measurement and correlation of isobaric vapour–liquid equilibrium data and excess properties of...

Fluid Phase Equilibria 215 (2004) 175–186

Measurement and correlation of isobaric vapour–liquidequilibrium data and excess properties of ethyl methanoate

with alkanes (hexane to decane)

Juan Ortega∗, Fernando Espiau, Ruth Dieppa

Laboratorio de Termodinámica y Fisicoqu´ımica, Escuela Superior de Ingenieros Industriales,Universidad de Las Palmas de Gran Canaria, Islas Canarias 35071, Spain

Accepted 14 August 2003

Abstract

This article is a theoretical–experimental study on the binary systems ethyl methanoate+ alkanes (hexane to decane). Vapour–liquidequilibrium (VLE) data at a pressure of 101.32 kPa are presented for the five systems studied and all were consistent with a point-to-point test.The only azeotropic binary system is ethyl methanoate+ hexane, with azeotropic coordinates atxaz = 0.709,Taz = 323.21 K. Also, for thesame group of systems the excess propertiesHE

m andV Em, measured at 318.15 K, are presented and an interpretation of the results obtained for

these is carried out. The excess properties are correlated with a new polynomial equation that is also proposed for the treatment of equilibriumdata and is included as an acceptable part of a more complete data processing.

For the five binary mixtures studied, the equilibrium thermodynamic property estimation for several group contribution models is performed.© 2003 Elsevier B.V. All rights reserved.

Keywords:Vapour–liquid equilibrium; Excess properties; Correlation; Ethyl methanoate; Alkanes

1. Introduction

There are few published thermodynamic studies on sys-tems that contain alkyl methanoate and especially few ex-perimental data on isobaric vapour–liquid equilibria (VLE)[1,2]. Our group has been building up an important database of VLE for several years concerning mixtures of alkylesters with alkanols and alkanes, and the first VLE datafor this type of systems were published previously[3], andmore recently[4] for methyl methanoate+heptane. We con-sider it interesting to provide data on the properties of thesesystems in order to better understand the behaviour of thesemethanoates in solution and to confirm the specificity ofthe HCOO– group. It is, therefore, important that, in a pre-liminary stage, we obtain data about binary mixtures withalkanes. Despite the scarcity of data on VLE in the literaturefor alkyl methanoate systems, values of excess propertieshave been collected[5–7] at a temperature of 298.15 K andat lower temperatures[8] for methyl methanoate+ alkanes.

∗ Corresponding author. Tel.:+34-928-457096; fax:+34-928-457097.E-mail address:[email protected] (J. Ortega).

In this work, the behaviour of isobaric VLE at 101.32 kPais studied together with the excess propertiesHE

m andVEm at

a temperature of 318.15 K of a group of five binary systemsof ethyl methanoate+ alkanes (C6–C10).

In line with previous works by our research team, we alsoattempt to analyse and improve the applicability of a ther-modynamic data correlation model[4] that is very useful tostudy the thermodynamic properties of multicomponent so-lutions, with temperature and pressure, and concentration asvariables. Finally, the efficacy of group contribution meth-ods [9–12] is studied with emphasis on the HCOO/CH2interaction in these mixtures and also the potential of thesemodels to estimate excess properties at temperatures over298.15 K which, in most cases, have served as a referenceto calculate interaction parameters.

2. Experimental

2.1. Products

All the compounds, supplied by Fluka, were degassed byultrasound before use and then treated with a 0.3 nm Fluka

0378-3812/$ – see front matter © 2003 Elsevier B.V. All rights reserved.doi:10.1016/j.fluid.2003.08.003

176 J. Ortega et al. / Fluid Phase Equilibria 215 (2004) 175–186

Table 1Physical properties of pure compounds

Compound Purity (%) T 0b,exp. (K) T 0

b,lit . (K) ρexp. (kg m−3) ρlit . (kg m−3) T (K) nD,exp. nD,lit .

Ethyl methanoate +99 327.29 327.46a 914.96 915.3a 298.15 1.3574 1.3575a

888.19 318.15 1.3475

Hexane >99 341.93 341.89a 654.59 654.84a 298.15 1.3724 1.37226a

341.88c 636.39 636.67b 318.15 1.3614 1.3615b

Heptane >99 371.18 371.57a 679.47 679.46a 298.15 1.3853 1.38511a

371.60c 662.13 662.32b 318.15 1.3748 1.3750b

Octane >99 398.65 398.82a,c 698.39 698.62a 298.15 1.3951 1.39505a

682.09 682.09b 318.15 1.3856 1.3855b

Nonane >99 423.66 423.97a,c 713.85 713.75a 298.15 1.4030 1.40311a

698.06 698.06b 318.15 1.3939 1.3939b

Decane >99 446.90 447.30a,c 726.19 726.35a 298.15 1.4095 1.40967a

711.14 711.43b 318.15 1.4006 1.4008b

a [13].b [14].c [15].

molecular sieve to eliminate any trace of moisture. Finally,the purity indicated by the manufacture was confirmed foreach substance with a HP-6890 gas chromatograph withFID, obtaining a quality >99.5% in weight for all substances.Table 1shows some of the experimentally determined phys-ical properties for the pure substances and their comparisonwith values found in literature.

2.2. Apparatus and procedure

The experimental equipment used to determine isobaricVLE is a small 60 ml vessel in which the two phasescirculate. The concentrations of the binary mixtures ethylmethanoate (1)+ alkanes (2) are calculated from thedensity-composition curves, obtained previously at 318.15 Kwith a DMA-55 Anton-Paar densimeter, with an uncertaintyof ±0.02 kg m−3. The temperature was measured with anASL-F25 thermometer periodically calibrated accordingto ITS-90, with an uncertainty of±10 mK, and constantpressure was reached with a regulation/measuring deviceby Desgranges et Huot, model PPC2, with an uncertaintyof ±0.02 kPa.

After reaching the equilibrium states reflected in experi-mental practise by the constancy of the intensive variablesof temperature and pressure, concentrations of the liquidand vapour phases were obtained using the (x1, ρ) curveobtained before. From these curvesVE

m versusx1 data werecalculated, which are plotted inFig. 1a. The accuracy in theconcentration of both equilibrium phases is estimated to be±0.002 units in mole fraction.

The excess enthalpiesHEm were measured directly by

calorimetry at a temperature of 318.15 K, using a standardsystem of the MS80D model by Setaram, electrically cali-brated and checked regularly using data at the same tempera-ture for ethanol+heptane[16]. The uncertainty in the experi-mental measurements was estimated to be around 1% inHE

m.

3. Presentation of results

3.1. Excess properties

Table 2shows the densitiesρ and the excess volumesVEm,

at different ester concentrations for the set of five binarysystems HCOOC2H5 (1) + CvH2v+2 (v = 6–10) (2) at atemperature of 318.15 K. Since the literature does not giveVE

m data for the mixtures of ethyl methanoate with heptaneand nonane at 298.15 K, data were also determined for thesesystems in an attempt to complement the literature data. Thevalues are given inTable 2. The set of values correspond-ing to the excess quantities (x1, YE

m) were correlated with apolynomial equation inz1 with coefficientsbi of the type:

YEm = z1z2

n∑i=0

bizi1

where z1 = x1

x1 + kx2and z2 = 1 − z1 (1)

YEm correspond to a generic excess property. In the case

of the excess volumes,YEm = 109VE

m (m3 mol−1) and thek parameter is the ratio of the molar volumes of the purecompounds at the working temperature,kv = V 0

2 /V01 . The

values calculated in this way are similar to those obtained bythe ratio of the volume parametersri for each substancei,rj/ri, obtained from the group volume parametersRk usingthe weighted sum

ri =∑k

υ(i)k Rk (2)

whereυ(i)k is the number ofk type groups in moleculei.The values ofRk are values of Van der Waals volumesgiven by Bondi[17]. The theoretical values calculated inthis way present small differences in relation to those ob-tained by the ratio of molar volumes,kv, although this

J. Ortega et al. / Fluid Phase Equilibria 215 (2004) 175–186 177

Fig. 1. (a) Experimental values (�) and curves ofVEm vs. x1 for binary mixtures HCOOC2H5 (1) + CvH2v+2 (2) at 318.15 K. Labels indicate thev-values.

(b) Representation of the variation of equimolar excess volumes with alkane chain length: (�) this work, (�) from [7], (�) calculated by Nitta et al.[12] model.

last method is more suitable when real values of the sub-stances at working temperatures are used and also becauseit enables regio-isomers to be distinguished, which is notpossible with the group contribution method.Table 4givesthe values calculated forkv and those obtained for the co-efficientsbi when a least-squares method is applied to thebinary mixture data and the standard deviationss. Fig. 1(a)shows the experimental points and the corresponding fit-ting curves, showing in theFig. 1(b) the ascending regularvariation of the equimolar excess volumes with the num-ber of carbonsv of the saturated hydrocarbon chain, at thetwo temperatures. The experimental values of this work arecoherent with those obtained previously[7].

The excess enthalpiesHEm, for the same mixtures at

298.15 K have been published previously[6] and will beused in this work to complete the study of VLE. The en-thalpies measured at 318.15 K for the set of binary systemsare shown inTable 3. The pairs (x1, HE

m) were also corre-lated withEq. (1), but, in the case of the enthalpies, thekvalues ofEq. (1)will be identified withkh that is calculatedas described below. The interactions in the mixture is as-sumed to take place at the surfaces of contact between themolecules of the compounds involved, both in the mixtureand in the pure components. Therefore, similar to the ap-proach followed with the volumes, when the enthalpies arecorrelated thekh value can be identified with a ratio of thesurface parametersqi of each substancei, qj/qi. Here too,

the values ofqi can be calculated theoretically from theweighted sum of the group area parameters,Qk:

qi =∑k

υ(i)k Qk (3)

whereQk is the group Van der Waals surface of groupk pre-sented by Bondi[17]. To calculatekv in the volumes, a realapproximation was used with the quotient ofV 0

i instead ofri. Here, we propose using a real approximation of the sur-face areas of the theoretical parameters of areaqi weightedwith that of real and theoretical volumes obtained by thegroup contribution as follows:

kh =(q2

q1

)(V 0

2

V 01

)2/3(r1

r2

)2/3

(4)

The values calculated forkh with this procedure and of thecoefficientsbi of the correlation of the dimensionless func-tionHE

m versusx1 are compiled inTable 4for the set of fivebinary systems studied here. In general,Eq. (1)does not pro-duce better correlations than another simplified form[4–7]of the same equation, in whichx(1 − x) appears instead ofz(1 − z), terms that are equivalent in only the casek = 1.However, we chose to use expression (1), since this modelcomes from a less empirical equation, with a more theoreti-cal base, as will be verified in future articles.Fig. 2ashowsthe fitting function and the experimental points ofTable 3,


Table 2Densitiesρ, and excess molar volumesVE

m for binary systems of ethyl methanoate (1)+ alkane (2) at two different temperatures

x1 ρ (kg m−3) 109VEm (m3 mol−1) x1 ρ (kg m−3) 109VE

m (m3 mol−1)

T = 298.15 KEthyl methanoate (1)+ heptane (2)

0.0491 684.59 286 0.4966 753.27 13560.1045 690.85 567 0.6166 780.53 12770.1945 702.26 913 0.7212 808.81 10870.2731 713.46 1136 0.8136 838.02 8470.3581 727.11 1287 0.8936 867.36 5690.4313 740.33 1341 0.9662 898.31 236

Ethyl methanoate (1)+ nonane (2)0.0586 717.93 340 0.5452 775.03 15180.1222 722.93 647 0.6637 798.67 14070.2313 732.91 1060 0.7588 822.34 12040.3188 742.29 1311 0.8419 847.48 9470.4051 753.27 1448 0.9134 873.81 6350.4768 763.65 1517 0.9714 899.65 278

T = 318.15 KEthyl methanoate (1)+ hexane (2)

0.0672 644.82 524 0.5909 744.63 14640.0987 648.83 731 0.6470 759.81 13670.1025 649.30 763 0.6991 774.93 12470.1787 660.45 1119 0.7456 789.33 11220.2543 672.70 1374 0.7942 805.38 9700.3327 686.78 1534 0.8415 822.05 8040.4083 701.83 1594 0.8818 837.30 6340.4706 715.33 1594 0.9220 853.21 4710.5142 729.67 1546 0.9601 869.55 271

Ethyl methanoate (1)+ heptane (2)0.0538 667.15 410 0.5555 743.43 16640.0941 671.35 654 0.6176 757.57 15900.1020 672.10 720 0.6691 770.36 14990.1201 674.13 810 0.7193 783.85 13910.1864 681.94 1125 0.7657 797.56 12350.2348 688.16 1313 0.8103 811.72 10770.3022 697.75 1488 0.8518 826.10 8890.3487 704.96 1571 0.8928 841.20 7060.4225 717.32 1671 0.9297 855.98 5090.4918 730.25 1697 0.9655 871.69 269

Ethyl methanoate (1)+ octane (2)0.0541 686.13 379 0.6364 767.00 16380.0778 688.09 526 0.6895 779.25 15490.1017 690.12 669 0.7396 792.17 14130.2065 700.10 1195 0.7839 804.88 12440.2926 709.90 1476 0.8257 817.80 10800.3809 721.47 1672 0.8639 830.59 9210.4506 731.99 1737 0.9009 844.22 7260.5161 743.07 1748 0.9357 858.19 5180.5777 754.65 1720 0.9681 872.55 279

Ethyl methanoate (1)+ nonane (2)0.0554 701.49 389 0.6645 777.13 16510.1035 704.82 674 0.7137 788.12 15490.1419 707.71 875 0.7548 798.23 14430.2062 713.06 1162 0.7979 810.00 12950.2657 718.46 1411 0.8389 822.31 11350.3237 724.44 1582 0.8747 834.31 9540.4063 734.25 1732 0.9090 846.99 7490.4825 744.74 1797 0.9408 859.78 5490.5476 754.96 1798 0.9715 873.67 2940.6099 766.10 1745


Table 2 (Continued)

x1 ρ (kg m−3) 109VEm (m3 mol−1) x1 ρ (kg m−3) 109VE

m (m3 mol−1)

Ethyl methanoate (1)+ decane (2)0.0916 715.73 598 0.6837 784.17 16450.1409 718.80 866 0.7307 794.25 15480.1885 721.96 1118 0.7749 804.93 14180.2475 726.50 1348 0.8162 816.15 12610.2940 730.41 1510 0.8537 827.55 10890.3465 735.30 1658 0.8859 838.39 9140.4267 743.95 1794 0.9163 849.59 7350.5034 753.68 1843 0.9464 861.80 5370.5699 763.48 1829 0.9739 874.45 2990.6289 773.57 1749

and in theFig. 2b the change in equimolar values with thealkane chain, at two temperatures.

The data fromFigs. 1 and 2reveal strong non-ideal ef-fects in the mixing process, generatingHE

m values higherthan 2000 J mol−1 for ethyl methanoate+decane and an ex-

Table 3Excess molar enthalpiesHE

m for binary systems of ethyl methanoate (1)+ n-alkane (2) at 318.15 K

x1 HEm

(J mol−1)x1 HE

m(J mol−1)

x1 HEm

(J mol−1)

Ethyl methanoate (1)+ hexane (2)0.1342 590.2 0.4981 1612.9 0.7087 1404.30.2218 948.1 0.5649 1610.6 0.7612 1231.70.3193 1280.5 0.6072 1581.30.4132 1521.6 0.6627 1490.7

Ethyl methanoate (1)+ heptane (2)0.1027 568.3 0.5178 1726.2 0.7755 1308.40.1817 955.8 0.5634 1719.2 0.8240 1125.60.2726 1302.7 0.5993 1686.5 0.8643 941.30.3518 1539.3 0.6469 1632.0 0.8930 748.20.4147 1649.2 0.6845 1558.8 0.9285 528.50.4679 1704.2 0.7288 1443.2 0.9716 243.5

Ethyl methanoate (1)+ octane (2)0.0864 499.0 0.5049 1820.9 0.7865 1418.70.1648 915.1 0.5478 1837.8 0.8347 1206.90.2425 1249.1 0.5838 1825.6 0.8900 899.60.3192 1515.9 0.6400 1772.4 0.9400 564.10.3902 1671.7 0.6862 1700.9 0.9742 262.20.4535 1768.5 0.7352 1577.3

Ethyl methanoate (1)+ nonane (2)0.0602 386.9 0.4973 1914.2 0.8152 1346.10.1244 772.4 0.5335 1923.8 0.8457 1194.10.1831 1065.7 0.5652 1925.2 0.8861 970.00.2366 1313.2 0.5962 1906.6 0.9227 732.50.3063 1540.9 0.6529 1820.7 0.9581 443.30.3623 1700.7 0.6902 1746.8 0.9776 256.10.4119 1818.1 0.7302 1648.80.4561 1878.2 0.7730 1513.0

Ethyl methanoate (1)+ decane (2)0.0801 505.7 0.4836 1994.9 0.7424 1764.20.1630 963.4 0.5303 2033.4 0.7878 1563.70.2396 1332.4 0.5714 2039.2 0.8303 1349.70.3110 1616.7 0.6244 2008.4 0.8773 1044.90.3767 1813.3 0.6598 1956.9 0.9239 720.30.4309 1935.1 0.6989 1872.8 0.9686 354.9

pansive effect of 1.85× 10−6 m3 mol−1 for VEm of the same

system at a temperature of 318.15 K. The data obtained rein-force the behavioural model explained in previous work[7].For the set of systems HCOOCuH2u+1 + CvH2v+2, strongendothermic processes are evident due to three types of in-teractions, Van der Waals attractions, dipole–dipole interac-tions and hydrogen bond formation, the latter owing to thefact that only the methanoates interactions decrease with theincrease in the chain lengthu.

3.2. Presentation of VLE data

Table 5shows the values of the quantities that characterisethe equilibrium states of the liquid and vapour phases,T,x1, y1 at a pressure ofp = 101.32 kPa, for the five binarysystems HCOOC2H5 (1) + CvH2v+2 (2) (v = 6–10). Withthese values, the activity coefficients of the liquid phase werecalculated according to the expression

ln γi = lnyip

xip0i

+ (Bii − V Li )(p− p0

i )

RT

+ p

2RT

n∑j=1

n∑k=1

yiyk(2δji − δjk) (5)

where the values ofδji and δjk can be calculated from thegeneral expressionδji = 2Bji − Bjj − Bii and the secondvirial coefficients of pureBii compounds and the cross-virialcoefficientsBij were determined by the expressions pro-posed by Tsonopoulos[18]. The molar volumes of the purecompounds ofV L

i in the liquid phase at the equilibriumtemperature are obtained by Rackett’s equation modifiedby Spencer and Danner[19], with theZRA coefficients ex-tracted from Reid et al.[15]. To obtain activity coefficientsγi with Eq. (5), the Antoine equation was used to calculatethe vapour pressuresp0

i of methanoate and of the alkanesas published in previous works[20–22]. The values ob-tained forγi are shown inTable 5together with the valuesof the dimensionless Gibbs functionGE

m/RT, at each equi-librium concentration. With the values shown in this table,the results for the five binary systems were consistent withthe point-to-point test proposed by Fredenslund et al.[23].Fig. 3 shows the quantities (y1 − x1) versusx1 for the five


Table 4Coefficients and standard deviations, obtained usingEq. (1) to correlate the excess quantities,VE

m andHEm/RT

Binary mixture kv b0 b1 b2 b3 109s(VEm)

(m3 mol−1)

YEm = 109VEm in (m3 mol−1)T = 298.15 K

Ethyl methanoate (1)+ heptane (2) 1.821 10965 −20325 19424 −6199 11Ethyl methanoate (1)+ nonane (2) 2.219 12824 −25436 25216 −8053 13

T = 318.15 KEthyl methanoate (1)+ hexane (2) 1.623 13784 −28598 30364 −11470 13Ethyl methanoate (1)+ heptane (2) 1.814 14170 −29268 33661 −14472 16Ethyl methanoate (1)+ octane (2) 2.008 14558 −28655 30040 −11522 12Ethyl methanoate (1)+ nonane (2) 2.203 15515 −32435 35287 −13593 10Ethyl methanoate (1)+ decane (2) 2.399 16606 −36602 39959 −15216 13

kh b0 b1 b2 b3 103s(YEm)

YEm = HE

m/RTT = 298.15 K

Ethyl methanoate (1)+ hexane (2)a 1.510 3.931 −3.945 1.972 4.5Ethyl methanoate (1)+ heptane (2)a 1.692 4.520 −5.266 2.606 6.0Ethyl methanoate (1)+ octane (2)a 1.876 5.053 −6.678 3.730 6.1Ethyl methanoate (1)+ nonane (2)a 2.060 5.625 −8.068 4.600 4.2Ethyl methanoate (1)+ decane (2)a 2.246 6.384 −10.411 6.423 8.8

T = 318.15 KEthyl methanoate (1)+ hexane (2) 1.508 2.703 0.222 −1.592 5.4Ethyl methanoate (1)+ heptane (2) 1.687 4.196 −3.989 1.919 4.3Ethyl methanoate (1)+ octane (2) 1.868 4.407 −4.881 2.755 3.5Ethyl methanoate (1)+ nonane (2) 2.050 5.458 −7.344 4.384 4.3Ethyl methanoate (1)+ decane (2) 2.232 5.735 −7.258 3.745 7.6

a [6].

Fig. 2. (a) Experimental values (�) and curves ofHEm vs. x1 for binary mixtures HCOOC2H5 (1) + CvH2v+2 (2) at 318.15 K. Labels indicate thev-values.

(b) Representation of the variation of equimolar excess enthalpies with alkane chain length: (�) this work at 318.15 K, (�) from [6] at 298.15 K, (�)calculated by UNIFAC[10] at 318.15 K, (�) calculated by UNIFAC[10] at 298.15 K, (�) calculated by Nitta et al.[12] model.


Table 5Experimental and calculated values for the isobaric VLE of the binarymixtures of ethyl methanoate (1)+ n-alkane (2) at 101.3 kPa

T (K) x1 y1 γ1 γ2 GEm/RT

Ethyl methanoate (1)+ hexane (2)340.89 0.0073 0.0386 3.458 0.993 0.002339.55 0.0173 0.0864 3.399 0.992 0.014338.35 0.0281 0.1314 3.300 0.990 0.024337.08 0.0382 0.1692 3.249 0.995 0.040335.65 0.0574 0.2195 2.931 0.997 0.059334.30 0.0787 0.2692 2.733 0.997 0.077333.02 0.1082 0.3165 2.433 1.004 0.100331.16 0.1452 0.3709 2.254 1.024 0.138330.23 0.1654 0.3971 2.182 1.036 0.159329.36 0.1869 0.4229 2.115 1.048 0.178327.77 0.2355 0.4748 1.985 1.070 0.213327.11 0.2556 0.4909 1.932 1.089 0.232326.64 0.2757 0.5054 1.873 1.105 0.245326.62 0.2779 0.5089 1.872 1.101 0.244326.11 0.2991 0.5243 1.823 1.118 0.258325.66 0.3232 0.5407 1.766 1.135 0.270325.21 0.3556 0.5586 1.683 1.164 0.283324.86 0.3806 0.5716 1.628 1.189 0.293324.62 0.4134 0.5808 1.535 1.239 0.303324.28 0.4466 0.6001 1.485 1.268 0.308324.01 0.4780 0.6132 1.430 1.313 0.313323.79 0.5099 0.6272 1.382 1.358 0.315323.60 0.5487 0.6405 1.319 1.432 0.314323.47 0.5740 0.6521 1.290 1.475 0.312323.33 0.6084 0.6655 1.248 1.550 0.306323.25 0.6420 0.6787 1.209 1.634 0.298323.23 0.6778 0.6926 1.169 1.738 0.284323.21 0.7092 0.7087 1.144 1.827 0.271323.25 0.7442 0.7255 1.114 1.955 0.252323.34 0.7744 0.7423 1.092 2.075 0.233323.50 0.8048 0.7626 1.074 2.198 0.211323.71 0.8345 0.7833 1.056 2.350 0.187324.02 0.8629 0.8077 1.042 2.492 0.161324.38 0.8900 0.8351 1.032 2.632 0.134324.82 0.9186 0.8654 1.021 2.861 0.104325.35 0.9442 0.9024 1.017 2.974 0.077325.94 0.9720 0.9473 1.017 3.140 0.048326.84 0.9904 0.9809 1.003 3.222 0.014327.08 0.9955 0.9903 0.999 3.463 0.005

Ethyl methanoate (1)+ heptane (2)368.00 0.0114 0.0998 2.709 0.997 0.008365.65 0.0203 0.1610 2.603 1.004 0.023363.03 0.0330 0.2419 2.571 0.993 0.025361.30 0.0436 0.2900 2.439 0.991 0.030358.40 0.0621 0.3656 2.329 0.987 0.040355.80 0.0789 0.4216 2.267 0.994 0.059353.01 0.1005 0.4842 2.206 0.993 0.073350.00 0.1246 0.5390 2.154 1.006 0.101348.85 0.1341 0.5539 2.125 1.022 0.120347.55 0.1459 0.5764 2.109 1.028 0.132345.80 0.1636 0.6074 2.085 1.032 0.147344.08 0.1835 0.6379 2.053 1.034 0.160342.54 0.2020 0.6612 2.023 1.045 0.177340.96 0.2246 0.6885 1.986 1.045 0.188339.39 0.2605 0.7150 1.865 1.060 0.205337.85 0.2934 0.7370 1.789 1.082 0.226336.42 0.3202 0.7529 1.750 1.113 0.252335.19 0.3558 0.7720 1.678 1.134 0.265334.26 0.4070 0.7844 1.535 1.206 0.285333.13 0.4532 0.8011 1.459 1.258 0.297

Table 5 (Continued)


332.14 0.5206 0.8169 1.337 1.371 0.302331.32 0.5668 0.8285 1.278 1.466 0.305330.67 0.5904 0.8391 1.269 1.492 0.305330.05 0.6300 0.8509 1.231 1.567 0.297329.48 0.6695 0.8609 1.194 1.673 0.289329.03 0.7119 0.8717 1.153 1.802 0.271328.56 0.7682 0.8833 1.100 2.074 0.242328.19 0.8075 0.8952 1.073 2.276 0.216327.86 0.8444 0.9086 1.053 2.489 0.186327.59 0.8809 0.9238 1.036 2.740 0.151327.36 0.9182 0.9417 1.020 3.082 0.111327.25 0.9446 0.9586 1.013 3.247 0.078327.21 0.9669 0.9729 1.006 3.564 0.048327.19 0.9838 0.9850 1.002 4.036 0.024

Ethyl methanoate (1)+ octane (2)391.18 0.0191 0.1986 1.886 0.100 0.012387.25 0.0281 0.2890 2.028 1.000 0.020380.95 0.0445 0.4123 2.101 1.011 0.044375.80 0.0604 0.4987 2.109 1.026 0.069369.54 0.0851 0.6027 2.103 1.017 0.079363.94 0.1138 0.6764 2.032 1.028 0.105358.93 0.1466 0.7342 1.951 1.040 0.132354.60 0.1788 0.7787 1.907 1.048 0.154351.21 0.2117 0.8085 1.837 1.067 0.180347.67 0.2474 0.8366 1.798 1.087 0.208345.21 0.2859 0.8554 1.708 1.112 0.229342.51 0.3227 0.8742 1.675 1.131 0.250340.24 0.3752 0.8883 1.567 1.190 0.277338.46 0.4023 0.8992 1.562 1.204 0.290336.92 0.4475 0.9075 1.486 1.271 0.310336.22 0.4675 0.9114 1.460 1.299 0.316335.16 0.5050 0.9173 1.406 1.362 0.325334.37 0.5228 0.9215 1.399 1.385 0.331333.82 0.5537 0.9250 1.349 1.447 0.331333.35 0.5782 0.9276 1.315 1.507 0.331333.09 0.5862 0.9291 1.310 1.520 0.331332.64 0.6051 0.9324 1.292 1.548 0.327332.11 0.6199 0.9350 1.286 1.580 0.330332.21 0.6264 0.9365 1.270 1.564 0.317331.43 0.6424 0.9394 1.274 1.611 0.326331.17 0.6530 0.9411 1.266 1.632 0.324330.79 0.6692 0.9431 1.254 1.680 0.323330.17 0.6878 0.9470 1.250 1.702 0.319330.03 0.6965 0.9478 1.241 1.734 0.317329.38 0.7348 0.9524 1.207 1.861 0.303328.89 0.7615 0.9561 1.188 1.948 0.290328.57 0.8139 0.9638 1.132 2.088 0.238328.54 0.8433 0.9685 1.099 2.161 0.200328.40 0.8813 0.9749 1.064 2.288 0.153328.27 0.9154 0.9806 1.034 2.496 0.108328.15 0.9304 0.9832 1.024 2.641 0.090328.06 0.9590 0.9888 1.002 3.001 0.047328.03 0.9752 0.9915 0.989 3.771 0.023

Ethyl methanoate (1)+ nonane (2)419.03 0.0058 0.1103 2.011 1.003 0.007415.15 0.0111 0.2023 2.062 1.001 0.009409.20 0.0194 0.3308 2.149 0.996 0.011401.08 0.0328 0.4778 2.145 0.994 0.020386.50 0.0623 0.6808 2.181 0.987 0.036383.50 0.0706 0.7119 2.151 0.992 0.047377.90 0.0871 0.7663 2.133 0.993 0.059372.95 0.1050 0.8055 2.092 1.005 0.082368.05 0.1245 0.8379 2.070 1.025 0.112


Table 5 (Continued)


362.60 0.1528 0.8700 2.012 1.047 0.146357.43 0.1804 0.8940 2.008 1.084 0.192352.87 0.2135 0.9140 1.964 1.107 0.224348.62 0.2637 0.9313 1.827 1.134 0.251344.46 0.3053 0.9441 1.804 1.175 0.292341.20 0.3673 0.9538 1.669 1.238 0.323338.70 0.4154 0.9604 1.603 1.290 0.345337.17 0.4667 0.9645 1.502 1.364 0.355335.44 0.5243 0.9682 1.417 1.488 0.372334.08 0.5832 0.9715 1.334 1.627 0.371333.20 0.6438 0.9740 1.246 1.813 0.353332.26 0.6970 0.9764 1.188 2.027 0.334331.70 0.7314 0.9783 1.155 2.162 0.313330.95 0.7807 0.9803 1.111 2.497 0.283330.34 0.8209 0.9823 1.080 2.833 0.250329.64 0.8585 0.9849 1.059 3.170 0.213329.07 0.8980 0.9876 1.034 3.718 0.164328.54 0.9274 0.9899 1.022 4.372 0.127328.13 0.9492 0.9923 1.014 4.866 0.094327.77 0.9667 0.9945 1.010 5.403 0.066327.51 0.9777 0.9961 1.009 5.799 0.048327.17 0.9898 0.9984 1.010 5.295 0.027

Ethyl methanoate (1)+ decane (2)440.92 0.0082 0.1345 1.213 1.009 0.011434.46 0.0159 0.2606 1.337 1.025 0.028423.12 0.0329 0.4649 1.384 1.026 0.036408.10 0.0565 0.6523 1.480 1.066 0.082397.93 0.0748 0.7549 1.579 1.063 0.091393.52 0.0839 0.7876 1.609 1.080 0.111387.61 0.0964 0.8303 1.675 1.076 0.116376.55 0.1268 0.8889 1.753 1.099 0.154369.02 0.1515 0.9199 1.822 1.098 0.171362.86 0.1793 0.9393 1.838 1.111 0.196356.87 0.2096 0.9540 1.871 1.134 0.231351.57 0.2526 0.9647 1.817 1.169 0.268346.91 0.2940 0.9721 1.796 1.217 0.311343.46 0.3391 0.9769 1.731 1.272 0.345339.87 0.4100 0.9809 1.601 1.408 0.395337.55 0.4653 0.9837 1.519 1.491 0.408335.73 0.5356 0.9857 1.399 1.655 0.414334.36 0.5924 0.9869 1.322 1.855 0.417333.32 0.6417 0.9880 1.263 2.042 0.406332.51 0.6919 0.9890 1.203 2.273 0.381331.89 0.7342 0.9899 1.157 2.501 0.351331.12 0.7714 0.9910 1.130 2.701 0.322330.58 0.8074 0.9919 1.100 2.971 0.287329.89 0.8415 0.9926 1.080 3.424 0.260329.26 0.8835 0.9935 1.051 4.235 0.212328.76 0.9158 0.9944 1.032 5.189 0.167327.84 0.9422 0.9963 1.036 5.256 0.129

mixtures studied. The discrete values of concentrations inTable 5, as well as those of temperature, can be correlatedusing an expression similar toEq. (1). When we apply tothese correlations the conditions that(y1 − x1) = 0 and(dT/dx1)p = 0, we obtain the azeotropic point of the ethylmethanoate (1)+ hexane (2) system, the only mixture thatpresents a singular point. This point is located at the coor-dinates (xaz = 0.709,Taz = 323.21 K), Lecat, see Horsley[24], predicts a pair of values of (0.708, 322.15), quite sim-

Fig. 3. Plots of experimental VLE points (�) at 101.32 kPa and correlationcurves (solid lines) of (y1 − x1) vs. x1 for binaries HCOOC2H5 (1)+ CvH2v+2 (2). Labels indicate thev-values. Dashed lines represent thepredicted curves using different group contribution models, (—) UNIFAC[9], (– – –) UNIFAC [10], (- - -) ASOG [11].

ilar to our experimental value.Fig. 4a–eshows the pointsobtained from the experimental values for Gibbs functionand the activity coefficients of each mixture studied.

4. Treatment of VLE data

The experimental data of the binary mixtures consideredin this work were correlated using a parametric model pre-sented previously[20] and later modified[22]. This model,that correlates experimental VLE data and excess enthalpies,uses the basic form of theEq. (1), but considers each ofthe bi coefficients as a function of temperature. The wayin which bi depends onT depends on the assumption thatCE

p = ξ(T), which gives us a model with a good degree ofversatility as we shall see later. Hence, assuming this rela-tion to be linear,CE

p = a+ bT, and taking into account thebasic thermodynamic relationships

CEp =

(∂HE

m

∂T

)p,x, −H

Em

RT= T

[∂(GE

m/RT)

∂T

]p,x, (6)

we obtain

GEm

RT= −a ln T − b

2T + I1

T+ I2 (7)

whereI1 andI2 are the corresponding integration constants.Replacing the term lnT by its development in the power


series of (T − h) (whereh > 0 establishes the interval forthat development) truncated in the first term, we obtain:

GEm

RT= −a

hT − a(ln h− 1)− b

2T + I1

T+ I2

= −(a

h+ b

2

)T + I1

T+ I2 − a(ln h− 1) (8)

Fig. 4. ExperimentalGEm/RT (�) and γi (�) vs. x1 obtained from VLE data at 101.32 kPa for the binaries ethyl methanoate (1)+ alkanes (2): (a)

hexane, (b) heptane, (c) octane, (d) nonane, (e) decane. Solid lines represent the correlation obtained usingEq. (9) or (12). Dashed lines represent thetheoretical estimations using several group contribution models, (—) UNIFAC[9], (– – –) UNIFAC [10], (- - -) ASOG [11]. The inset figures correspondto the differences between the excess enthalpies estimated by the correlation and the experimentals at 298.15 K (—), and at 318.15 K (– – –).

This would be the type of relationship or temperature func-tion that can be adopted for thebi coefficients ofEq. (1),producing a model for dimensionless Gibbs function asfollows:

GEm

RT(T, x1) = z1(1 − z1)

m∑i=0

(Ai1T + Ai2

T+ Ai3

)zi1 (9)


Fig. 4. (Continued).

This expression, as a polynomial inz1, presents an unnec-essary over-parametrization that can be resolved if only theterms corresponding to the even exponents are considered.The excess enthalpy function can be obtained from this ex-pression (9) by usingEq. (6)and considering the parameterk to be independent of temperature:

HEm

RT(T, x1) = z1(1 − z1)

m∑i=0

(Ai2

T− Ai1T

)zi1 (10)

The versatility of the proposed model is based on the pos-sibility of proposing other relationships ofCE

p with T. Thisproduces different models for Gibb’s dimensionless func-tion, although all of these have the generic form of theEq. (1). Hence, in a previous work[20], CE

p could be con-sidered to be independent of temperature, giving rise to itsmore simplified form.

GEm

RT(T, x1) = z1(1 − z1)

m∑i=0

(Ai1

T+ Ai2

)zi1 (11)

In contrast, for a broader and more complete form, aquadratic dependence could be considered forCE

p = ξ(T):

GEm

RT(T, x1) = z1(1 − z1)

m∑i=0

(Ai1T

2 + Ai2T

+Ai3 ln T + Ai4

T+ Ai5

)zi1 (12)

where expression (9) is an intermediate form between ex-pressions (11) and (12). This procedure can be used to opt fora model which, correlated satisfactorily to the experimental

data, contains the smallest number of parameters. Hence, forthe ethyl methanoate+ hexane mixture the more simplifiedmodelEq. (11)was suitable, while for the rest of the mix-tures,Eq. (9) was the most appropriate, takingm = 2 andthe terms corresponding to the even powers of this model.

Another important aspect of the correlation procedure is todefine the objective function and the mathematical algorithmthat optimises the fitting data. The sets of experimental datato be correlated are as follows: on the one hand VLE dataare obtained{(Tj, x1j, ln γ1j, ln γ2j); j : 1, . . . , n}, whereln γ1j and lnγ2j are the natural logarithms of the activitycoefficients of the first component,x1j, at temperatureTjand on the other hand,{⌊x1i, (H

Em/RT1)i

⌋ ; i : 1, . . . , n1}and{⌊x1i, (H

Em/RT2)i

⌋ ; i : 1, . . . , n2} are, respectively, thesets of values of excess enthalpies at temperature ofT1 =298.15 K andT2 = 318.15 K. The experimental equilibriumconcentrations do not coincide with those achieved in theenthalpy experiments.

To correlate model (9) or (11), in the conditions de-scribed, to the experimental data, one least-squares proce-dure was used, establishing an objective function OF thatminimises the difference between experimental data andthose calculated by the model, including VLE and excessenthalpies. However, as the excess enthalpies and the activ-ity coefficients are on different scales, this objective func-tion could cause an imbalance in the correlation of the dif-ferent quantities, obtaining better fits for one of the quanti-ties and poorer ones for the other. Therefore, the OF usedhere has been modified appropriately by weighting each ofthe terms. Hence, the objective function is established asfollows:

OF =n1∑i=1

[(HE

m/RT(T1, x1i)− (HEm/RT1)i)

σH(T1)

]2

+n2∑i=0

[(HE

m/RT(T2, x1i)− (HEm/RT2)i)

σH(T2)

]2

+n∑j=1

[(ln γ1(Tj, x1j)− ln γ1j)

σγ1

]2

+n∑j=1

[(ln γ2(Tj, x1j)− ln γ2j)

σγ2

]2

(13)

whereσ now correspond to the maximum experimental val-ues of each of the amounts appearing in the subscripts. Inthis way, the scale of the discrepancies for both magnitudesis normalised.

To avoid the multiplicity of roots in the manipulation ofnon-linear equations, optimisation of OF is done by im-plementing a generic algorithm. The numerical results ofthe fits for each of the systems are presented inTable 6,together with the standard deviations and ther2 (in paren-thesis) as a measure of the goodness of fit. Thek value inEq. (9)was identified here askg, different to those proposedfor the excess properties and submitted to the correlation


Table 6Parameters obtained forEqs. (9) and (11)used in correlation of VLE data of binary mixtures ethyl methanoate (1)+ n-alkanes (2), and standarddeviations obtained for activity coefficientss(γi), non-dimensional Gibbs functions(GE

m/RT), and excess enthalpiess(HEm). The values between parenthesis

correspond to the goodness of fit,r2

Ethyl methanoate(1) + hexane (2)

Ethyl methanoate(1) + heptane (2)

Ethyl methanoate(1) + octane (2)

Ethyl methanoate(1) + nonane (2)

Ethyl methanoate(1) + decane (2)

A01 −0.0044 −0.0019 0.0002 −0.0010 −0.0085A02 92.4156 487.0924 916.1586 710.2192 −21.5509A03 2.0128 0.1097 −1.5795 −0.6461 3.9248A21 0.0088 0.0007 −0.0172 −0.0095 0.0002A22 1621.7799 591.3975 −1672.4665 −481.2592 685.6399A23 −6.5756 −1.1591 10.7324 5.4580 −0.7659kg 0.6193 0.7617 1.1717 0.8890 0.7879s(γi) 0.188 (0.99) 0.047 (0.99) 0.195 (0.92) 0.114 (0.99) 0.191 (0.95)s(GE

m/RT) 0.008 (0.99) 0.007 (0.99) 0.02 (0.97) 0.017 (0.98) 0.048 (0.88)s(HE

m) 65.9 (0.97) 37.1 (0.99) 37.4 (0.99) 34.4 (0.99) 79.8 (0.98)

procedure.Fig. 4a–eshow, as a continuous line, the linescorresponding to the correlations obtained from the dimen-sionless functionGE

m/RTand from the coefficientsγi, whilethe inset figures show the differences in the estimationsof excess enthalpies for each system at temperatures of298.15 and 318.15 K. The results of the procedure is goodfor the systems, demonstrated by both the qualitative andquantitative estimation, with the weakest being that of ethylmethanoate+decane, possibly due to the difficulty to obtainisobaric data for this mixture because of the great differencebetween the boiling points of the pure compounds, of al-most 120 K. However, estimation of theHE

m of this system,in spite of the fact that it produces the greatest mean errorof the five systems, can be considered as acceptable, beingbelow 5 and 6% at temperatures of 298.15 and 318.15 K,respectively.

5. Application of group contribution models

In order to assess the predictive power of some groupcontribution models[9–12] for systems containing ethylmethanoate, the predicted values were obtained for mix-tures of different thermodynamic quantities, such as isobaricVLE, excess enthalpies and excess volumes, depending onthe possibilities of the model. This information is importantto be able to begin to update interaction parameters, specif-ically, those corresponding to HCOO/CH2, characteristic ofthis type of mixtures. The original version of the UNIFACmodel presented in Hansen et al.[9] gives some not veryaccurate isobaric estimations of VLE, with values ofγi, seeFig. 4a–e, and of concentrations,Fig. 3, very different fromthe experimental ones. With the version of Gmehling et al.[10], of the same model, all the values of VLE and the excessenthalpies can be estimated with the same set of parameters.This model gives a better mean evaluation of the activity co-efficients than the original model of Hansen et al.[9], evenreproducing the maxima inγ1 at low concentrations of ethylmethanoate, seeFig. 4a–e. This finding becomes increas-

ingly apparent when the chain of saturated hydrocarbons in-creases in length. However, it estimates higher methanoateconcentrations in the vapour phase than the experimentalones. The model reproduces the azeotrope of the mixture ofethyl methanoate+hexane in (0.660, 321.81) somewhat dif-ferent to that found experimentally, and predicts an azeotropefor ethyl methanoate+heptane systems, that is not observedexperimentally.Fig. 2b shows the equimolar values of en-thalpies estimated by this model for this set of mixtures.These are lower than experimental values, both at 298.15and at 318.15 K, with highly acceptable mean differences,lower than 6%. Both the change in enthalpy with hydro-carbon chain length and the quantity of(∂HE

m/∂T)p,x > 0are effectively reproduced with this version of the UNIFACmodel.

The ASOG[11] model presents the best estimations of themixtures with low molecular weight hydrocarbons, predict-ing an azeotrope for the hexane mixture at (0.730, 323.23)which is nearer to the experimental values than predicted bythe UNIFAC model. However, the VLE estimation becomesincreasingly less accurate for the heavier alkanes. This modeldoes not reproduce in any case the unusual behaviour ofγ1at low concentrations of ester.

Finally, the model with the greatest predictive capac-ity, that of Nitta et al. [12], was also used. This modelhad yielded acceptable results in a previous work[21] fornon-methanoates with alkanes and can predict all the prop-erties studied in this work. The results show that this modelis not suitable for ethyl methanoate+ alkane systems. Onone hand, the values estimated forγi and the Gibbs functionare too high, even higher than those obtained with the origi-nal version of UNIFAC[9]. This is why they are not shownin Fig. 4a–e. Also, estimation of the excess volumes givesa variation relative to chain length with a very steep slopeand a variation of(∂VE

m/∂T)p,x less than that obtained in theexperiments, seeFig. 1b. However, the excess enthalpies ob-tained are acceptable when estimated at 298.15 K but not at318.15 K (Fig. 2b) since this model produces a coefficient(∂HE

m/∂T)p,x∼= 0.


List of symbolsbi coefficients inEq. (1)Bij second virial coefficients

CEp excess thermal capacity

GEm excess Gibbs energy

HEm excess molar enthalpy

k parameter inEq. (1)kh parameter defined byEq. (4)kv ratio of molar volumes of the pure compoundsOF objective functionp absolute pressurep0i vapour pressure of pure compoundi

Qk group Van der Waals surface for groupkR universal gas constantRk group Van der Waals volume for groupks standard deviationT temperatureV 0i molar volume of pure compoundiVE

m excess molar volumexi mole fraction (liquid phase) of componentiyi mole fraction (vapour phase) of componentiYE

m generic excess propertyzi volumetric fraction defined inEq. (1)ZRA parameter of Rackett equation

Greek lettersγi activity coefficient of componentiδ absolute difference between two valuesρ density

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measurement and correlation of isobaric vapour–liquid equilibrium data and excess properties of...

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