A Study on Alkane + Ester + Ester Systems. Physicochemical Behavior

Article pubs.acs.org/jced

A Study on Alkane + Ester + Ester Systems. Physicochemical Behavior of Binaries and Ternaries of Octane or Iso-octane with Methyl Esters (Ethanoate, Butanoate, Pentanoate) Juan Ortega,* Luis Fernández, Maykel Castro, Elena Ortega, and Raul Rios Grupo de Ingeniería Térmica (Sección de Termodinámica y Fisicoquímica de Fluidos), Universidad de Las Palmas de Gran Canaria, Parque Científico-Tecnológico Campus de Tafira, 35071 Las Palmas de GC, Spain ABSTRACT: This work presents an experimental contribution with values of properties arising from mixing processes (enthalpies and volumes) of ternaries of octane and iso-octane (2,2,4-trimethylpentane) with methyl pentanoate or methyl butanoate and methyl ethanoate, measured at 298.15 K. Values of hE and vE of the binaries of these compounds are also obtained. In all cases, the mixtures are endothermic with expansive volumetric effects. The structural interpretation of these is analyzed in relation to the two most important effects, van der Waals forces and electrostatic interactions due to the presence of dipoles on the esters. A slightly different interpretation is made for the ester−ester binaries, which have less significant effects in the ternaries. Experimental data of binaries and ternaries are represented using the authors own model with excellent results. The UNIFAC model gives good representations of hE for the octane−ester systems, but values much higher than real ones for the ester−ester systems. The repercussion of these values in the ternary is negligible since the interaction energies in the ester−ester correspond to only around 10% of the alkane-ester.

1. INTRODUCTION The search for alternative fuels has given rise to lines of research aimed at increasing our knowledge of the physicochemical behavior of some synthetic solutions. This could be a useful tool, among other things, to complement and certify a suitable structural model for those solutions that could influence the design of some engineering processes. Our group has been working with binary solutions of ester + alkane,1−3 ester + alkanol3−5 and ternaries of ester + ester + alkane6 and ester + ester + alkanol.7 Although there is already an extensive database for binaries, data are limited for studies on solutions with a greater number of components. The experience obtained with a series of previous works has resulted in the creation of a model of intermolecular behavior that attempts to explain the nature of the macroscopic quantities measured,2,8,9 especially in ester + alkane binaries, emphasizing how the dipolar interactions of the ester contribute significantly in justifying the final results. In spite of this, in all cases the van der Waals interactions are dominant. Experimentation of this work was carried out measuring enthalpies hE and volumes vE at 298.15 K and atmospheric pressure for a set of four ternaries comprising methyl esters (ethanoate, butanoate, pentanoate) with octane or 2,2,4trimethylpentane (iso-octane). Values of the same properties were also obtained for the eight corresponding binaries to the mentioned compounds. Of all these solutions, theoretical and/or experimental studies have been found in the literature of vE,10−15 and of hE,13−16 for the binary octane + methyl ethanoate at several temperatures and of vE,13,17,18 and hE,13 for the binaries octane + methyl butanaote, or + methyl pentanoate. No information has © 2016 American Chemical Society

been found for the remaining binary and ternary solutions chosen for this work. To perform a better analysis of the experimental data, an analytical representation of these was performed using our own model19 which gives excellent results in the treatment of thermodynamic data. It has been interesting to confirm the structural model established for ester + alkane systems and to study the ester + ester binaries in greater depth. The properties of energetic nature for all the binary and ternary solutions considered in this work were estimated using the UNIFAC group contribution method,20 which is of great value in the field of process simulation. Especially interesting, the results obtained by the predictive model for solutions containing isomers and in those formed by compounds of the same chemical nature, as in previous studies,6,7,9 were unacceptable. The COSMO-RS model,21 based on a quantum-chemistry approximation, was also used to obtain additional information about the nature of the physicochemical interactions of these solutions, since in a recent experiment with compounds of the same chemical nature22 the method provided acceptable estimates of hE. Analysis of the interactions estimated with the ab initio methodology and their repercussions on the properties of binary and ternary solutions has broadened the utility of this procedure to know better the structural behavior of solutions. Received: September 22, 2015 Accepted: January 14, 2016 Published: February 3, 2016 1177

DOI: 10.1021/acs.jced.5b00813 J. Chem. Eng. Data 2016, 61, 1177−1191

Journal of Chemical & Engineering Data

Article

Table 1. Description of the Material Used: Purity, Supplier, and Characterization

a

compound

CAS No.

supplier

physical treatment

% purity w/w

moisture ppm

analytic methoda

methyl ethanoate methyl butanoate methyl pentanoate octane iso-octane nonane water

79-20-9 623-42-7 624-24-8 111-65-9 540-84-1 111-84-2 7732-18-5

Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich

molecular sieve molecular sieve molecular sieve molecular sieve molecular sieve molecular sieve bidistillation

99.3 99.6 99.6 98.9 99.7 99.1 < 2 μSm−1

98 106 104 50 47 32

GC, KF GC, KF GC, KF GC, KF GC, KF GC, KF Cond.

GC, gas chromatography; KF, Karl Fischer titration; Cond, conductivity meter.

were used to calculate the excess volumes vE, which were estimated with a combined standard uncertainties (95% confidence level, k = 2) less than 2·109 m3·mol−1. In ternaries, density is a function of the compositions of two of the components ρ = ρ(x1,x2), so their experimental description requires a sufficient number of points inside the ℜ2 -space where x1,x2 ∈ [0,1]. Following the procedure described in previous works,6,7 a series of tests were conducted preparing binary solutions of octane(1) or iso-octane(1) with methyl butanoate(2) or methyl pentanoate(2), establishing for each of these the ratio x1/x2. These binaries are considered as a single pseudocompound that is subsequently diluted with a third component, methyl ethanoate(3), in suitable proportions to establish the behavior in the interval x ∈ [0,1]. Densities of the ternaries were measured with the described densimeter, calculating the excess volumes as described below. The combined standard uncertainty of the latter is 5 × 109 m3·mol−1, while the corresponding standard uncertainty to compositions was estimated to be 0.0005. Excess enthalpies, hE, were measured with a Calvet MS80D calorimeter by Setaram, calibrated by the procedure described in previous works.21 The controller of the apparatus allows thermal oscilations of (T ± 0.002) K. The thermograms obtained in the experimentation were processed by the SetSoft software provided by Setaram. The correct functioning of the apparatus was checked by reproducing hE for a known system,27 estimating a standard uncertainty for the quantities of [x ± 2·10−4, (hE ± 1%) J mol−1]. Measurements for the ternary solutions were obtained by following a similar procedure to that described before for volumes, by adding known quantities of methyl ethanoate (3) to a pseudocompound (as noted above) that remains in the calorimetric cell, which corresponds to a known solution of the other two compounds (1) + (2). The uncertainties calculated for the hE of the ternaries were found to be slightly higher than those calculated for the binaries.

2. EXPERIMENTAL SECTION 2.1. Chemicals. All the chemical compounds were supplied by Sigma-Aldrich and were of the maximum commercial purity available. The quality of products was verified with an Agilent GC, model 6890N, and values obtained were similar to those provided by the manufacturer. Nonetheless, all products were degasified by ultrasound and stored in the dark, over a 0.3 nm (SAFC) molecular sieve, for at least 24 h before use. The water contents of all the products was determined by a Karl Fischer coulometric procedure, giving values close to 100 ppm in all cases. Table 1 shows the characteristics of the substances used; additionally the quality of the products was also certified with measurements of two physical properties. The values obtained for the density ρ and refractive index nD of all compounds and the comparison with values provided by literature14,23−26 are compiled in Table 2. Table 2. Experimental Propertiesa (ρ, nD) of Pure Compounds Measured at 298.15 K and Atmospheric Pressure (p = 0.1 MPa), and Comparison with Those from Literature ρ/kg·m−3 compound

nD

exp

lit

exp

lit

octane

698.58

1.3952

1.39505c

iso-octane

687.75

1.3890

methyl ethanoate

927.16

1.38898c 1.3890e 1.3589c,b,f

methyl butanoate

892.34

methyl pentanoate

884.84

698.49c 698.60b 687.81c 687.67e 927.9c 927.01b 927.14f 892.16d 892.52f 884.80d 884.58f

1.3588

1.3845 1.3968

1.3847d 1.3852f 1.3971d 1.3947f

a Standard uncertainties (0.68 level of confidence): u(T) = 0.01 K, u(nD) = 0.0002. Relative standard uncertainty for pressure: ur(p) = 1%. Instrument standard uncertainty for density = 0.02 kg·m−3. The combined expanded uncertainty (0.95 level of confidence, k = 2) for Uc(ρ) = 1 kg·m−3. bReference 14. cReference 23. dReference 24. e Reference 25. fReference 26.

3. RESULTS 3.1. Experimental Data and Mathematical Treatment. Binaries. The values of (x1,ρ,vE) and (x1,hE) measured at 298.15 K for the six alkane + ester binaries: octane(1) + methyl butanoate(2), or + methyl pentanoate(2), or + methyl ethanoate(3), iso-octane(1) + methyl butanoate(2), or + methyl pentanoate(2), or + methyl ethanoate(3), and for the two ester + ester binaries: methyl butanoate(2) + methyl ethanoate(3), methyl pentanoate(2) + methyl ethanoate(3) are recorded, respectively, in Tables 3 and 4. The sets of data (xi, yE = vE,hE) for all the systems were mathematically correlated by an equation that relates the excess property with the molar fraction via the socalled active f raction. The generic expression for the binaries is

2.2. Apparatus and Procedures. Densities were determined with an Anton-Paar DMA-60/602 densimeter with estimated uncertainties at a 0.95 confidence level of 0.02 kg·m−3, maintaining the temperature stable at (298.15 ± 0.01) K using a Julabo F-25 circulating water bath. The apparatus was calibrated at the working temperature with water and nonane, as proposed in previous works.1−7 Binary mixtures were prepared synthetically by weighing in the interval of compositions of x ∈ [0,1], estimating the uncertainties of the molar fractions to be around 2·10−4. Values obtained for each of the binary solutions (xi,ρ)

yijE = zizj(yij0 + yij1zi + yij2 zi2) 1178

(1) DOI: 10.1021/acs.jced.5b00813 J. Chem. Eng. Data 2016, 61, 1177−1191


Article

Table 3. Experimental Densities ρ Measured at 298.15 K and Atmospheric Pressure (p = 0.1 MPa) and Excess Molar Volumes vE Calculated for the Binaries Indicated Belowa x1

ρ kg·m

−3

109vE m ·mol 3

x1 −1

ρ kg·m

−3

109vE

x1 −1

m ·mol 3

Octane(1) + Methyl Pentanoate(2) 0.3625 804.47 0.4427 788.93 0.4558 786.45 0.5104 776.34 0.5504 769.10 0.6116 758.45 0.6541 751.22

0.0000 0.0514 0.1005 0.1610 0.2134 0.2601 0.3084

884.84 872.35 860.71 846.85 835.46 825.47 815.53

0 109 215 332 386 448 484

559 604 610 623 630 602 582

0.0000 0.0590 0.1109 0.1520 0.2051 0.2557 0.2992 0.3501

892.34 875.04 860.65 849.82 836.56 824.52 814.89 803.53

0 184 332 433 535 621 640 744

0.0000 0.0493 0.1011 0.1517 0.2033 0.2530 0.3008 0.3471

927.16 901.46 878.04 857.91 839.55 823.66 809.86 797.79

0 351 639 864 1061 1218 1333 1401

0.0000 0.0537 0.1588 0.2505 0.3544 0.4518

884.84 871.44 846.38 825.53 803.10 783.06

0 30 75 125 172 220

Octane(1) + Methyl Butanoate(2) 0.4045 792.24 792 0.4516 782.90 821 0.4978 774.12 835 0.5469 765.18 834 0.5862 758.27 828 0.6551 746.75 786 0.6989 739.74 750 0.7471 732.42 676 Octane(1) + Methyl Ethanoate(3) 0.3946 786.15 1489 0.4523 773.45 1538 0.4951 764.76 1561 0.5307 758.11 1547 0.5777 749.93 1506 0.5898 747.92 1492 0.6146 743.98 1449 0.6388 740.27 1403 Iso-octane(1) + Methyl Pentanoate(2) 0.4984 773.84 236 0.5417 765.44 253 0.6420 746.75 266 0.6854 738.97 262 0.7425 728.98 252 0.7967 719.79 230

0.0000 0.0344 0.0633 0.1096 0.1334 0.1539 0.2013

892.34 881.71 873.20 860.10 853.55 848.00 835.70

0 75 117 172 204 233 276

Iso-octane(1) + Methyl Butanoate(2) 0.2471 824.10 0.2981 811.90 0.3973 789.58 0.4410 780.30 0.5431 760.00 0.5901 751.22 0.6801 735.30

0.0000 0.0375 0.1025 0.1652 0.1775 0.2189 0.2615 0.3020

927.16 906.89 876.58 851.09 846.59 832.07 818.03 805.95

0 214 470 696 723 826 955 1031

0.0000 0.0496 0.1001 0.1536 0.2027 0.2511 0.3522

927.16 922.92 919.44 916.04 913.18 910.53 905.55

0 80 109 134 149 163 178

345 388 467 499 530 532 515

Iso-octane(1) + Methyl Ethanoate(3) 0.3902 782.41 1173 0.4061 778.52 1196 0.4249 774.09 1215 0.4627 765.54 1254 0.5239 752.92 1271 0.5411 749.57 1275 0.6100 737.18 1237 0.6612 728.76 1190 Methyl Pentanoate(2) + Methyl Ethanoate(3) 0.4013 903.35 181 0.4497 901.35 178 0.4935 899.62 175 0.5444 897.75 165 0.5935 896.01 158 0.6563 893.98 138 0.7383 891.47 116 1179

ρ kg·m

−3

109vE m ·mol−1 3

0.7081 0.7535 0.8013 0.8518 0.9059 0.9521 1.0000

742.25 734.86 727.38 719.71 711.73 705.03 698.58

549 521 459 375 268 179 0

0.7931 0.8428 0.9009 0.9367 0.9651 0.9655 1.0000

725.70 718.65 710.74 706.37 702.84 702.79 698.58

591 500 378 218 120 119 0

0.6699 0.7238 0.7841 0.8333 0.8887 0.9311 0.9585 1.0000

735.52 728.10 720.49 714.64 708.75 704.69 702.21 698.58

1371 1235 1049 899 655 418 252 0

0.8148 0.8415 0.8779 0.8999 0.9409 1.0000

716.75 712.32 706.53 702.99 696.52 687.75

226 218 169 159 130 0

0.7243 0.8239 0.8708 0.8863 0.9158 0.9816 1.0000

727.90 712.20 705.20 703.02 698.80 689.84 687.75

493 400 345 307 264 124 0

0.6786 0.7359 0.8086 0.8803 0.9521 1.0000

726.10 717.60 708.07 699.86 692.07 687.75

1158 1078 878 576 313 0

0.7902 0.8430 0.8918 0.9372 1.0000

890.02 888.62 887.40 886.30 884.84

96 73 50 29 0



Article

Table 3. continued x1

ρ kg·m

0.0000 0.0106 0.0564 0.1023 0.1361 0.2030 0.2536

109vE

−3

m ·mol 3

927.16 926.21 923.86 921.52 919.91 916.91 914.74

ρ

x1 −1

kg·m

109vE

−3

kg·m

Methyl Butanoate(2) + Methyl Ethanoate(3) 0.3054 912.64 105 0.4122 908.65 110 0.4511 907.30 109 0.5456 904.19 104 0.5906 902.80 99 0.6148 902.08 96 0.6958 899.76 83

0 37 49 68 77 89 99

ρ

x1 −1

m ·mol 3

0.7394 0.7873 0.8368 0.8884 0.9538 0.9740 1.0000

−3

109vE m ·mol−1 3

898.57 897.29 896.07 894.85 893.32 892.87 892.34

76 69 54 37 20 14 0

Standard uncertainties (0.68 level of confidence): u(T) = 0.01 K, u(x) = 0.0002, u(109·vE) = 2 m3·mol−1. Relative standard uncertainty for pressure: ur(p) = 1%. Instrument standard uncertainty = 0.02 kg·m−3. The combined expanded uncertainty (0.95 level of confidence, k = 2) for Uc(ρ) = 1 kg·m−3.

a

Table 4. Experimental Excess Molar Enthalpies hE Measureda Directly at 298.15 K and Atmospheric Pressure (p = 0.1 MPa) for the Binaries Indicated Below x1

hE

x1

J·mol−1

a

hE

x1

J·mol−1

0.0427 0.0951 0.1523 0.2098 0.2677

162 337 511 659 784

0.3234 0.3770 0.4266 0.4619 0.4695

0.0438 0.0922 0.1440 0.1978

213 413 602 771

0.2521 0.3043 0.3543 0.4030

0.0466 0.1009 0.1504 0.2057

415 813 1135 1415

0.2580 0.3043 0.3516 0.3642

0.0438 0.0963 0.1589 0.2206 0.2692

144 281 438 574 664

0.3311 0.3825 0.4360 0.4818 0.5239

0.0389 0.0858 0.1367 0.1916 0.2446

161 332 499 651 779

0.2982 0.3481 0.3959 0.4256 0.4407

0.0200 0.0525 0.0892 0.1241 0.1687

155 414 660 858 1047

0.2084 0.2560 0.3079 0.3608 0.3915

0.0539 0.1130 0.1716 0.2347

50 96 135 173

0.2915 0.3440 0.3954 0.4441

0.0270 0.0962 0.1645 0.2260

22 53 83 102

0.2888 0.3478 0.4002 0.4437

hE

x1

J·mol−1

Octane(1) + Methyl Pentanoate(2) 882 0.5113 956 0.5126 1005 0.5411 1042 0.5701 1043 0.6364 Octane(1) + Methyl Butanoate(2) 911 0.4321 1021 0.4779 1104 0.5368 1164 0.6033 Octane(1) + Methyl Ethanoate(3) 1634 0.3999 1786 0.4460 1905 0.5006 1943 0.5742 Iso-octane(1) + Methyl Pentanoate(2) 742 0.5638 801 0.5679 843 0.6024 866 0.6258 881 0.7031 Iso-octane(1) + Methyl Butanoate(2) 884 0.4767 962 0.5375 1018 0.6052 1050 0.6813 1053 0.7629 Iso-octane(1) + Methyl Ethanoate(3) 1217 0.4323 1385 0.4764 1544 0.5406 1659 0.6163 1712 0.6888 Methyl Pentanoate(2) + Methyl Ethanoate(3) 198 0.5055 218 0.5754 231 0.6517 239 0.7339 Methyl Butanoate(2) + Methyl Ethanoate(3) 120 0.4822 135 0.5276 143 0.5725 149 0.6268

hE J·mol−1

1053 1048 1042 1039 987

0.7090 0.7745 0.8541 0.9325

888 757 548 229

1196 1217 1207 1155

0.6760 0.7570 0.8413 0.9231

1052 880 640 362

2005 2039 2038 1955

0.6631 0.7615 0.8485 0.9324

1743 1384 945 448

885 884 871 856 789

0.7813 0.8452 0.9243

658 505 297

1064 1065 1030 941 789

0.8494 0.9353

566 302

1763 1789 1759 1644 1456

0.7833 0.8597 0.9422

1149 792 356

238 228 212 178

0.8188 0.9036

126 75

151 149 146 138

0.6958 0.7669 0.8497 0.9313

122 100 69 36

Standard uncertainties (0.68 level of confidence): u(T) = 0.005 K, u(x) = 0.0002. Relative standard uncertainties: ur(p) = 1%, and ur(hE) = 1%. 1180



Article

Table 5. Coefficients yij of eq 1 and Standard Deviations s(yE) Obtained in the Corresponding Correlation of Excess Properties: (xi,vE) and (xi,hE) for the Binaries (i-j) Indicated Below 109vE/ m3·mol−1 binary C8H18 (1) + C6H12O2 (2) C8H18 (1) + C5H10O2 (2) C8H18 (1) + C3H6O2 (3) i-C8H18 (1) + C6H12O2 (2) i-C8H18 (1) + C5H10O2 (2) i-C8H18 (1) + C3H6O2 (3) C6H12O2 (2) + C3H6O2 (3) C5H10O2 (2) + C3H6O2 (3)

ki‑j v

v0ij

0.803 2090 0.700 2639 0.489 4710 0.790 570 0.689 1636 0.481 3861 0.609 929 0.698 639 hE/J·mol−1

v1ij

v2ij

109s(vE)

−685 −845 −4181 −711 −2011 −5622 −835 −786

2555 3756 11461 2493 4893 12739 811 744

12 13 24 10 21 25 5 3

binary

ki‑j h

h0ij

h1ij

h2ij

s(hE)

C8H18 (1) + C6H12O2 (2) C8H18 (1) + C5H10O2 (2) C8H18(1) + C3H6O2 (3) i-C8H18 (1) + C6H12O2 (2) i-C8H18 (1) + C5H10O2 (2) i-C8H18 (1) + C3H6O2 (3) C6H12O2(2) + C3H6O2 (3) C5H10O2 (2) + C3H6O2 (3)

0.896 0.795 0.529 0.873 0.776 0.515 0.590 0.665

3334 3927 5167 2912 3354 4696 539 389

1795 1272 1681 295 899 −420 579 308

−286 855 6390 1602 1550 8003 295 125

12 8 5 6 9 10 2 3

Figure 2. Representation of experimental (x1,hE) values and correlation curves (eq 1) () for the binaries: (a) octane (1) + methyl ester (2) (u = 2, u = 4, u = 5) (b) iso-octane (1) + methyl ester (2) (u = 2, u = 4, u = 5) (c) methyl ester (2) (u = 4, u = 5) + methyl ethanoate (3). Comparison with those from literature: (×) ref 13, (▲) ref 15, (▽) ref 16. (u = 2, ethanoate; u = 4, butanoate; u = 5, pentanoate); (red dashed line) curves obtained with UNIFAC.20

procedure for linear functions. The following equation establishes a general mathematical definition for zi of a multicomponent system, υx xi = n zi = n i i ∑ j = 1 υjxj ∑ j = 1 (υj /υi)xj (2) where the υi parameters are characteristic of each substance and the property studied. The active f raction is used instead of the molar fraction in the data treatment in an attempt to represent better the effect of each component, with some of its molecular properties, on the excess quantity in the property studied. For a binary, eq 2 takes the following simplified form, when compound 1 is considered as a reference: x1 z1 = x1 + k1 ‐ 2x 2 (3) In the data treatment of vE, the coefficient υi identifies with the molar volume of the pure product, υi = voi , and in this case, the parameter kij is called kijv and is calculated as the quotient: kijv = voj /voi . When working with enthalpies, υi is related to the molecular surface, and is called kijh:

Figure 1. Representation of experimental (x1,vE) values and correlation curves (eq 1) () for the binaries: (a) octane (1) + methyl ester (2) (u = 2, u = 4, u = 5); (b) iso-octane (1) + methyl ester (2) (u = 2, u = 4, u = 5); (c) methyl ester (2) (u = 4, u = 5); + methyl ethanoate (3) (u = 2, ethanoate; u = 4, butanoate; u = 5, pentanoate). Comparison with those from literature: (○) ref 11, (▽) ref 12, (×) ref 13, (+) ref 14, (▲) ref 15.

k hij

2/3 qjo ⎛ vjo r o ⎞ ⎛ k ij ⎞2/3 i = o = o ⎜⎜ o o ⎟⎟ = kqij⎜ vij ⎟ si qi ⎝ vi r j ⎠ ⎝ kr ⎠

sjo

(4)

where soK is the molecular surface of a generic compound K = i,j, in pure state, while, roK and qoK, are, respectively, the parameters van

where yiij are parameters adjustable to the distribution of experimental points obtained by a least-squares optimization

der Waals for volume and surface, calculated from Bondi’s group 1181



Article

Table 6. Experimental Densities ρ and Excess Molar Volumes vE123 Obtained at 298.15 K and Atmospheric Pressure (p = 0.1 MPa) for Ternaries Indicated Belowa x1

x2

ρ −3

kg·m 0.006 0.011 0.021 0.026 0.035

0.050 0.097 0.185 0.230 0.311

0.014 0.026 0.038 0.051 0.064 0.086 0.112

0.042 0.079 0.115 0.153 0.190 0.256 0.334

0.029 0.054 0.077 0.101 0.128 0.154 0.228

0.028 0.052 0.075 0.099 0.125 0.150 0.223

0.042 0.080 0.153 0.187 0.267 0.301 0.375

0.014 0.027 0.051 0.062 0.088 0.100 0.124

0.050 0.093 0.183 0.227 0.282 0.313 0.361 0.401 0.447

0.006 0.011 0.021 0.026 0.032 0.036 0.041 0.046 0.051

0.005 0.009 0.014 0.017 0.021 0.030 0.037 0.047 0.051 0.064

0.040 0.074 0.117 0.149 0.184 0.254 0.314 0.407 0.438 0.551

0.009 0.016 0.024 0.032 0.038 0.040 0.047

0.029 0.051 0.078 0.105 0.125 0.131 0.154

109vE123 m ·mol 3

x1

x2

−1

ρ kg·m

Octane(1) + Methyl Pentanoate(2) + Methyl Ethanoate(3), x′1 = 0.101 920.09 92 0.056 0.495 914.38 160 0.075 0.668 905.33 196 0.085 0.753 900.96 233 0.089 0.792 893.68 304 x1′ = 0.251 915.70 215 0.126 0.376 908.05 259 0.137 0.409 900.66 332 0.150 0.448 893.41 391 0.162 0.484 887.34 378 0.210 0.627 876.55 498 0.226 0.675 865.88 554 0.232 0.691 x′1 = 0.506 909.78 238 0.251 0.245 896.65 390 0.277 0.271 885.33 540 0.301 0.294 874.93 634 0.375 0.366 864.24 724 0.421 0.411 854.86 790 0.450 0.439 831.63 947 0.472 0.461 x′1 = 0.752 904.22 312 0.416 0.138 886.06 537 0.443 0.147 856.54 851 0.519 0.172 844.79 944 0.552 0.183 820.27 1148 0.661 0.219 811.25 1193 0.696 0.230 793.71 1250 x1′ = 0.898 900.66 371 0.490 0.056 880.83 626 0.535 0.061 846.37 971 0.576 0.066 831.92 1101 0.619 0.071 815.45 1257 0.662 0.075 807.02 1322 0.704 0.080 795.13 1373 0.745 0.085 786.12 1384 0.801 0.091 776.29 1415 0.834 0.095 Octane(1) + Methyl Butanoate(2) + Methyl Ethanoate(3), x1′ = 0.105 922.19 65 0.071 0.606 918.39 107 0.077 0.655 914.00 143 0.080 0.688 910.84 200 0.083 0.710 907.53 231 0.086 0.734 901.29 250 0.089 0.761 896.36 286 0.094 0.806 889.48 348 0.096 0.826 887.29 346 0.100 0.854 880.05 369 0.103 0.880 x′1 = 0.235 920.56 94 0.092 0.298 915.95 141 0.103 0.334 910.61 211 0.117 0.380 905.61 269 0.132 0.428 902.06 305 0.146 0.474 900.10 398 0.177 0.574 896.98 357 0.191 0.620 1182

−3

109vE123 m3·mol−1

880.47 870.68 866.79 865.06

333 334 263 259

860.71 856.85 852.70 849.20 836.53 832.28 831.70

575 593 588 565 502 561 430

825.41 818.87 813.25 798.46 790.07 785.44 782.11

973 988 990 863 829 756 699

784.90 779.63 766.31 760.97 745.43 741.40

1285 1273 1174 1134 921 750

767.74 759.85 752.90 746.48 740.03 734.50 729.18 722.80 719.58

1436 1371 1344 1228 1177 1047 958 729 521

876.85 874.08 872.33 871.18 869.99 868.62 866.46 865.48 864.26 863.10

346 338 366 348 333 337 337 351 308 303

875.40 870.60 865.02 859.48 854.70 844.91 840.92

503 549 580 600 602 612 601



Article


x2

ρ −3

kg·m

109vE123 m ·mol 3

x1

x2

−1

ρ kg·m

−3

109vE123 m3·mol−1

x1′ = 0.235 0.062 0.070 0.078

0.203 0.228 0.254

889.07 885.26 881.47

429 450 479

0.024 0.050 0.080 0.102 0.125 0.149 0.176 0.201 0.233 0.249

0.024 0.050 0.081 0.103 0.126 0.149 0.177 0.202 0.234 0.250

913.13 899.40 884.95 875.05 865.55 856.88 847.11 838.86 829.20 824.75

184 349 520 652 763 805 921 999 1069 1087

0.030 0.056 0.081 0.105 0.133 0.154 0.200 0.257 0.307

0.009 0.016 0.024 0.031 0.039 0.045 0.059 0.075 0.090

910.60 897.65 886.41 875.52 864.53 856.70 840.25 822.99 809.05

234 396 499 670 762 830 1029 1126 1240

0.034 0.058 0.088 0.117 0.143 0.171 0.227 0.257 0.317 0.368 0.423

0.004 0.007 0.011 0.015 0.018 0.022 0.029 0.033 0.041 0.047 0.055

0.005 0.011 0.016 0.020 0.026 0.031 0.036 0.041

0.043 0.094 0.139 0.180 0.226 0.269 0.316 0.363

0.015 0.029 0.039 0.053 0.063 0.076 0.087 0.102

0.043 0.085 0.118 0.158 0.189 0.226 0.261 0.304

0.029 0.052 0.076 0.101

0.029 0.052 0.077 0.102

0.206 0.214 0.221

0.670 0.696 0.718

836.74 834.70 833.09

604 591 560

0.274 0.295 0.323 0.350 0.376 0.400 0.426 0.449 0.476

0.275 0.297 0.324 0.351 0.377 0.401 0.428 0.451 0.478

818.20 812.90 806.38 800.51 794.90 790.32 785.35 781.36 777.30

1101 1120 1117 1101 1123 1085 1084 1044 923

0.333 0.402 0.483 0.579 0.623 0.646 0.675 0.704 0.734

0.098 0.118 0.142 0.170 0.183 0.189 0.198 0.206 0.215

802.26 786.27 770.16 753.91 747.36 744.26 740.32 736.86 733.14

1300 1363 1346 1233 1143 1060 991 852 764

0.059 0.071 0.081 0.089 0.093 0.096 0.100 0.104 0.112 0.110

772.81 756.79 744.02 735.34 731.31 728.38 724.90 721.39 714.21 716.11

1432 1416 1329 1199 1047 1013 886 788 458 528

880.50 877.75 875.09 870.55 868.47 866.37 862.30

203 191 181 168 135 108 32

0.408 0.447 0.482 0.552 0.590 0.625 0.658 0.696

855.93 851.75 848.11 841.33 837.96 835.09 832.55 829.44

403 333 343 282 279 226 178 160

0.225 0.249 0.276 0.302

831.03 824.21 817.39 810.99

666 642 638 630

x′1 = 0.499

x′1 = 0.773

x1′ = 0.886 908.86 253 0.462 897.19 392 0.548 883.27 581 0.627 871.24 702 0.688 860.61 857 0.721 850.65 924 0.743 831.84 1107 0.773 822.47 1212 0.803 806.05 1298 0.872 793.08 1405 0.854 780.72 1446 Iso-octane(1) + Methyl Pentanoate(2) + Methyl Ethanoate(3), 921.10 68 0.056 914.86 103 0.061 909.72 147 0.066 905.39 202 0.075 900.95 186 0.080 896.99 202 0.085 893.00 227 0.096 889.34 240 x′1 = 0.251 916.05 100 0.136 906.82 154 0.150 900.44 200 0.161 892.61 239 0.185 886.76 321 0.197 880.62 325 0.209 875.25 370 0.220 868.97 374 0.233 x1′ = 0.497 909.79 157 0.222 897.69 233 0.247 885.62 345 0.273 874.43 418 0.299 1183

x1′ = 0.102 0.490 0.535 0.581 0.665 0.707 0.752 0.843



Article


x2

ρ −3

kg·m

109vE123 m ·mol 3

x1

x2

−1

ρ kg·m

−3

109vE123 m3·mol−1

x′1 = 0.497 0.121 0.146 0.175 0.198

0.122 0.148 0.177 0.200

865.97 856.22 846.07 838.54

487 552 588 619

0.015 0.019 0.078 0.114 0.150 0.180 0.256 0.292 0.330

0.005 0.007 0.028 0.041 0.054 0.065 0.092 0.106 0.119

918.85 916.03 886.85 870.64 856.28 845.19 820.76 810.31 800.40

57 128 330 493 598 682 806 881 906

0.048 0.095 0.177 0.225 0.189 0.314 0.359 0.404 0.445

0.006 0.011 0.020 0.026 0.022 0.036 0.041 0.046 0.051

0.006 0.011 0.026 0.031 0.041 0.050

0.052 0.097 0.226 0.271 0.360 0.440

0.011 0.021 0.028 0.039 0.050 0.058 0.069 0.077 0.086

0.026 0.052 0.070 0.096 0.122 0.141 0.168 0.189 0.210

0.028 0.055 0.065 0.129 0.152 0.175 0.203 0.227

0.028 0.053 0.063 0.125 0.147 0.169 0.197 0.220

0.041 0.077 0.117 0.150 0.188 0.224 0.266 0.411

0.013 0.025 0.038 0.049 0.061 0.072 0.086 0.133

0.364 0.415 0.461

0.368 0.419 0.466

796.80 787.37 779.60

567 443 341

0.367 0.436 0.470 0.540 0.573 0.612 0.645 0.681

0.133 0.158 0.170 0.195 0.207 0.221 0.233 0.246

791.35 776.48 769.85 757.54 752.18 746.55 741.89 737.10

939 914 886 780 730 596 510 404

0.057 0.062 0.066 0.071 0.076 0.081 0.085 0.093

761.35 753.31 746.31 740.03 732.33 727.22 721.27 714.39

1095 1053 1033 984 922 774 718 354

884.87 881.87 876.23 873.86 871.91 869.48

254 214 193 176 175 134

0.258 0.270 0.282 0.374 0.431 0.531 0.620 0.642 0.689

870.11 868.12 866.06 852.00 844.14 832.03 822.68 820.42 815.94

436 435 446 462 489 457 405 402 378

0.247 0.292 0.316 0.342 0.362 0.386 0.410 0.430

821.02 808.46 802.52 796.34 792.02 786.69 781.87 778.03

725 777 747 727 705 701 652 603

0.147 0.169 0.183 0.192 0.200 0.203 0.230

771.15 757.61 750.10 745.68 741.49 740.48 728.72

973 937 924 851 827 773 524

x′1 = 0.733

x1′ = 0.897 901.87 212 0.494 879.50 439 0.537 846.67 700 0.576 830.16 807 0.614 842.49 715 0.663 803.31 984 0.701 791.59 1023 0.743 780.54 1085 0.805 771.48 1088 Iso-octane(1) + Methyl Butanoate(2) + Methyl Ethanoate(3), 920.97 69 0.054 916.21 107 0.060 904.14 151 0.071 900.15 189 0.076 892.99 236 0.080 887.31 248 0.086 x′1 = 0.290 919.74 71 0.105 912.96 157 0.110 908.54 204 0.115 902.46 227 0.153 896.73 241 0.176 893.57 165 0.217 886.86 316 0.253 882.84 351 0.262 878.72 369 0.281 x′1 = 0.508 910.48 180 0.255 897.02 232 0.301 891.86 291 0.326 864.07 448 0.353 854.50 581 0.373 846.23 623 0.398 836.60 693 0.423 829.15 712 0.444 x1′ = 0.756 904.92 203 0.453 887.30 363 0.523 869.77 501 0.565 856.42 615 0.593 842.49 708 0.619 830.25 796 0.627 817.03 895 0.712 780.03 988 1184

x′1 = 0.102 0.477 0.528 0.624 0.668 0.704 0.753



Article


x2

ρ kg·m−3

109vE123

x1

x2

m3·mol−1

ρ kg·m−3

109vE123 m3·mol−1

x′1 = 0.912 0.093 0.141 0.181 0.228 0.272 0.313 0.365 0.408

0.009 0.014 0.017 0.022 0.026 0.030 0.035 0.039

880.58 860.60 845.26 829.02 815.14 803.06 789.30 778.95

427 577 715 833 930 1029 1096 1123

0.495 0.587 0.631 0.674 0.716 0.763 0.816 0.852

0.048 0.057 0.061 0.065 0.069 0.074 0.079 0.082

759.99 743.00 735.66 728.92 722.80 716.46 710.06 705.81

1174 1112 1068 1017 943 831 628 513

Standard uncertainty (0.68 level of confidence): u(T) = 0.01 K, u(x) = 0.0005, u(109·vE123) = 5 m3·mol−1. Relative standard uncertainty for pressure: ur(p) = 1%. Instrument standard uncertainty for density = 0.02 kg·m−3. The combined expanded uncertainty (0.95 level of confidence, k = 2) for Uc(ρ) = 1 kg·m−3. x1 or x2: mixing compositions referenced to compound 1 or 2, respectively. x′1, composition of compound 1 in the pseudobinary; ρ, density of ternary mixtures; vE123, excess volumes for ternary mixtures. a

contribution procedure.28 The experimental data are correlated by a least-squares procedure, using an algorithm for linear functions, employing for the objective function (OF) the standard deviation defined as

the calorimeter and those calculated using eq 6 are recorded in Table 7. Ternary solutions are modeled using a generalization of eq 1, which has been described in previous works.6,7 E E E y123 = y12E + y13E + y23 + Δy123

N

OF = s(y E ) = [∑ (yiE,exp − yiE,cal )2 /N ]1/2 i=1

where the refer to the specific contribution of the binary i-j to the value of the global property of the ternary that is determined by eq 1 with the corresponding coefficients of Table 5. This calculation is carried out by considering that the pairs i-j are isolated in a global ternary system; to do this the molar fractions and active fractions are normalized, and it is also verified that ∑z′i = 1. Of the different methods recommended in the literature, the one proposed by Kohler29 for molar fractions is used, as this method has no effect on the active fractions, being zi′ = zi. The final summand of eq 7, ΔyE123, represents the synergic effect caused by the simultaneous presence of three substances, given by an expression of the type

(5)

The data correlations were good and the coefficients obtained are recorded in Table 5. These data were used to produce the graphical representations in Figures 1 and 2, where an acceptable fit of the experimental properties can be observed. In the graphs, our results are compared with those published in the literature10−16 for binaries containing octane at the same working temperature, Figures 1a and 2a, showing a good agreement for vE, while for hE our results differ from those published by Grolier et al.15 for the binary octane + methyl ethanoate. Figure 2a shows a curve of hE = hE(x) determined by these authors, with an asymmetry not justified, while the hE data presented by Kehlen et al.16 are very small and present a very irregular distribution. Differences at the maximum in relation to the values obtained by our group in a previous work14 are around 5%. No data have been found in the literature for systems with iso-octane. A comparison of the hE data of this work for binaries of octane with the other two methyl esters (butanoate and pentanoate), see Figure 2a, is acceptable. Ternaries. Table 6 shows the values of (x1,x2,ρ, vE123) for the four ternaries selected for this work obtained at 298.15 K: octane(1) + methyl butanoate(2) + methyl ethanoate(3), octane(1) + methyl pentanoate(2) + methyl ethanoate(3), isooctane(1) + methyl butanoate(2) + methyl ethanoate(3), isooctane(1) + methyl pentanoate(2) + methyl ethanoate(3). Five experiments were carried out for each of these with different relative compositions x1′ = x1/(x1 + x2), which are specified in Table 6. On the other hand, enthalpic data (x1,x2, hE123) are shown in Table 7 for the same set of mixtures, for which each experimental point is the result of the energetic effect caused by adding the third compound (3) to a pseudocompound that corresponds to a solution of the other two components (1 + 2). Mathematically, this effect can be expressed as hE3+12, hence the net mixing enthalpy for the ternary hE123, is calculated by E E h123 = h3E+ 12 + (1 − x3)h12 (x1′)

(7)

yEij

E 0 1 2 3 4 Δy123 = z1z 2z 3(y123 + y123 z1 + y123 z 2 + y123 z12 + y123 z 22 5 + y123 z1z 2)

(8)

which arises when taking into consideration a high degree of interaction, up to five, among the three types of molecules that constitute the solution. A different mathematical treatment may be used for each ternary, depending on the nature of the species involved and the distribution of the experimental data. The quality of fitting curves to experimental data depends on the investigator, in other words, for the correlation of a given ternary a simpler expression can be used for ΔyE123. Data correlation for the ternary is done using a least-squares procedure in MATLAB for linear functions using the same objective function as was used for the binaries, eq 5. The results of the fits can be analyzed using the yi123 values in Table 8 and are used to produce the different representations of Figures 3−6. The triangular diagrams produced by the surfaces yE123 = yE123(x1, x2, x3) generated by the model are represented in Figures 3 and 5 together with the experimental points. The base of these diagrams show the isolines projected when the surfaces are dissected by planes of yE123 = constant. The figures show an adequate qualitative description of the quantities vE123 and hE123 in the entire ℜ3-space composed by (x1,x2, yE123). The quality of the correlations of vE123 and hE123 is acceptable for all cases. Figures 4 and 6 show the curves corresponding to the application of the model, eq 7, with the values of x1′ determined for each solution.

(6)

where hE12(x1′ ) is the energy obtained in the mixing process of the binary (1 + 2) with composition x1′ . Both values obtained using 1185



Article

Table 7. Excess Enthalpies h3E+ 12 for the Pseudobinaries for Which the Composition is Indicated and Excess Enthalpies, hE123, for the Ternaries Below, Measured at 298.15 K and Atmospheric Pressurea (p = 0.1 MPa) x1

x2

h3E+ 12

hE123

J·mol−1

J·mol−1

x1

x2

h3E+ 12

hE123

J·mol−1

J·mol−1


x2

h3E+ 12 −1

J·mol

hE123 −1

J·mol

x1

x2

h3E+ 12 −1

J·mol

hE123 J·mol−1

x1′ = 0.769 0.185 0.056 1075 1282 0.454 0.136 1235 1742 0.205 0.062 1135 1364 0.515 0.155 1104 1679 0.228 0.069 1194 1448 0.573 0.172 925 1564 0.254 0.076 1250 1533 0.642 0.194 656 1375 0.283 0.085 1292 1608 0.701 0.211 412 1194 Iso-octane(1) + Methyl Pentanoate(2) + Methyl Ethanoate(3), x1′ = 0.239 0.060 0.192 389 541 0.134 0.428 479 818 0.067 0.213 414 582 0.148 0.473 456 831 0.074 0.235 436 622 0.164 0.524 419 834 0.082 0.261 456 662 0.180 0.574 369 824 0.091 0.289 472 701 0.193 0.617 318 807 0.099 0.317 484 735 0.209 0.667 248 776 0.110 0.350 490 767 0.224 0.715 168 734 0.122 0.389 488 796 x1′ = 0.435 0.107 0.139 514 722 0.215 0.280 672 1091 0.110 0.143 549 764 0.240 0.312 651 1119 0.121 0.157 581 817 0.267 0.347 611 1132 0.133 0.172 611 869 0.294 0.382 553 1125 0.146 0.189 636 919 0.323 0.419 478 1191 0.160 0.207 659 970 0.352 0.457 383 1068 0.177 0.230 670 1014 0.381 0.495 268 1011 0.195 0.253 677 1056 0.411 0.534 143 944 x′1 = 0.687 0.164 0.075 882 1074 0.360 0.164 1084 1505 0.181 0.083 927 1139 0.401 0.183 1034 1503 0.198 0.091 968 1200 0.446 0.203 950 1471 0.216 0.099 1013 1266 0.495 0.226 829 1408 0.239 0.109 1049 1328 0.545 0.249 669 1306 0.264 0.120 1078 1386 0.596 0.272 471 1168 0.292 0.133 1101 1442 0.647 0.295 262 1018 0.325 0.148 1102 1482 x1′ = 0.778 0.202 0.058 1067 1240 0.454 0.129 1194 1582 0.227 0.065 1138 1333 0.518 0.148 1066 1509 0.258 0.074 1205 1426 0.591 0.168 855 1361 0.296 0.084 1255 1508 0.665 0.190 585 1155 0.340 0.097 1279 1570 0.723 0.206 343 962 0.393 0.112 1263 1599 Iso-octane(1) + Methyl Butanoate(2) + Methyl Ethanoate(3), x′1 = 0.166 0.039 0.195 234 371 0.086 0.431 316 619 0.042 0.211 246 394 0.094 0.472 311 643 0.045 0.228 259 419 0.104 0.520 296 661 0.050 0.248 274 448 0.114 0.573 272 675 0.054 0.270 286 476 0.124 0.624 242 681 0.059 0.295 297 505 0.136 0.682 199 678 0.064 0.323 308 535 0.146 0.732 158 673 0.071 0.356 314 564 0.152 0.785 104 653 0.078 0.390 317 591 x′1 = 0.432 0.109 0.143 498 761 0.224 0.295 655 1197 0.118 0.155 530 815 0.247 0.324 639 1235 0.128 0.168 563 872 0.272 0.358 607 1265 0.140 0.185 589 928 0.297 0.391 565 1283 0.153 0.201 615 985 0.326 0.428 506 1293 0.168 0.221 636 1043 0.352 0.463 435 1286 0.185 0.244 649 1097 0.382 0.503 339 1263 0.205 0.269 657 1152 0.405 0.533 252 1232 x′1 = 0.495 0.115 0.118 537 786 0.247 0.252 775 1308 0.125 0.127 586 856 0.271 0.277 766 1352

Octane(1) + Methyl Pentanoate(2) + Methyl Ethanoate(3), x′1 = 0.176 0.043 0.201 384 523 0.086 0.404 445 724 0.047 0.222 403 556 0.096 0.451 428 740 0.052 0.243 419 587 0.109 0.510 391 743 0.057 0.268 435 620 0.121 0.567 340 732 0.063 0.297 443 648 0.135 0.633 271 708 0.070 0.327 450 676 0.149 0.698 187 669 0.078 0.364 451 703 0.163 0.766 93 622 x1′ = 0.425 0.104 0.141 650 898 0.215 0.291 766 1277 0.116 0.157 688 964 0.240 0.326 730 1303 0.128 0.173 716 1021 0.267 0.362 658 1295 0.141 0.191 743 1079 0.298 0.404 548 1258 0.156 0.212 764 1136 0.332 0.450 428 1219 0.174 0.235 775 1188 0.364 0.494 289 1157 0.193 0.271 777 1246 0.397 0.538 140 1086 x1′ = 0.605 0.139 0.091 837 1069 0.291 0.190 1074 1562 0.153 0.100 875 1131 0.327 0.214 1036 1584 0.155 0.102 914 1174 0.367 0.240 963 1577 0.170 0.111 956 1241 0.409 0.267 856 1541 0.187 0.122 1002 1316 0.457 0.298 699 1464 0.209 0.136 1039 1389 0.506 0.331 498 1346 0.233 0.152 1067 1458 0.556 0.363 283 1215 0.260 0.170 1082 1518 x′1 = 0.709 0.166 0.068 1029 1236 0.340 0.140 1259 1683 0.183 0.075 1075 1303 0.380 0.156 1215 1689 0.201 0.083 1129 1380 0.428 0.176 1115 1648 0.222 0.091 1184 1461 0.483 0.198 968 1570 0.247 0.101 1225 1532 0.537 0.221 789 1459 0.274 0.113 1250 1591 0.594 0.244 558 1299 0.304 0.125 1264 1643 0.652 0.268 299 1111 Octane(1) + Methyl Butanoate(2) + Methyl Ethanoate(3), x′1 = 0.143 0.041 0.248 241 447 0.086 0.512 257 684 0.046 0.277 257 488 0.096 0.576 228 708 0.052 0.313 270 531 0.108 0.644 189 726 0.059 0.352 279 573 0.118 0.707 145 734 0.067 0.399 283 616 0.128 0.764 93 730 0.076 0.453 276 654 0.137 0.819 40 723 x′1 = 0.422 0.126 0.172 618 1001 0.269 0.368 594 1414 0.142 0.194 646 1077 0.305 0.418 504 1433 0.161 0.220 669 1158 0.336 0.460 404 1427 0.183 0.251 681 1238 0.371 0.507 270 1398 0.208 0.284 681 1313 0.402 0.550 136 1359 0.237 0.325 653 1376 x1′ = 0.664 0.149 0.075 862 1104 0.335 0.169 1081 1624 0.167 0.084 925 1195 0.370 0.187 1043 1642 0.188 0.095 984 1290 0.415 0.210 959 1632 0.212 0.107 1031 1375 0.459 0.232 845 1589 0.239 0.121 1067 1454 0.510 0.258 676 1503 0.266 0.135 1097 1529 0.567 0.287 454 1374 0.2981 0.151 1104 1588 0.614 0.311 263 1260 x1′ = 0.769 0.135 0.041 880 1031 0.316 0.095 1327 1679 0.150 0.045 943 1110 0.358 0.107 1326 1725 0.166 0.050 1016 1202 0.401 0.121 1305 1752 1186



Article


x2

h3E+ 12 −1

J·mol 0.129 0.141 0.154 0.168 0.185 0.204 0.223

0.132 0.144 0.157 0.172 0.189 0.208 0.228

621 653 683 713 738 759 775

0.160 0.175 0.191 0.211 0.234 0.261 0.291 0.327

0.061 0.066 0.072 0.080 0.088 0.099 0.110 0.124

830 878 922 969 1016 1052 1082 1090

hE123

x1

h3E+ 12

x2

−1

J·mol−1

0.307 0.339 0.371 0.405 0.439 0.474

736 684 617 525 409 265

1386 1403 1404 1383 1338 1268

0.139 0.157 0.175 0.198 0.214 0.237 0.254

1076 1026 964 846 702 484 295

1517 1526 1521 1474 1381 1237 1102

J·mol

x′1 = 0.495 900 0.301 957 0.332 1015 0.364 1076 0.397 1138 0.430 1199 0.464 1258 x1′ = 0.726 1023 0.367 1088 0.417 1152 0.464 1222 0.523 1297 0.565 1366 0.626 1431 0.672 1483

hE123

−1

J·mol

a

Standard uncertainties (0.68 level of confidence): u(T) = 0.005 K, u(x) = 0.0005. Relative standard uncertainties: ur(p) = 1%, and ur(hE123) = 3%. x1, x2, mixing compositions referenced to compound 1 or 2, respectively; x 1, composition of compound 1 in the pseudobinary; hE123, excess enthalpy for ternary mixtures; h3E+ 12, excess enthalpy obtained for the binary formed by the compound 3 (methyl ethanoate) and the pseudobinary of octane or iso-octane(1) + methyl butanoate or pentanoate(2) Figure 3. 3D-Plot for the surface vE123 = vE123(x1, x2, x3) by eq 7 and the experimental values (●) obtained at 298.15 K for the ternaries: (a) octane(1) + methyl pentanoate(2) + methyl ethanoate(3); (b), octane(1) + methyl butanoate(2) + methyl ethanoate(3); (c), isooctane(1) + methyl pentanoate(2) + methyl ethanoate(3); (d), isooctane(1) + methyl butanoate(2) + methyl ethanoate(3). (x1,x2,x3)Plane show the isolines corresponding to the horizontal projections of the surface at constant values of vE123 which are indicated by labels in (mm)3 mol−1.

4. DISCUSSION OF RESULTS 4.1. Binaries. Interpretation of the results of the systems studied here depends upon a series of circumstances related to the nature of the compounds involved. However, one common factor to all the systems is that all mixing processes are expansive and endothermic, see Figures 1 and 2. A differential analysis must explain, on the one hand, the behavior of binaries comprising ester + alkane (solutions of polar + apolar compounds, which explain the results mentioned previously), and, on the other hand, the ester + ester binaries (polar + polar, partial justification of results). For the former group, it is also important to specify that the mixing processes corresponding to the branched hydrocarbon generate quantitatively smaller volumetric and energetic effects than those of octane. On the other hand, it is important to point out that the size of the ester influences the properties of the solutions differently depending on whether these correspond to alkane + ester (these decrease with increasing chain length of the ester), or the ester + ester

binaries (they increase when passing from butanoate to pentanoate with methyl ethanoate). It is interesting to note the influence of the variation in the acid chain R of the methyl alkanoate, Cu‑1H2u‑1CO2CH3, with the associated permanent dipolar moment, μ·1030 (C·m),30−32 associated with the carboxylate group −COO−, being 5.60 for u = 2, 5.68 for u = 3, 5.74 for u = 4, and 5.77 for u = 5 (obtained by extrapolation). This must cause an increase in dipole−dipole attractions, for both the pure components and also the mixtures, although less pronounced in the solutions due to the greater distance

Table 8. Coefficients and Standard Deviations Obtained in the Correlation Procedure of Properties for Ternaries Indicated Below, Using eq 7 ternary

v0123

v1123

v2123

v3123

v4123

v5123

s(vE123)

−7423 −15323 −40787 −49237 h4123

−16033 4510 −55115 −69595 h5123

26 27 29 26 s(hE123)

−6247 27279 43942 16733

9196 71956 −6593 76912

11 22 18 20

109vE123/m3·mol−1 C8H18 (1) + C6H12O2(2) + C3H6O2(3) C8H18 (1) + C5H10O2(2) + C3H6O2(3) i-C8H18 (1) + C6H12O2(2) + C3H6O2(3) i-C8H18 (1) + C5H10O2(2) + C3H6O2(3) ternary

−9245 −6473 −20609 −20578 h0123

38438 24412 76416 72007 h1123

12405 12362 48174 55243 h2123

−32603 −19270 −70299 −64347 h3123 hE123/J mol−1

C8H18 (1) + C6H12O2(2) + C3H6O2(3) C8H18 (1) + C5H10O2(2) + C3H6O2(3) i-C8H18 (1) + C6H12O2(2) + C3H6O2(3) i-C8H18 (1) + C5H10O2(2) + C3H6O2(3)

6360 10025 6066 7544

−6795 −28272 2391 −16640

−561 −27190 −26199 −24901 1187

−4069 6172 6572 1222



Article

Figure 4. Plot of the projection of the surface φ(x1,x2, vE123) = 0 on the vE123-x1 plane () for the different values of x1′ indicated in Table 6 together with the vE12 -x1 curve (  ) for the corresponding binary (1 + 2): (a) octane(1) + methyl pentanoate(2) + methyl ethanoate(3); (b) octane(1) + methyl butanoate(2) + methyl ethanoate(3); (c) isooctane(1) + methyl pentanoate(2) + methyl ethanoate(3); (d) isooctane(1) + methyl butanoate(2) + methyl ethanoate(3).

Figure 5. 3D-Plot for the surface hE123 = hE123(x1, x2, x3) by eq 7 and the experimental values (●) obtained at 298.15 K for the ternaries: (a) octane(1) + methyl pentanoate(2) + methyl ethanoate(3); (b) octane(1) + methyl butanoate(2) + methyl ethanoate(3); (c) isooctane(1) + methyl pentanoate(2) + methyl ethanoate(3); (d) isooctane(1) + methyl butanoate(2) + methyl ethanoate(3). (x1,x2,x3)-Plane show the isolines corresponding to the horizontal projections of the surface at constant enthalpies of hE123 which are indicated by labels in J·mol−1.

between them. However, the evolution of the experimental results shows that the second effect is negligible compared with the dominant effect in these solutions, corresponding to the size of the ester molecules. Hence, as u decreases, and the ester molecules become less voluminous, the permanent dipoles approach each other (the distance between them decreases) causing (despite smaller values of μ) greater dipole−dipole attractions; which increases both the endothermicity and dilatation. In other words, as the effect of the dipole−dipole attractions on the mixing process becomes less important, the van der Waals forces become more relevant. In the most limiting situation (when u ≫ 5), the latter would be the only ones controlling the mixing process. A similar explanation can be established for the branched hydrocarbon, although in this case the smaller contact surface of the isooctane gives rise to weaker van der Waals interactions, which would explain how the mixing properties are quantitatively lower than those obtained in binaries of straight chain hydrocarbons. The UNIFAC group contribution model gives an acceptable representation of the energetic effects of the ester + alkane solutions as can be observed in Figure 2a,b, as it shows the physical interactions (van der Waals) generated by the model, which are predominant in the binaries elected. Figures 1c and 2c represent, respectively, the results of the properties vE and hE arising from the molecular interactions (polar−polar) of the binaries of methyl butanoate(2) + methyl ethanoate(3) and methyl pentanoate(2) + methyl ethanoate(3), showing positive values in all cases. Here, in addition to the van der Waals interactions it is also necessary to take into account

those due to the dipoles of the carboxylic groups of both esters, which become weaker in the final solution than in the pure products, owing to an increased distance between the charges due to the steric impediment of the hydrocarbon chains. With all the information available for these binaries,6,7 the properties arising from the mixing process can be observed to present a regular variation with molecular size. Hence, an increase in the chain length of the compound (2) (passing from methyl butanoate to methyl pentanoate) produces greater values for the mixing properties with increasing values of μ, as mentioned before. Nonetheless, the small differences shown by the dipolar moments are not sufficient to explain the behavior observed. The molecular size of the substances present clearly has an influence on the behavior of the final solution, as explained before, and the results can be attributed to an major component of van der Waals forces which, in turn, are proportional to the contact surfaces. To verify this, the equimolar values obtained for the quantity pvE(J mol−1) (volumetric behavior) and for i‑j hE (J mol−1) (energetic behavior) versus the ratios, ki‑j v and kh , respectively, are represented in Figure 7, revealing a quasi-direct relationship between the quantities compared. Application of the UNIFAC model20 reveals important discrepancies in relation to the ester−ester interactions, as the model in itself does not take into account interactions other than those corresponding to the electrostatic forces (van der Waals), such as those that can occur between the substances with carboxylic groups. Figure 2c shows how the UNIFAC estimates 1188



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Figure 8. Plots of the isolines obtained at constant hE for the ternaries: (a) octane(1) + methyl pentanoate(2) + methyl ethanoate(3); (b) isooctane(1) + methyl butanoate(2) + methyl ethanoate(3). Isoenthalpics have been calculated with the proposed model, eq 7, (), and UNIFAC20 (− − −).

(alkane) and another polar one (ester), attributing these to repulsive interactions between them, which vary according to the molecular size of the compounds. Hence, those repulsions diminish with increasing chain length of the hydrocarbon radical linked to the CO group of the ester, an increase that also produces greater attractive interactions with apolar groups of the saturated hydrocarbon. Quantitatively, the model bases its energetic effects on the sum of three kinds of contributions (Misfit + VdW + HB), with a net endothermic effect in all cases, although much lower than experimental values, see Figure 2a for the binaries with octane. Of the three contributions, electrostatic ones (Misfit), as mentioned above, are the most significant, the van der Waals forces (VdW) are negligible (slightly negative in the ester + alkane binaries and positive in the ester + ester ones), and the contributions of the hydrogen bonds (HB) are almost zero. These results are different from those posed by the structural model of these solutions in previous works, so a reparametrization of the partial contributions above is suggested. Ternaries. Representations of (x1, vE123) data are shown in Figure 4a−d for each of the x′1 = Cte recorded in Table 6, including in each case the vE curve for the binary used as a reference. The resulting ternaries have expansive effects over the entire range of compositions, increasing with the molar fraction x′1. For the same alkane, the solutions of three substances of identical composition (x1,x2,x3) show that the vE123 of the ternaries with methyl pentanoate (2) are lower than those containing methyl butanoate (2), analogically to the situation that occurs in the binaries, see x1−vE123 plane in Figure 4a−d. The excess volumes of the ternaries with iso-octane are quantitatively lower than those of the systems with octane, which is only to be expected taking into account the data obtained in the binaries. For the volumes, the contribution of the ternary constitutes an expansive effect of around 10% of that contributed by the addition of the binaries (eq 7) based on the composition. The graphical representations of the energetic interactions of the ternaries are shown in Figures 5 and 6. Figure 6a−d shows the projections in the x1-hE123 plane of the isolines corresponding to the modeled surface, which are represented in Figures 5a−d. The results of the estimates of the UNIFAC model are also shown in these projections in Figure 6a−d for each value of x′1. The endothermic effect of the ternary is estimated to be around 8% of the value obtained by summing the corresponding binary contributions (eq 7), although it is not possible to estimate the small negative contributions of the ester−ester binaries. As mentioned previously, the UNIFAC method gives an acceptable representation of the binaries, with slightly lower values for octane, which also has repercussions in the ternary, giving a

Figure 6. Plot of the projection of the surface φ(x1,x2, hE123) = 0 on the hE123-x1 plane () for the different values of x1′ indicated in Table 7 together to hE12 -x1 curve (  ) for the corresponding binary (1 + 2): (a) octane(1) + methyl pentanoate(2) + methyl ethanoate(3); (b) octane(1) + methyl butanoate(2) + methyl ethanoate(3); (c) isooctane(1) + methyl pentanoate(2) + methyl ethanoate(3); (d) isooctane(1) + methyl butanoate(2) + methyl ethanoate(3). (red dashed lines) estimations by UNIFAC.20

Figure 7. Graph showing the relationship between the energetic (hE) i‑j and volumetric (pvE) effects and the ratios ki‑j h and kv , respectively, for the binaries studied according to mixtures of (open symbols) methyl butanoate or (closed symbols) methyl pentanoate, with (circle) methyl methanoate; (square), methyl ethanoate; (triangle), methyl propanoate; (diamond) methyl butanoate; (cross) methyl pentanoate.

are much higher than the experimental curves of the ester−ester solutions studied, as the method does not take into account the presence of effects other than those mentioned, which could have a negative character. The COSMO-RS21 estimates the mixing energies for the binaries of an apolar compound 1189



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(9) Ortega, J.; Toledo, F. Thermodynamic properties of (an ethyl ester + a branched alkane). XV. HmE and VmE values for (an ester + an alkane). J. Chem. Thermodyn. 2002, 34, 1439−1459. (10) Qin, A.; Hoffman, D. E.; Munk, P. Excess volumes of mixtures of alkanes with carbonyl compounds. J. Chem. Eng. Data 1992, 37, 55−61. (11) Awwad, A. M.; Jbara, K. A.; Al-Dujaili, A. H. Volumes of mixing and viscosities of methyl acetate + n-alkanes and n-butyl acetate + nalkanes at 298.15 K. An interpretation in terms of the Van-Patterson, the absolute rate and free volume theory. Thermochim. Acta 1988, 129, 249−262. (12) Matos, J. S.; Trenzado, J. L.; Romano, E.; Caro, M. N.; Perez, M. E. Excess molar volumes of (methyl ethanoate + 1-chlorooctane + an nalkane). Ternary mixtures and their constituent binaries at 25° C. J. Solution Chem. 2001, 30, 263−279. (13) Ortega, J.; Gonzalez, E.; Matos, J. S.; Legido, J. L. Thermodynamic properties of (a methyl ester + an n-alkane). I. HEm and VEm for {xCH3(CH2)u‑1CO2CH3 (u = 1 to 6) + (1-x) CH3(CH2)6CH3}. J. Chem. Thermodyn. 1992, 24, 15−22. (14) Fernández, L.; Pérez, E.; Ortega, J.; Canosa, J.; Wisniak, J. Multiproperty modeling for a set of binary systems. Evaluation of a model to correlate simultaneously several mixing properties of methyl ethanoate + alkanes and new experimental data. Fluid Phase Equilib. 2013, 341, 105−123. (15) Grolier, J.-P. E.; Ballet, D.; Viallard, A. Thermodynamics of estercontaining mixtures. Excess enthalpies and excess volumes for alkyl acetates and alkyl benzoates + alkanes, + benzene, + toluene, + ethylbenzene. J. Chem. Thermodyn. 1974, 6, 895−908. (16) Kehlen, V. H.; Hering, R. Excess enthalpies in binary systems of octane + methylacetate and nonane + methylacetate. Z. Phys. Chem. 1975, 256, 778−780. (17) Matos, J. S.; Trenzado, J. L.; Gonzalez, E.; Alcalde, R. Volumetric properties and viscosities of the methyl butanoate + n-heptane + noctane ternary system and its binary constituents in the temperature range from 283.15 to 313.15 K. Fluid Phase Equilib. 2001, 186, 207−234. (18) Trenzado, J. L.; Matos, J. S.; Segade, L.; Carballo, E. Densities, Viscosities, and Related Properties of Some (Methyl Ester + Alkane) Binary Mixtures in the Temperature Range from 283.15 to 313.15 K. J. Chem. Eng. Data 2001, 46, 974−983. (19) Ortega, J.; Espiau, F.; Wisniak, J. New Parametric Model to Correlate the Gibbs Excess Function and Other Thermodynamic Properties of Multicomponent Systems. Application to Binary Systems. Ind. Eng. Chem. Res. 2010, 49, 406−421. (20) Gmehling, J.; Li, M.; Schiller, M. A Modified UNIFAC Model 2. Preesnt Parameter Matrix and Results for Different Thermodynamic Properties. Ind. Eng. Chem. Res. 1993, 32, 178−193. (21) Klamt, A. COSMO-RS. From Quantum Chemistry to Fluid Phase Thermodynamics and Drug Design, 1st ed.; Elsevier: Amsterdam, 2005. (22) Ortega, J.; Fernández, L.; Sabater, G. Solutions of alkyl methanoates and alkanes: Simultaneous modeling of phase equilibria and mixing properties. Estimation of behavior by UNIFAC with recalculation of parameters. Fluid Phase Equilib. 2015, 402, 38−49. (23) Riddick, J. A.; Bunger, W. B.; Sakano, T. K. Organic Solvents. Physical Properties and Methods of Purification, 4th ed.; WileyInterscience: New York, 1986. (24) Camacho, A. G.; Moll, J. M.; Canzonieri, S.; Postigo, M. A. VaporLiquid Equilibrium Data for the Binary Methyl Esters (Butyrate, Pentanoate, and Hexanoate) (1) + Propanenitrile (2) Systems at 93.32 kPa. J. Chem. Eng. Data 2007, 52, 871−875. (25) Peña, M. P.; Martínez-Soria, V.; Montón, J. B. Densities, Refractive Indices, and Derived Excess Properties of the Binary Systems Toluene + Isooctane and Methylcyclohexane + Isooctane and the Ternary Systems tert-Butyl Alcohol + Toluene + Isooctane and tertButyl Alcohol + Methylcyclohexane + Isooctane at 298.15 K. Fluid Phase Equilib. 1999, 166, 53−65. (26) Ortega, J.; Espiau, F.; Tojo, J.; Canosa, J.; Rodriguez, A. Isobaric Vapor-Liquid Equilibria and Excess Properties for the Binary Systems of Methyl Esters + Heptane. J. Chem. Eng. Data 2003, 48, 1183−1190. (27) Van Ness, H. C.; Abbott, M. M. Int. Data Ser., Sel. Data Mixtures, Ser. A 1976, 1, 22.

slightly lower graph, see Figure 6a,b. For the ternaries with isooctane, the model predicts well the alkane + ester binary, in this case with positive effects in the ternary, giving rise to a slightly higher endothermic effect than that calculated experimentally. Figure 8 shows projections in the 9 3-plane (x1,x2,x3) of the isoenthalpics obtained by horizontal planes in the surfaces in Figure 5, every 80 J mol−1, together with the isolines estimated by UNIFAC, where the differences observed already were mentioned before in Figure 6d. To summarize, the UNIFAC model gives a good representation of the behavior of the ternaries, revealing that physical effects tend to prevail over other effects due to the presence of the carboxylate group, with no distinction among the different types of interaction. The observations made with the application of the COSMO-RS methodology can also explain the effects of the ternary, because the method does not propose any specific effect due to the interaction of the three compounds in solution but the addition of the particular effects of the corresponding binaries.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Funding

This work was supported by a grant from Spanish Government, Ministerio de Economia y Competitividad, under project CTQ2012−37114. Notes

The authors declare no competing financial interest.

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REFERENCES

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A Study on Alkane + Ester + Ester Systems. Physicochemical Behavior

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