecular size and shape.

Table 6 Experimental VLE data for the binary system isopropanol (1) + isopropyl lactate (2) at 101.33 kPa T (K)

x1

y1

γ1

γ2

430.21 428.63 427.80 424.94 421.50 414.35 412.78 411.50 408.82 406.58 404.31 401.50 399.00 396.49 389.72 388.37 383.99 380.14 378.03 376.13 373.55 372.14 370.49 368.26 361.39 360.81 359.94 358.22 358.15 357.49 356.96 355.87 355.72 355.36

0.0000 0.0030 0.0076 0.0184 0.0318 0.0614 0.0738 0.0813 0.0971 0.1079 0.1165 0.1406 0.1571 0.1751 0.2359 0.2549 0.2999 0.3505 0.3816 0.4121 0.4551 0.4824 0.5183 0.5626 0.7620 0.7820 0.8063 0.8742 0.8782 0.9057 0.9275 0.9797 0.9856 1.0000

0.0000 0.0245 0.0648 0.1462 0.2360 0.4044 0.4579 0.4730 0.5164 0.5569 0.5771 0.6347 0.6657 0.7004 0.7803 0.8053 0.8374 0.8736 0.8960 0.9100 0.9160 0.9247 0.9379 0.9460 0.9800 0.9817 0.9855 0.9918 0.9920 0.9940 0.9944 0.9986 0.9991 1.0000

– 0.9306 0.9896 0.9839 0.9953 1.0498 1.0284 0.9960 0.9752 1.0033 1.0228 1.0056 1.0113 1.0244 1.0313 1.0256 1.0365 1.0446 1.0534 1.0542 1.0471 1.0458 1.0445 1.0486 1.0262 1.0233 1.0290 1.0187 1.0169 1.0130 1.0097 1.0008 1.0010 1.0013

0.9992 1.0193 1.0037 1.0009 0.9988 0.9873 0.9544 0.9722 0.9854 0.9800 1.0150 0.9875 1.0009 0.9977 1.0016 0.9561 0.9998 0.9714 0.9124 0.8963 1.0028 1.0035 0.9534 1.0045 0.9293 0.9535 0.8854 0.8359 0.8451 0.8448 1.0518 0.9898 0.9036 –

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201

Fig. 1. Isobars at 101.3 kPa for the binary systems ethanol (1) + ethyl lactate (2) (a), isopropanol (1) + isopropyl lactate (2) (b) and n-butanol (1) + n-butyl lactate (2) (c). Solid symbols represent the liquid phase and open symbols the vapor phase. The continuous lines represent the VLE as calculated by NRTL (α12 = 0.3).

Table 7 Experimental VLE data for the binary system n-butanol (1) + n-butyl lactate (2) at 101.33 kPa T (K)

x1

y1

γ1

γ2

460.75 457.75 448.89 437.50 431.27 425.10 419.40 415.77 414.45 411.10 409.19 408.21 407.10 404.73 404.17 400.95 400.00 398.67 397.60 394.27 392.77 392.34 391.99 391.59 391.35 390.88

0.0000 0.0175 0.0712 0.1487 0.2029 0.2636 0.3376 0.3773 0.4049 0.4556 0.4941 0.5113 0.5357 0.5835 0.5940 0.6699 0.6887 0.7218 0.7534 0.8587 0.9106 0.9238 0.9398 0.9536 0.9667 1.0000

0.0000 0.1033 0.3410 0.5475 0.6444 0.7220 0.7983 0.8334 0.8410 0.8830 0.8947 0.8994 0.9065 0.9290 0.9316 0.9505 0.9589 0.9671 0.9683 0.9800 0.9880 0.9895 0.9913 0.9924 0.9938 1.0000

– 0.9337 0.9250 0.9361 0.9469 0.9624 0.9730 1.0082 0.9852 1.0148 1.0041 1.0049 1.0000 1.0124 1.0149 1.0166 1.0284 1.0332 1.0262 1.0174 1.0174 1.0191 1.0156 1.0157 1.0116 1.0000

0.9928 0.9760 0.9523 0.9728 0.9763 0.9927 0.9549 0.9416 0.9811 0.8809 0.9090 0.9291 0.9436 0.8662 0.8728 0.8693 0.7916 0.7435 0.8397 1.0438 1.0464 1.0915 1.1598 1.3343 1.5305 –

Experimental (P, T, x, y) data were correlated by using the nonlinear regression method, based on the maximum likelihood principle, proposed by Prausnitz et al. [19]. The NRTL and UNIQUAC liquid phase models were used to calculate the activity coefficients. The properties and parameters needed for VLE data correlation are presented in Table 8. Table 9 reports the values of the binary interaction parameters A12 and A21 of the liquid phase models obtained from experimental VLE data correlation for the three systems subject of this work, together with the root-meansquared deviations for pressure, temperature and vapor- and liquid-phase compositions. Different values of the parameter α12 were fixed in the NRTL equation, although no significant differences were found in the statistics of the correlations. The point-to-point test of Fredenslund et al. [21], using a Legendre’s polynomial of order 3, was applied to the experimental data to check for thermodynamic consistency. The average values of the residuals, y = |yexp − ycalc |, were y = 0.0079, y = 0.0072 and y = 0.0074 for the systems ethanol + ethyl lactate, isopropanol + isopropyl lactate and n-butanol + n-butyl lactate, respectively, indicating that the VLE results for the three systems are thermodynamically consistent.

Table 8 Properties and parameters of the components used in VLE data reduction Compound

UNIQUAC parameters r

q

Ethanol Isopropanol Butanol Ethyl lactate Isopropyl lactate n-Butyl lactate

2.11a 2.78a 3.45a 4.46c 5.13c 5.80c

1.97a 2.51a 3.05a 3.93c 4.46c 5.01c

a b c

Tc (K)

Pc (MPa)

Vc (cm3 mol−1 )

ZRA

RD (× 1010 m)

µ (D)

513.92b 508.30b 563.00b 586.85c 584.95c 614.56c

6.148b 4.7616b 4.413b 3.941c 3.539c 3.138c

167b 223.0b 274b 354.5c 404.5c 466.5c

0.2520a 0.2540a 0.2590a 0.216c 0.1827c 0.2103c

2.250a 2.726a 3.225a 3.622c 4.803c 5.086c

1.69a 1.66a,b 1.75b 2.4b 2.69c 1.9c

Prausnitz et al. [19]. Riddick et al. [14]. Estimated or calculated through different methods included in Aspen-Plus [20].

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Table 9 Correlation parameters of the activity coefficient equations for the binary systems ethanol (1) + ethyl lactate (2), isopropanol (1) + isopropyl lactate (2) and n-butanol (1) + n-butyl lactate (2) Equation

Equation parameters

Root Mean Squared Deviations

A12 (K)

A21 (K)

α12

P (kPa)

T (K)

x1

y1

Ethanol (1) + ethyl lactate (2) UNIQUAC −148.67 NRTL 419.25 NRTL 340.77 NRTL 304.14

341.77 −235.48 −171.57 −141.85

0.3 0.4 0.47

0.09 0.09 0.09 0.09

0.33 0.33 0.33 0.33

0.0024 0.0023 0.0023 0.0023

0.0040 0.0039 0.0039 0.0039

Isopropanol (1) + isopropyl lactate (2) UNIQUAC −48.47 NRTL 772.67 NRTL 647.54 NRTL 587.54

114.64 −450.21 −354.24 −308.80

0.3 0.4 0.47

0.08 0.08 0.08 0.08

0.25 0.26 0.26 0.26

0.0013 0.0012 0.0012 0.0012

0.0040 0.0033 0.0033 0.0034

n-Butanol (1) + n-butyl lactate (2) UNIQUAC 480.53 NRTL 908.69 NRTL 775.48 NRTL 711.48

−268.70 −554.19 −446.32 −394.62

0.3 0.4 0.47

0.13 0.12 0.12 0.12

0.40 0.38 0.38 0.38

0.0016 0.0017 0.0017 0.0017

0.0041 0.0030 0.0031 0.0031

List of symbols A, B, C Antoine equation parameters Ak Ridlich–Kister equation parameters, Eq. (1) A12 , A21 adjustable parameter for the activity coefficients equations n (D) refractive index P total pressure Pc critical pressure P0 vapor pressure RD mean radius of gyration r, q UNIQUAC parameters T temperature Tc critical temperature Vc critical volume VE excess molar volume ViL molar liquid volume of pure component i at temperature T and pressure P x, y mole fraction of the liquid and vapor phases

Greek letters αij parameter in NRTL equation Φi fugacity coefficient of component i Φ0i fugacity coefficient of pure saturated vapor for component i at temperature T and pressure Pi0 γi activity coefficient of component i µ dipole moment ρ density Subscripts calc calculated exp experimental i component 1 volatile component of the mixture 2 heavy component of the mixture

Acknowledgement Financial support provided by the “Junta de Castilla y Le´on” through grant BU019A/05 is gratefully acknowledged.

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