Measurements and Correlations of the Isobaric ... - ACS Publications

Article pubs.acs.org/jced

Measurements and Correlations of the Isobaric Vapor−Liquid Equilibria of Binary Mixtures and Excess Properties for Mixtures Containing an Alkyl (Methyl, Ethyl) Butanoate with an Alkane (Heptane, Nonane) at 101.3 kPa Raúl Ríos, Juan Ortega,* and Luís Fernández Laboratorio de Termodinámica y Fisicoquímica de Fluidos, Parque Científico-Tecnológico, Universidad de Las Palmas de Gran Canaria, Canary Islands, Spain ABSTRACT: In this work, the measurements of the isobaric vapor−liquid equilibrium (VLE) data at 101.32 kPa and the excess molar volumes (vE), obtained at 10 K intervals of temperature in the range (288.15 to 328.15) K, for four binary systems comprised of methyl or ethyl butanoate with two alkanes (heptane and nonane) are presented. The vE are positive for the four mixtures, and their variation with temperature presents a thermal coefficient (∂vE/∂T)p > 0, and the behavior of these systems is interpreted. Experimental VLE data (p,T,x,y), obtained in a small capacity ebulliometer, present a positive consistency according to the method of Fredenslund. The methyl butanoate + heptane system presents a minimum boiling-temperature azeotrope with the following coordinates at the working pressure: (x1,az = 0.404; Taz = 367.65 K). Measurements of (T,poi ) are also shown for all of the compounds and were determined using the same equilibrium equipment. Experimental data are correlated with an appropriate polynomial model proposed by the authors. A simultaneous correlation is performed for the characteristic VLE properties and the hE values taken from the literature. For the correlation of properties of methyl butanoate + heptane system, values of cEp from the literature were included in the correlation process. In all cases the multiproperty goodness of fit is acceptable. Another correlation procedure by successive steps in the order (x,cEp )→(x,hE)→(x,gE) is also applied when the experimental data exist for the binaries studied; the results obtained with both procedures are similar. The universal functional activity coefficient (UNIFAC) method is applied to estimate the VLE values, hE and cEp , with different results. The VLE prediction is acceptable in all cases except for the methyl butanoate + heptane mixture, although the estimation of the other thermodynamic quantities is not adequate.

■

INTRODUCTION Following on from other works1−9 on mixtures of esters + alkanes, here we present a theoretical-experimental study of the binary mixtures of two alkyl butanoates (methyl, ethyl) with two alkanes (heptane, nonane). Although the literature presents sufficient experimental and theoretical information4−16 about these mixtures, there are not enough data about the equilibria between phases of systems containing high molecular weight alkyl alkanoates. Hence, for the mixtures indicated here, the vapor−liquid equilibria (VLE) are measured at a pressure of 101.32 kPa and also the excess volumes vE at several temperatures in the interval (288.15 to 328.15) K. In addition to contributing to improving knowledge about the chosen mixtures, the real data will be used to analyze the utility of a multiproperty correlation model previously designed and published by the authors17,18 and established for the excess Gibbs function, gE. To obtain a better interpretation of the ester− alkane systems, it is necessary to use the enthalpy values of the mixture hE, measured at several temperatures. These have already previously been published4−7 for alkyl butanoates + alkanes and the heat capacities cEp for the methyl butanoate + heptane system.14 © 2012 American Chemical Society

A multiproperty correlation will be planned to validate the model proposed. The final part of this work gives the results of the application of the UNIFAC group contribution method,19 for which the efficacy seems to diminish when properties are estimated for systems containing long-chained compounds, possibly as databases were used to determine the interaction parameters that contained limited information about compounds of this nature.

■

EXPERIMENTAL SECTION Materials. The alkyl butanoates and hydrocarbons used in this work were supplied by Aldrich, with a commercial purity of 99 % (w/w), and before use were subjected to a series of operations to verify their quality. First, they were slowly distilled in a semimicro apparatus, degasified in an ultrasound bath, and stored for several days before use over a 0.3 nm molecular sieve from SAFC, to remove any moisture. Received: July 17, 2012 Accepted: September 6, 2012 Published: September 18, 2012 3210

dx.doi.org/10.1021/je300799f | J. Chem. Eng. Data 2012, 57, 3210−3224

Journal of Chemical & Engineering Data

Article

Table 1. Properties of Pure Compounds at 101.32 kPaa ρ(298.15 K)/kg·m−3

(Tob,i/K) compound

ppm

exptl

heptane

53.9

371.38

nonane

55.7

423.90

methyl butanoate

125.6

375.74

ethyl butanoate

109.4

394.31

lit.

exptl e

nD(298.15 K)

lit.

371.35 371.25i 371.58m 423.94b 423.66j 423.95m 375.53e 375.30l

679.62

393.95i 394.18k 394.70m

873.50

713.85

892.31

c

679.52 679.30e 679.51g,m 713.85b,j 713.86f 713.81m 892.52e 892.17g 892.40h 892.37l 873.56d 873.94k,m

exptl

lit.

1.3853

1.3855c 1.3853e 1.38511m 1.4031b 1.4030j 1.40311m 1.3852e 1.3851l

1.4032

1.3851

1.3898

1.3900d 1.3898k

Uncertainties u are: u(T) = ± 0.02 K, u(n) = ± 0.0002, and u(ρ) = ± 0.02 kg·m−3. bReference 1. cReference 4. dReference 7. eReference 8. Reference 13. gReference 14. hReference 15. iReference 16. jReference 17. kReference 20. lReference 21. mReference 22.

a f

Table 1 shows the final values for water contents measured with a Karl Fischer coulometric titrator (Mettler-Toledo C20), together with the values obtained for a set of properties. The final quality of the products was verified using the measurements of several thermophysical properties such as density ρ, refractive index nD, and normal boiling point Tob,i. The results obtained are shown in Table 1, and comparisons made with results published in the literature are acceptable. Apparatus and Procedures. The refractive indices (nD ± 0.0002) of the pure compounds were measured with an Abbe refractometer from Zuzi, model 320, at a temperature of (298.15 ± 0.02) K. The temperature was controlled with continuous water circulation provided by a Hetobirkeroad CB7 bath, which maintains the temperature of the apparatus in the interval indicated. Densities were determined at several temperatures with a DMA-55 Anton-Paar digital densimeter (ρ ± 0.02) kg·m−3 with a temperature control of (T ± 0.02) K with a circulating water provided by a 1166D Polyscience thermostatic bath. Mixtures were synthetically prepared for the entire range of compositions, and paired values of compositiondensity were determined, obtaining the function ρ = ρ(x) and also the vE at each temperature. Molar fractions of the ester were calculated with an uncertainty of ± 0.0003 units, and vE estimates had an uncertainty lower than ± 2·109 m3·mol−1. The experimental determination of VLE data was carried out in a small-capacity ebulliometer (∼60 cm3) described in a previous study.23 Pressure was controlled with a PPC2 apparatus manufactured by DH, which maintains pressure at (101.32 ± 0.02) kPa for the duration of the entire experiment. Equilibria were reached after a mean time of approximately 20 min when the temperature, measured by a model 6800 Comarks digital apparatus with periodically calibrated PT100 probes, in accordance with ITS90 regulations, and a reading error of ± 20 mK, remained constant. At constant p and T, liquid and vapor samples were extracted and introduced into the aforementioned digital densimeter to measure densities at 298.15 K. These densities were used to estimate the composition of the phases by regression of ρ = ρ(x1) at the indicated temperature by applying the equation:

where ρ, ρ1, and ρ2 are the mixing densities of the ester and alkane, respectively. With the density of the samples of each of the phases ρ, the compositions of the liquid phase x1 and the vapor phase y1 in ester were calculated, defining the set of experimental values that characterize the VLE of the samples {methyl or ethyl butanoate) (1) + alkanes (C7, C9) (2)}(p ± 0.02, T ± 0.02, x1 ± 0.002, y1 ± 0.002).

■

RESULTS Excess Properties. The presentation and treatment of the experimental data of excess volumes (x1,vE) measured here for the binary systems {CH3(CH2)2COOCuH2u+1 (1) + CnH2n+2 (2) (with u = 1,2; n = 7,9)} at 10 °C interval between (288.15 and 328.15) K are recorded in detail. Table 2 shows the data corresponding to (x1,ρ,vE). Data were correlated, and a mathematical function was generated for excess volumes of the type vE = ϑ(x1,T), v E = z1(1 − z1)(v0 + v1z1 + v2z12)

(2)

where z1 is the corresponding active f raction of the reference compound (the ester in this work), for which the relationship with the composition are established through the following expression that includes the parameter kv, which is dependent on pressure and temperature, and corresponds to a quotient of the molar volumes of the substances present. x1 x1 z1 = = x1 + [v2o(p , T )/v1o(p , T )]x 2 x1 + kv(p , T )x 2 (3)

The dependence of eq 2 on temperature is established through the coefficients vi: 2

vi =

∑ VijT j − 1 = j=0

Vi0 + Vi1 + Vi2T T

(4)

In this work, see Figure 1, it was checked that the variation of the parameter kv with temperature is minimum by comparing the values with those obtained by estimating the quotient of the volume parameters rk, kr = r2/r1, which are independent of temperature and are determined by a group contribution method from the corresponding van der Waals group parameters, presented in Bondi.24 For nonane mixtures, it can be observed that both parameters (kv and kr) are almost

ρ(x1) = [(ρ1 − ρ2 )x1 + ρ2 ] + [x1(1 − x1)(ax12 + bx1 + c)] (1) 3211



Article

Table 2. Densities ρ and Excess Molar Volumes vE for the Binaries of an Alkyl Butanoate (1) + an Alkane (2) at Several Temperaturesa ρ x1

kg·m

109·vE −3

−1

m ·mol 3

0.0000 0.0478 0.0940 0.1411 0.2025 0.2476 0.2996

688.16 695.54 702.79 710.56 720.91 728.91 738.37

0 143 287 386 517 575 632

0.0000 0.0485 0.0876 0.1389 0.2122 0.2586 0.3020

679.62 686.88 693.00 701.34 713.65 721.76 729.67

0 177 287 398 541 614 649

0.0000 0.0630 0.1170 0.1870 0.3025 0.4170 0.5047

670.96 680.36 688.78 700.22 720.34 741.86 759.48

0 224 375 530 689 759 755

0.0000 0.0768 0.0890 0.1535 0.2117 0.2567 0.3050

662.33 673.72 675.62 685.70 695.29 702.97 711.44

0 266 297 483 595 663 727

0.0000 0.0440 0.0921 0.1388 0.1890 0.2611 0.3006

653.61 659.99 667.12 674.29 682.37 694.33 701.19

0 161 330 468 572 713 760

0.0000 0.0544 0.0804 0.1647 0.2172 0.2378 0.2963

721.65 727.14 729.99 739.66 746.06 748.63 756.43

0 222 293 506 626 675 754

0.0000 0.0495 0.0998 0.1729 0.1935 0.2473

713.85 718.76 724.04 732.49 734.88 741.54

0 202 379 537 600 705

ρ x1

kg·m

109·vE −3

−1

m ·mol 3

Methyl Butanoate (1) + Heptane (2) 288.15 K 0.3531 748.53 659 0.4112 759.90 682 0.4484 767.46 678 0.5023 778.63 675 0.5526 789.52 642 0.5984 799.70 612 0.6471 810.83 573 298.15 K 0.3571 739.98 685 0.4019 748.57 711 0.4492 758.07 701 0.5017 768.87 692 0.5573 780.67 674 0.5952 789.01 646 0.6466 800.69 608 308.15 K 0.5651 772.28 716 0.5933 778.47 687 0.6532 791.90 626 0.7045 803.77 575 0.7487 814.31 520 0.7648 818.37 478 0.7890 824.36 441 318.15 K 0.3544 720.36 778 0.4042 729.76 796 0.4351 735.72 804 0.5011 748.89 796 0.5487 758.83 760 0.5962 768.97 729 0.6971 791.66 618 328.15 K 0.4098 721.06 848 0.4532 729.42 851 0.5031 739.32 837 0.5522 749.41 811 0.5979 759.10 776 0.6473 769.85 732 0.7060 783.28 634 Methyl Butanoate (1) + Nonane (2) 288.15 K 0.3419 762.85 801 0.3986 771.19 856 0.4425 778.04 877 0.5007 787.63 881 0.5488 796.09 861 0.6040 806.21 845 0.6553 816.39 782 298.15 K 0.3035 748.92 792 0.3558 756.23 843 0.4462 769.69 917 0.5497 786.99 902 0.6465 805.02 831 0.7509 826.86 685

3212

ρ x1

kg·m

109·vE −3

m3·mol−1

0.7077 0.7463 0.7980 0.8912 0.9493 1.0000

825.20 834.68 847.73 872.29 888.46 903.31

507 455 379 240 132 0

0.7063 0.7424 0.7993 0.8623 0.9015 0.9507 1.0000

814.61 823.41 837.66 853.85 864.37 878.23 892.31

538 480 387 302 231 101 0

0.8514 0.8818 0.9257 0.9603 1.0000

840.37 848.32 860.13 869.83 881.19

322 269 185 97 0

0.7469 0.7973 0.8454 0.8948 0.9513 1.0000

803.40 815.75 827.90 840.81 856.25 870.06

552 465 375 276 132 0

0.7456 0.7926 0.8600 0.9028 0.9508 1.0000

792.62 803.93 820.85 832.08 845.05 858.80

566 490 354 251 132 0

0.6959 0.7507 0.8114 0.8553 0.8988 0.9507 1.0000

824.67 836.81 850.96 862.13 873.46 888.13 903.31

754 647 551 429 348 194 0

0.7772 0.8038 0.9052 0.9530 1.0000

832.78 839.14 864.60 878.19 892.31

644 569 353 175 0



Article

Table 2. continued ρ

109·vE

x1

kg·m−3

m3·mol−1

x1

0.0000 0.0554 0.1002 0.1653 0.2108 0.2545 0.3082

705.96 711.45 716.10 723.29 728.63 734.04 740.93

0 208 361 550 654 734 830

0.3598 0.4090 0.4594 0.4993 0.5504 0.6001 0.6482

0.0000 0.0234 0.0731 0.1033 0.1552 0.1993 0.2571 0.3123

698.06 700.32 705.17 708.28 713.83 718.91 725.77 732.79

0 86 291 394 558 654 789 880

0.0000 0.0272 0.0562 0.0780 0.1041 0.1502 0.2023 0.2654

690.17 692.57 695.34 697.49 700.12 704.97 710.73 718.16

0 150 266 348 440 583 726 862

0.0000 0.0502 0.0918 0.1473 0.2022 0.2465 0.2880

688.16 696.39 703.35 712.80 722.42 730.35 737.84

0 143 241 356 431 478 516

0.0000 0.0522 0.0904 0.1404 0.1901 0.2539 0.2962

679.62 688.18 694.54 703.05 711.58 722.68 730.22

0 129 216 304 390 493 538

0.0000 0.0461 0.0952 0.1445 0.2034 0.2497 0.3081

670.96 678.42 686.44 694.69 704.70 712.78 723.17

0 119 246 345 450 503 551

0.0000 0.0532 0.0950 0.1397 0.2087 0.2565 0.3048

662.33 670.78 677.56 684.91 696.59 704.87 713.30

0 157 262 362 470 522 577

ρ

109·vE

kg·m−3

m3·mol−1

308.15 K 748.08 872 755.11 928 762.76 954 769.14 961 777.76 944 786.60 918 795.68 867 318.15 K 0.3568 738.79 928 0.4135 746.74 992 0.4555 753.07 1001 0.5093 761.51 1012 0.5565 769.30 1013 0.6043 777.70 983 0.6544 787.04 924 0.7067 797.40 846 328.15 K 0.3073 723.36 936 0.3624 730.61 1006 0.4120 737.45 1057 0.4567 744.00 1076 0.5083 751.95 1084 0.5549 759.51 1076 0.6157 770.10 1024 0.6554 777.42 974 Ethyl Butanoate (1) + Heptane (2) 288.15 K 0.3987 758.41 565 0.4488 767.94 576 0.5008 778.03 568 0.5456 786.84 555 0.6023 798.22 522 0.6584 809.63 484 0.6999 818.26 444 298.15 K 0.3543 740.87 565 0.4000 749.31 587 0.4430 757.44 591 0.5517 778.51 557 0.6018 788.45 531 0.6480 797.84 483 0.6976 808.02 433 308.15 K 0.3441 729.57 594 0.4060 741.01 602 0.4563 750.35 618 0.5053 759.76 596 0.5505 768.46 586 0.6038 778.99 544 0.6498 788.17 512 318.15 K 0.3608 723.30 617 0.4046 731.26 632 0.4532 740.30 629 0.5065 750.34 619 0.5517 759.04 593 0.6007 768.46 584 0.6492 778.12 534

3213

ρ

109·vE

x1

kg·m−3

m3·mol−1

0.6945 0.7463 0.7964 0.8451 0.8948 0.9497 1.0000

804.91 815.78 827.07 838.68 851.33 866.34 881.19

807 734 625 512 375 194 0

0.7541 0.8037 0.8594 0.9068 0.9511 1.0000

807.31 818.40 831.69 843.76 855.91 870.06

769 653 504 360 189 0

0.7027 0.7490 0.8511 0.9051 0.9506 1.0000

786.49 795.99 819.04 832.64 844.76 858.80

918 828 563 366 201 0

0.7486 0.8042 0.8481 0.9010 0.9347 0.9527 1.0000

828.54 840.42 850.01 861.58 869.11 873.20 884.01

382 316 246 180 124 92 0

0.7463 0.7884 0.8473 0.9054 0.9524 1.0000

818.17 827.06 839.64 852.26 862.74 873.50

380 326 254 177 89 0

0.7026 0.7544 0.7880 0.8424 0.9009 0.9512 1.0000

798.87 809.60 816.69 828.13 840.82 851.86 862.85

463 400 346 286 189 106 0

0.6934 0.7390 0.7947 0.8554 0.8861 0.9515 1.0000

787.02 796.28 807.72 820.65 827.23 841.48 852.26

485 439 381 270 221 101 0



Article

Table 2. continued

a

ρ

109·vE

x1

kg·m−3

m3·mol−1

0.0000 0.0535 0.0975 0.1485 0.1785 0.2367 0.3034

653.61 662.06 669.12 677.41 682.40 692.21 703.69

0 150 263 382 435 524 606

0.0000 0.0379 0.1046 0.1502 0.2013 0.2499 0.3047

721.65 725.80 733.19 738.59 744.84 751.04 758.28

0 110 320 422 523 599 669

0.0000 0.0486 0.0906 0.1007 0.1495 0.2442 0.2985

713.85 719.05 723.69 724.84 730.49 742.05 749.08

0 153 273 296 411 591 667

0.0000 0.0505 0.0818 0.1528 0.1872 0.2112 0.2818

705.96 711.25 714.63 722.65 726.67 729.53 738.36

0 167 259 437 516 567 671

0.0000 0.0435 0.1009 0.1439 0.2001 0.2489 0.2861

698.06 702.45 708.56 713.46 719.85 725.77 730.43

0 168 341 420 567 642 692

0.0000 0.0481 0.1134 0.1627 0.2102 0.2589 0.3111

690.17 695.05 701.93 707.35 712.81 718.53 725.00

0 157 353 480 579 681 752

x1

ρ

109·vE

kg·m−3

m3·mol−1

328.15 K 0.3590 713.56 630 0.4538 730.76 654 0.5087 741.00 646 0.5511 749.04 627 0.6093 760.27 587 0.6471 767.65 561 0.6967 777.52 508 Ethyl Butanoate (1) + Nonane (2) 288.15 K 0.3427 763.52 700 0.3961 771.15 728 0.4355 776.91 751 0.4957 786.14 757 0.5455 794.09 747 0.5857 800.76 728 0.6498 811.78 686 298.15 K 0.3131 750.97 692 0.3518 756.23 729 0.4357 768.18 774 0.5028 778.32 777 0.5511 785.92 771 0.5974 793.57 736 0.7030 811.93 641 308.15 K 0.3302 744.66 732 0.3685 749.81 769 0.4260 757.85 807 0.4773 765.37 812 0.5187 771.59 820 0.5712 779.88 795 0.6420 791.55 750 318.15 K 0.3550 739.26 792 0.4020 745.62 829 0.4556 753.18 848 0.4988 759.53 848 0.5470 766.88 831 0.6011 775.45 801 0.6560 784.53 753 328.15 K 0.3588 731.17 795 0.4020 736.91 831 0.4562 744.36 863 0.5565 759.06 866 0.5996 765.77 845 0.6524 774.29 806 0.7062 783.42 734

ρ

109·vE

x1

kg·m−3

m3·mol−1

0.7390 0.7999 0.8397 0.9086 0.9533 1.0000

786.07 798.54 806.83 821.54 831.27 841.55

456 381 320 191 98 0

0.7067 0.7520 0.8019 0.8502 0.9040 0.9569 1.0000

822.09 830.65 840.45 850.42 861.91 873.91 884.01

627 564 487 380 270 118 0

0.7460 0.7879 0.8532 0.9053 1.0000

819.92 827.92 841.01 852.07 873.50

579 517 395 267 0

0.6753 0.7260 0.7822 0.8330 0.8780 0.9384 1.0000

797.37 806.38 816.86 826.88 836.10 848.96 862.85

704 646 558 442 331 181 0

0.6951 0.7543 0.7999 0.8485 0.8947 0.9545 1.0000

791.27 801.83 810.52 819.97 829.27 842.03 852.26

703 625 513 415 321 152 0

0.7544 0.8060 0.8433 0.8917 0.9532 1.0000

791.91 801.44 808.67 818.28 831.23 841.55

664 560 465 351 157 0

Uncertainties u are: u(T) = ± 0.02 K, u(ρ) = ± 0.02 kg·m−3, u(x) = ± 0.0003, u(109 vE) = ± 2 m−3·mol−1.

identical, with only small differences in the slopes, < −6·10−5, with respect to the horizontal of kr. For the calculations required here, it is therefore possible to establish the independence of kv values from temperature (the corresponding values are shown in Table 3) in the simultaneous correlation of vE with the composition of butanoate x1 and T. A simultaneous correlation is performed for vE data, for each system and at different temperatures, using a nonlinear regression process implemented in

Matlab, minimizing the standard deviation established by the following equation: N

s(v E) = [(∑ (v E(x , T )i ,exp − v E(x , T )i ,calc )2 )/(N − 1)]1/2 i=1

(5)

The coefficients of fit and the parameters of goodness of fit obtained are shown in Table 3. To avoid confusion 3D-representations of the 3214



Article

be confirmed here. The increased length of the saturated hydrocarbon chain produces expansive and endothermic effects owing to the change in the interactional order of the hydrocarbons in the mixture. On the other hand, the presence of the butanoates confers the mixture opposite effects, producing an increase in the permanent dipolar moment associated with the alkyl butanoates, CH3(CH2)2COOCvH2v+1, μ·1030/(C·m), of 5.74 for v = 1 and 5.87 for v = 2, which should produce an increase in the dipole−dipole interactions between the molecules of the pure compounds and the mixtures. These are not as strong as would be expected for these solutions because the presence of the hydrocarbon increases intermolecular distances, although the molecular size of the butanoates has a more dominant effect. This explains the reduced endothermic effects with the increase in v. The increased temperature has only a negligible influence on excess properties because, on the one hand, it generates small relative expansions in the large molecules and, on the other hand, the positive thermal gradient slightly increases the Brownian motion, weakening the intermolecular attractions. Some of these aspects has already been mentioned in a previous work,6 where it was showed the enthalpic slope for three of the mixtures studied (∂vE/∂T)p,x < 0, confirming the negative values of cEp . Vapor Pressures. The pairs corresponding to vapor pressures (T,poi ) were determined experimentally for all of the compounds of the study using the ebulliometer described above. Although acceptable data are presented in the literature for vapor pressures, it was decided to extend the working range of measurements. The direct values obtained are presented in Tables 4 and 5 giving the values of the constants (A, B, and C) for Antoine’s equation, for which a nonlinear regression procedure was used as part of the Matlab software. This table also includes the values published in different literature sources for purposes of comparison. The same software was also used to calculate the constants of the reduced form of the Antoine equation.

Figure 1. Variation of the parameters kv (black line) and kr (red line) as a function of temperature for the binaries: methyl butanoate + heptane (c), methyl butanoate + nonane (a), ethyl butanoate + heptane (d), ethyl butanoate + nonane (b).

Table 3. Coefficients Vij for eqs 2 to 4 and Standard Deviations, 109·s(vE), Obtained in the Correlation of vE = φ(x1,T) for the Binaries of an Alkyl Butanoate (1) + an Alkane (2) methyl butanoate (1) + V00 V01 V02 V10 V11 V12 V20 V21 V22 kv s(vE)(T s(vE)(T s(vE)(T s(vE)(T s(vE)(T

= = = = =

288.15 298.15 308.15 318.15 328.15

K) K) K) K) K)

ethyl butanoate (2) +

heptane (2)

nonane (2)

heptane (2)

nonane (2)

1.40·106 −9.50·103 32 6.77·106 −5.27·104 83 −9.31·106 6.98·104 −121 1.288 6 10 7 7 6

2.37·107 −1.56·104 276 −5.35·107 3.42·105 −568 3.67·107 −2.31·104 374 1.567 12 15 7 10 17

5.56·106 −3.49·104 66 −1.24·107 7.67·104 −126 9.27·106 −5.74·104 92 1.109 6 6 7 7 5

1.57·106 −7.54·103 23 −1.44·107 8.25·104 −128 2.79·107 −1.73·105 271 1.350 8 6 7 13 6

log pro = a −

b Tr − c

(6)

which was employed to obtain values for the acentric factor ω for each of the compounds, which are also recorded in Table 5. Figure 4 shows the straight lines log por = φ(1/Tr), for which the vertical Tr = 0.7 is inside the experimental temperature interval used here. Application of the Pitzer equation is also represented graphically:30 ω = −(log por )Tr=0.7 − 1. The values obtained for ω are shown in Table 5 and were used for the data characterization of VLE data; the ω values are compared favorably with other data in the literature and with data estimated by the Lee−Kesler method.29 VLE Data. Experimental VLE data (p,T,x1,y1) at a pressure of (p = 101.32 ± 0.02) kPa are shown in Table 6 for the four systems {alkyl butanoate (methyl, ethyl) (1) + alkane (heptane, nonane) (2)}, showing in Figure 5 the corresponding graphs of (y1 − x1) vs x1 and of T vs x1,y1. Figure 6 has been included to compare the experimental values reported here with those from the literature8 for the methyl butanoate + heptane system, showing some differences between them, especially in temperature for an intermediate interval of compositions that reach the azeotropic point, where the thermal difference is around 0.6 °C. The activity coefficients

data have been included (see Figure 2) which show the experimental values of Table 2 and the curves obtained with eq 2 for each case. In Figure 3a,b our experimental vE values are compared with those from literature. For the methyl butanoate + C7,C9 systems our values coincide well with those from other authors;11−14 however, they are slightly lower than those reported previously.8,9 For ethyl butanoate + C9 mixture, as in Figure 3b, the vE obtained in this work are coincident with literature values7 but higher in the case of the ethyl butanoate + C7 system.7 In the vertical plane, corresponding to x1 = 0, the variation in equimolar values with temperature is projected. The slope can be seen to present a clearly positive gradient (∂vE/∂T)p,x > 0 for all of the mixtures, which increases in a quasi-linear manner with the hydrocarbon chain and decreases with the butanoate chain. This is the behavior expected for this type of mixture for which the structural model, already presented in previous works,25,26 can also 3215



Article

Figure 2. Experimental and correlation curves of vE vs x1 obtained at several temperatures between (288.15 and 328.15) K, for the binaries: (a) methyl butanoate (1) + heptane (2) (black) or nonane (2) (blue), and (b) ethyl butanoate (1) + heptane (2) (black) or nonane (2) (blue).

Figure 3. Comparison of excess molar volumes at 298.15 K obtained in this work with those from literature for the binaries containing: a, methyl butanoate, and b, ethyl butanoate with heptane (black line), and nonane (blue line). +, ref 14; ◆, ref 11; ■, refs 12 and 13; ▲, ref 9; ▼, ref 7; ×, ref 8; ●, experimental.

described by Yamada and Gunn.32 The second virial coefficients corresponding to the pure compounds, Bii and Bjj, and to the mixtures Bij, were estimated with the method recommended by Tsonopoulos.33 The vapor pressures at each equilibrium temperature poi were obtained using the Antoine equation and the constants shown in Table 5. All of this information was used to calculate the activity coefficients γi and the values of excess Gibbs function gE/RT for each equilibrium phase of each of the systems, recording all of the data in Table 6 and graphical representations in Figure 7a−d.

for the liquid phase were calculated by eq 7, considering the nonideal nature of the vapor phase. ⎛ py ⎞ (Bii − vio)(p − po ) p i ln γi = ln⎜⎜ io ⎟⎟ + + (2Bij − Bii − Bjj )yj2 x p RT RT ⎝ ii ⎠

(7)

Molar volumes voi of the pure compounds at the equilibrium temperature were determined with a modified version of Rackett’s equation,31 using values of ZRA found in this reference for the three compounds studied here; for ethyl butanoate that parameter was estimated with the method 3216



Article

Table 4. Experimental Vapor Pressures for Pure Compoundsa

a

T/K

poi /kPa

354.10 355.47 356.79 358.10 359.34 360.56 361.72 362.84 363.94 364.99 366.05 367.04 368.03 369.00 370.01 370.93 371.84 372.72 373.58 374.42

50.00 52.50 55.00 57.50 60.00 62.50 65.00 67.50 70.00 72.50 75.00 77.50 80.00 82.50 85.00 87.50 90.00 92.50 95.00 97.50

377.33 378.63 379.81 380.99 382.10 383.23 384.31 385.34 386.35 387.34 388.31 389.25 390.17 391.06 391.94 392.81 393.66 394.26

60.00 62.50 65.00 67.50 70.00 72.50 75.00 77.50 80.00 82.50 85.00 87.50 90.00 92.50 95.00 97.50 100.00 101.32

346.23 347.76

45.00 47.50

T/K

poi /kPa

Methyl Butanoate 375.27 100.00 375.74 101.32 376.91 105.00 378.42 110.00 379.91 115.00 381.34 120.00 382.73 125.00 384.07 130.00 385.37 135.00 386.63 140.00 387.87 145.00 389.07 150.00 390.24 155.00 391.38 160.00 392.48 165.00 393.58 170.00 394.64 175.00 395.67 180.00 396.70 185.00 397.68 190.00 Ethyl Butanoate 395.43 105.00 397.05 110.00 398.57 115.00 400.10 120.00 401.54 125.00 402.99 130.00 404.34 135.00 405.62 140.00 406.96 145.00 408.22 150.00 409.45 155.00 410.61 160.00 411.77 165.00 412.95 170.00 414.05 175.00 415.01 180.00 416.08 185.00 417.14 190.00 Heptane 369.32 95.00 370.19 97.50

T/K

poi /kPa

T/K

poi /kPa

398.67 399.61 400.54 401.46 402.37 403.25 404.13 404.97 405.81 406.64 407.45 408.26 409.05 409.83 410.58 411.35 412.09 412.83

195.00 200.00 205.00 210.00 215.00 220.00 225.00 230.00 235.00 240.00 245.00 250.00 255.00 260.00 265.00 270.00 275.00 280.00

349.29 350.70 352.07 353.41 354.69 355.94 357.14 358.32 359.45 360.54 361.61 362.66 363.68 364.71 365.65 366.61 367.53 368.42

50.00 52.50 55.00 57.50 60.00 62.50 65.00 67.50 70.00 72.50 75.00 77.50 80.00 82.50 85.00 87.50 90.00 92.50

418.15 419.14 420.12 421.10 422.01 422.94 423.85 424.79 425.67 426.53 427.35 428.20 429.04 429.84 430.65 431.42 432.23 433.00

195.00 200.00 205.00 210.00 215.00 220.00 225.00 230.00 235.00 240.00 245.00 250.00 255.00 260.00 265.00 270.00 275.00 280.00

395.53 397.25 398.89 400.50 402.04 403.51 404.94 406.33 407.66 408.95 410.24 411.45 412.64 413.81 414.94 416.07 417.16 418.22 419.24 420.25

45.00 47.50 50.00 52.50 55.00 57.50 60.00 62.50 65.00 67.50 70.00 72.50 75.00 77.50 80.00 82.50 85.00 87.50 90.00 92.50

393.30 394.34

185.00 190.00

Uncertainties u are: u(T) = ± 0.01 K and u(p) = ± 0.02 kPa.

poi /kPa

T/K

Heptane 371.07 100.00 371.51 101.32 372.72 105.00 374.31 110.00 375.85 115.00 377.34 120.00 378.77 125.00 380.18 130.00 381.52 135.00 382.84 140.00 384.13 145.00 385.36 150.00 386.60 155.00 387.78 160.00 388.94 165.00 390.08 170.00 391.17 175.00 392.25 180.00 Nonane 421.24 95.00 422.22 97.50 423.18 100.00 423.87 101.32 425.10 105.00 426.76 110.00 428.48 115.00 430.15 120.00 431.71 125.00 433.28 130.00 434.77 135.00 436.25 140.00 437.64 145.00 439.03 150.00 440.38 155.00 441.68 160.00 442.99 165.00 444.25 170.00 445.46 175.00 446.65 180.00

T/K

poi /kPa

395.37 396.37 397.35 398.29 399.24 400.17 401.07 401.97 402.84 403.72 404.57 405.42 406.25 407.05 407.87 408.65 409.42 410.22

195.00 200.00 205.00 210.00 215.00 220.00 225.00 230.00 235.00 240.00 245.00 250.00 255.00 260.00 265.00 270.00 275.00 280.00

447.83 448.99 450.12 451.20 452.29 453.35 454.41 455.44 456.45 457.45 458.43 459.41 460.35 461.28 462.19 463.08 463.95 464.86 465.73 466.59

185.00 190.00 195.00 200.00 205.00 210.00 215.00 220.00 225.00 230.00 235.00 240.00 245.00 250.00 255.00 260.00 265.00 270.00 275.00 280.00

■

TREATMENT OF DATA AND PREDICTIONS BY UNIFAC Values of the excess Gibbs function gE (in J·mol−1) were calculated from the corresponding adimensional quantities presented for each equilibrium phase shown in Table 6. Hence, these values were correlated for the four binary systems with a similar expression to eq 2, as follows:

The quality of VLE data for the four systems of this work was checked thermodynamically with the global condition recommended by Fredenslund et al.34 and were found to obey it, δ̅ ≤ 0.01, in all cases considered. Both the table of data and Figure 5 show that the only system that presents a azeotropic point is the methyl butanoate + heptanes system. The coordinates of this minimum boiling-temperature azeotrope are (xaz = 0.404, Taz = 367.65 K), and the corresponding values found in the literature for purposes of comparison at the same pressure of 101.32 kPa, are: (0.398, 368.22);8 (0.346, 368.15).35 The first of these corresponds with those determined in a study by our group, for which the discrepancy has been explained previously, and the other, with an even greater discrepancy is a Lecat prediction, recorded by Gmehling et al.35

2

g E(x1 , T ) = z1(1 − z1) ∑ giz1i i=0

(8)

where z1 has the same significance as described in the previous section, see eq 3, in relation to the alkyl butanoate composition. The parameters gi were temperature-dependent through a 3217



Article

Table 5. Coefficients A, B, and C of the Antoine Equation, log(poi /kPa) = A − B/[(T/K) − C] and Acentric Factors ω for Pure Compounds Used in This Work and Comparison with Those Found in the Literature A

B

C

6.32280 (2.78200) 6.3036 6.3259 6.11584 (2.63004) 6.36031 5.9061 6.01075 (2.57290) 5.9705

1407.85 (2.5389) 1381.64 1373.32 1324.55 (2.3197) 1493.89 1213.54 1251.31 (2.3166) 1229.82

49.56 (0.089) 53.60 57.16 71.95 (0.126) 51.13 83.10 59.06 (0.109) 61.37

6.09705 (2.73730) 6.0241

1451.26 (2.4408) 1399.51

68.93 (0.116) 75.67

ethyl butanoate

heptane

nonane

a

ω

compound methyl butanoate

0.376a 0.367 0.376b 0.411a 0.421 0.412b 0.349 0.345 0.349b 0.442a 0.445 0.443b

range T/K

references

354−413 349−384 317−361

this work 21 27

377−433 375−407 332−373

this work 20 28

346−410 300−400

this work 1

396−467 360−455

this work 1

Values obtained by using eq 6 and the Pitzer relationship. bEstimated by Lee−Kesler.

similar relationship to that of eq 4 but adapted to the function to be correlated by the expression: 2

gi =

∑ GijT j − 1 = j=0

Gi0 + Gi1 + Gi2T T

(9)

The reason for using this approach is that in previous works by our group 17,18 an equation was used for different purposes, containing the fundamental variables (p,T,x1,y1). Hence, the inclusion of temperature in the equation means that other derived quantities can also be obtained; such as the potential function of enthalpy hE. ⎛ ∂g E ⎞ ⎟ hE = g E − T ⎜ ⎝ ∂T ⎠ p , x ⎛ ∂g ⎞ ⎛ ∂z ⎞⎛ ∂k ⎞ = g E − Tz1(1 − z1) ∑ ⎜ i ⎟z1i − T ⎜ 1 ⎟⎜ ⎟Y ⎝ ∂k ⎠⎝ ∂T ⎠ ⎝ ∂T ⎠ (10)

Figure 4. Vapor pressure lines in reduced coordinates for the different compounds of this work: d, heptane; c, methyl butanoate; b, ethyl butanoate; a, nonane.

(11)

mixtures, in the literature14 cEp values have only been found for the binary system methyl butanoate + heptane that will also be subjected to the multiproperty correlation process. The derivative of eq 12 in relation to temperature gives:

where: 2

2

Y = (1 − 2z1) ∑ giz1i + z1(1 − z1) ∑ igiz1i − 1 i=0

i=0

In the practical part of the data mathematical treatment, it can be assumed that (∂k/∂T) = 0, since, in the corresponding section, it has been verified that kv is quasi-independent of temperature and, by extension, the corresponding values for enthalpy and for Gibbs function. For this purpose, the last summand of eq 11 is omitted giving rise to an expression simpler for hE. Therefore, starting with eqs 8 and 9, this is reduced to:

2 2 ⎛ ∂ 2g ⎞ ⎛ 2G ⎞ cpE = −Tz1(1 − z1) ∑ ⎜⎜ 2i ⎟⎟z1i = − z1(1 − z1) ∑ ⎜ 2i0 ⎟z1i ⎝ T ⎠ T ∂ ⎠ i=0 ⎝ i=0

(13)

2

⎛ 2G ⎞ hE = z1(1 − z1) ∑ ⎜ i0 + Gi1⎟z1i ⎝ T ⎠ i=0

Other derived properties can also be established in this way. One of these which is valuable for interpreting the behavior of the mixture is the entropy, which is also obtained from previous functions,

(12)

In this work, the mixing enthalpies of the binary mixtures being studied have not been measured, but the values published previously at two temperatures 4−7 will be used in the treatment together with the VLE data of this work; this justifies the presence of eq 12. For these

2 ⎛ dg ⎞ ⎛ dz ⎞ −Ts E = g E − hE = z1(1 − z1) ∑ ⎜ i ⎟z1i+⎜ 1 ⎟Y dT ⎠ ⎝ dT ⎠ i=0 ⎝

(14) 3218



Article

Table 6. Experimental Values and Calculated Properties for the Isobaric VLE of the Binaries Formed by an Alkyl Butanoate (1) + an Alkane (2) at 101.32 kPaa γ1

T/K

x1

y1

371.38 370.85 370.64 370.47 370.32 370.28 370.11 369.76 369.55 369.36 369.23 368.88 368.81 368.53 368.45 368.38 368.30 368.23 368.13 368.03 367.97 367.87 367.82 367.80 367.75 367.66 367.65 367.65 367.66

0.000 0.018 0.028 0.036 0.044 0.048 0.057 0.078 0.092 0.107 0.117 0.147 0.156 0.186 0.196 0.205 0.218 0.230 0.246 0.263 0.280 0.299 0.317 0.334 0.357 0.379 0.404 0.426 0.447

0.000 0.029 0.043 0.054 0.066 0.071 0.083 0.110 0.128 0.145 0.158 0.190 0.199 0.228 0.238 0.247 0.259 0.268 0.283 0.297 0.311 0.326 0.340 0.353 0.369 0.386 0.404 0.419 0.433

1.832 1.777 1.771 1.756 1.734 1.731 1.696 1.674 1.641 1.635 1.583 1.570 1.525 1.513 1.498 1.481 1.458 1.444 1.420 1.398 1.378 1.357 1.337 1.313 1.293 1.273 1.252 1.233

423.90 418.67 415.89 413.88 407.75 405.58 403.43 400.20 397.25 395.74 394.41 393.01 391.37 389.52 388.15 386.99 385.96 385.02

0.000 0.042 0.065 0.081 0.141 0.166 0.187 0.227 0.272 0.298 0.324 0.344 0.388 0.432 0.469 0.506 0.536 0.569

0.000 0.163 0.240 0.295 0.441 0.487 0.532 0.595 0.647 0.672 0.694 0.715 0.742 0.770 0.788 0.805 0.821 0.834

1.328 1.342 1.376 1.358 1.341 1.365 1.366 1.328 1.309 1.285 1.294 1.243 1.215 1.189 1.162 1.148 1.128

371.38 371.40 371.62 371.75 371.85 371.99 372.12 372.27 372.42 372.61

0.000 0.008 0.029 0.049 0.066 0.084 0.101 0.120 0.139 0.160

0.000 0.007 0.023 0.039 0.052 0.065 0.078 0.091 0.104 0.118

1.610 1.601 1.597 1.555 1.526 1.509 1.474 1.446 1.416

γ2

(gE/RT)

T/K

x1

Methyl Butanoate (1) + Heptane (2) 1.000 0.000 367.69 0.466 1.009 0.020 367.72 0.486 1.010 0.026 367.79 0.505 1.011 0.031 367.84 0.524 1.012 0.036 367.91 0.541 1.011 0.037 367.99 0.559 1.012 0.043 368.10 0.576 1.015 0.054 368.18 0.591 1.016 0.062 368.45 0.629 1.018 0.069 368.62 0.663 1.018 0.074 368.83 0.698 1.024 0.088 369.17 0.736 1.025 0.091 369.43 0.759 1.032 0.104 369.71 0.782 1.034 0.108 370.03 0.803 1.037 0.112 370.46 0.830 1.040 0.116 370.85 0.848 1.044 0.120 371.04 0.861 1.048 0.126 371.35 0.876 1.054 0.131 371.63 0.888 1.060 0.136 371.78 0.897 1.068 0.142 372.03 0.905 1.075 0.146 372.24 0.914 1.082 0.149 373.22 0.948 1.093 0.154 373.35 0.957 1.106 0.160 373.90 0.969 1.117 0.164 374.43 0.981 1.131 0.166 374.97 0.992 1.145 0.169 375.74 1.000 Methyl Butanoate (1) + Nonane (2) 1.000 0.000 384.04 0.606 0.991 0.003 383.16 0.640 0.991 0.011 382.34 0.673 0.987 0.014 381.48 0.711 0.989 0.033 380.71 0.744 0.993 0.043 380.09 0.775 0.989 0.049 379.39 0.806 0.986 0.060 378.82 0.833 0.998 0.076 378.37 0.859 1.006 0.084 377.95 0.881 1.015 0.091 377.62 0.897 1.014 0.098 377.25 0.916 1.036 0.106 376.91 0.936 1.055 0.115 376.58 0.954 1.083 0.124 376.36 0.966 1.111 0.128 376.30 0.969 1.127 0.130 375.74 1.000 1.156 0.131 Ethyl Butanoate (1) + Heptane (2) 1.000 0.000 376.24 0.449 1.006 0.010 376.42 0.459 1.004 0.018 376.79 0.482 1.004 0.027 377.18 0.503 1.007 0.035 377.70 0.530 1.008 0.043 378.10 0.550 1.010 0.050 379.04 0.598 1.013 0.058 379.62 0.623 1.016 0.065 381.90 0.708 1.020 0.072 382.86 0.738 3219

y1

γ1

γ2

(gE/RT)

0.447 0.461 0.474 0.488 0.499 0.511 0.524 0.534 0.563 0.589 0.616 0.649 0.671 0.693 0.714 0.742 0.765 0.780 0.797 0.814 0.825 0.837 0.850 0.902 0.918 0.939 0.960 0.983 1.000

1.218 1.203 1.188 1.176 1.164 1.150 1.141 1.131 1.110 1.097 1.083 1.070 1.064 1.057 1.052 1.043 1.040 1.039 1.034 1.032 1.031 1.029 1.028 1.022 1.026 1.020 1.015 1.011 1.000

1.157 1.171 1.184 1.198 1.211 1.228 1.240 1.255 1.289 1.327 1.372 1.424 1.453 1.487 1.515 1.569 1.584 1.608 1.651 1.667 1.693 1.702 1.728 1.816 1.832 1.867 1.888 1.968

0.170 0.171 0.171 0.171 0.170 0.169 0.167 0.165 0.160 0.156 0.152 0.143 0.137 0.130 0.122 0.112 0.103 0.099 0.091 0.085 0.082 0.077 0.072 0.052 0.051 0.039 0.027 0.016 0.000

0.849 0.862 0.874 0.887 0.899 0.909 0.922 0.932 0.941 0.948 0.955 0.963 0.971 0.978 0.984 0.986 1.000

1.107 1.091 1.075 1.058 1.047 1.033 1.028 1.021 1.013 1.008 1.007 1.005 1.001 0.999 0.999 0.999 1.000

1.192 1.224 1.265 1.320 1.369 1.432 1.466 1.516 1.583 1.645 1.674 1.712 1.800 1.864 1.882 1.849

0.131 0.129 0.125 0.120 0.115 0.106 0.096 0.087 0.076 0.067 0.059 0.049 0.038 0.028 0.020 0.018 0.000

0.305 0.312 0.328 0.343 0.363 0.380 0.415 0.436 0.519 0.554

1.158 1.156 1.143 1.131 1.118 1.112 1.086 1.075 1.048 1.043

1.111 1.113 1.124 1.134 1.147 1.155 1.188 1.205 1.252 1.262

0.124 0.125 0.125 0.125 0.123 0.123 0.119 0.115 0.099 0.092



Article

Table 6. continued

a

T/K

x1

y1

γ1

γ2

372.80 373.05 373.30 373.60 373.88 374.17 374.55 374.96 375.23 375.54 375.90

0.180 0.207 0.231 0.258 0.283 0.308 0.336 0.363 0.382 0.404 0.426

0.131 0.149 0.164 0.181 0.196 0.211 0.229 0.249 0.261 0.275 0.290

1.392 1.363 1.329 1.302 1.281 1.255 1.231 1.222 1.208 1.193 1.176

423.90 422.86 420.81 419.42 418.32 417.15 415.85 414.64 413.58 411.47 410.77 410.15 409.47 408.66 407.83 407.06 406.31 405.49 404.76 404.04 403.32

0.000 0.014 0.042 0.062 0.080 0.098 0.122 0.144 0.166 0.215 0.231 0.248 0.268 0.289 0.310 0.334 0.356 0.380 0.405 0.436 0.463

0.000 0.039 0.112 0.163 0.204 0.244 0.289 0.330 0.364 0.430 0.451 0.470 0.491 0.513 0.539 0.562 0.582 0.605 0.625 0.647 0.665

1.359 1.386 1.394 1.380 1.381 1.357 1.349 1.326 1.277 1.265 1.249 1.225 1.213 1.211 1.196 1.185 1.181 1.165 1.140 1.123

(gE/RT)

T/K

x1

Ethyl Butanoate (1) + Heptane (2) 0.079 385.01 0.807 0.087 386.16 0.837 0.094 387.93 0.879 0.100 388.85 0.899 0.106 389.66 0.916 0.110 390.45 0.932 0.114 391.15 0.944 0.118 391.90 0.960 0.120 392.52 0.971 0.122 393.20 0.982 0.123 394.31 1.000 Ethyl Butanoate (1) + Nonane (2) 1.000 0.000 402.62 0.486 1.001 0.006 401.92 0.516 1.002 0.015 401.28 0.550 1.000 0.021 400.59 0.579 0.999 0.025 399.95 0.609 0.998 0.029 399.36 0.642 0.997 0.035 398.89 0.671 0.996 0.039 398.13 0.711 0.998 0.045 397.59 0.739 1.005 0.056 397.05 0.779 1.007 0.060 396.55 0.812 1.012 0.064 396.20 0.836 1.018 0.067 395.90 0.861 1.025 0.073 395.59 0.887 1.024 0.076 395.33 0.906 1.030 0.079 395.08 0.929 1.037 0.084 394.89 0.946 1.040 0.088 394.70 0.963 1.052 0.092 394.53 0.980 1.067 0.094 394.41 0.992 1.087 0.098 394.31 1.000 1.024 1.030 1.037 1.044 1.051 1.060 1.069 1.074 1.081 1.089 1.098

y1

γ1

γ2

(gE/RT)

0.633 0.677 0.742 0.780 0.811 0.841 0.870 0.901 0.927 0.954 1.000

1.023 1.018 1.010 1.010 1.007 1.003 1.004 1.002 1.001 1.000 1.000

1.330 1.354 1.394 1.387 1.403 1.446 1.417 1.445 1.454 1.478

0.074 0.065 0.048 0.042 0.035 0.027 0.023 0.017 0.012 0.007 0.000

0.684 0.706 0.724 0.744 0.763 0.780 0.797 0.821 0.841 0.860 0.879 0.896 0.908 0.925 0.938 0.951 0.963 0.974 0.985 0.994 1.000

1.123 1.112 1.087 1.081 1.073 1.057 1.045 1.038 1.037 1.021 1.015 1.014 1.007 1.004 1.004 1.000 0.999 0.998 0.997 0.997 1.000

1.090 1.100 1.132 1.147 1.161 1.198 1.223 1.253 1.258 1.327 1.367 1.368 1.433 1.458 1.458 1.524 1.541 1.589 1.643 1.740

0.101 0.101 0.102 0.103 0.101 0.100 0.096 0.092 0.086 0.079 0.070 0.063 0.055 0.046 0.039 0.030 0.022 0.015 0.007 0.001 0.000

Uncertainties u are: u(T) = ± 0.01 K, u(p) = ± 0.02 kPa, u(x1) = ± 0.002, and u(y1) = ± 0.002.

(OF) that enables the differences to be minimized between the values obtained from experimentation and those of the model for the properties indicated below:

This expression can also be simplified by eliminating the final summand, as mentioned previously, by considering (∂z1/∂T) = 0. Other properties related to the VLE data correspond to the activity coefficients that can be calculated from the expression: ⎛ ∂g E ⎞ ⎟ RT ln γi = gi̅ = g − ∑ xk ⎜ ⎝ ∂xk ⎠ k≠i E

OF = c0s(g E) + c1s(ln γ1) + c 2s(ln γ2) + c3s(hE) + c4s(cpE) (17)

E

p , T , xj ≠ k , i

where ci are corrective coefficients to equiparate the significance of the different quantities included in the standard deviations s, which are achieved for specific properties through similar expressions to that of eq 5. Table 7 shows the values obtained for the model fitting the data mentioned previously, together with the parameter goodness of fit for each property, representing the whole set, as can be seen in Figures 7 and 8. To get a good correlation of different properties the k-parameters established for each of them (kg for gE, kh for hE, and kc for cEp ) were obtained in the same fitting procedure, and they are presented in Table 7. Additional details of this procedure were presented previously.18 Figure 9 shows the result of the correlation of excess heat capacities for the methyl butanoate + heptane mixture at 298.15 K, showing an excellent reproduction. A global valuation is that the model proposed is suitable for the simultaneous correlation of different properties of a binary solution giving average errors lower than 5 % in the representation of gE and of 2 % for hE

(15)

And taking into account eq 8 the following generic expression is obtained for the activity coefficients: 2

RT ln γi = zi(1 − zi) ∑ gjz ij + (1 − xi) j=0

⎛ z ⎞2 × [∑ (j + 1)(gj − gj − 1)zij]k ⎜ i ⎟ ⎝ xi ⎠ j=0 3

(16)

with g−1 = g3 = 0. The equations shown here have been used to perform the simultaneous or combined correlation of VLE data and enthalpies of mixture hE previously published for the binaries being studied. For this purpose, a regression procedure was designed for nonlinear functions, using the commercial software in Matlab with an objective function 3220



Article

Figure 5. Plots of experimental VLE values and correlation curves () for the binaries: a, methyl butanoate (1) + heptane (2); b, methyl butanoate (1) + nonane (2); c, ethyl butanoate (1) + heptane (2); d, ethyl butanoate (1) + nonane (2). ○, y1−x1 vs x1; △, T vs x1; □, T vs y1; - - -, curves by UNIFAC.19

and cEp . Figure 8 also shows the entropic variation TsE for each mixture that produces a change in the same direction as the other properties hE and vE. Starting from eq 16, the activity coefficients were determined at infinite dilution for each of the compounds of the mixture, giving rise to: o o o RTb,2 ln γ1∞ = lim RTb,2 ln γ1 ≡ lim RTb,2 ln γ1 = x1→ 0

z1→ 0

g0 kg

(18)

o o o RTb,1 ln γ2∞ = lim RTb,1 ln γ2 ≡ lim RTb,1 ln γ2 = kg(g0 + g1 + g2) x2 → 0

z2→0

(19)

The values obtained are shown in Table 8, but the authors found no data for this parameter in the literature for purposes of comparison. Extending the database of γ∞ i in the near future by including mixtures with other alkanes or analogous solutions could provide us an additional information about the structural model established previously for these systems.25,26 The model used in its polynomial form has the advantage of generating a stepwise correlation in the following order (x,cEp )→(x, hE)→(x,gE). This step-by-step procedure was also used in the present work with similar results to those described,

Figure 6. Comparison between our experimental VLE data obtained for the binary methyl butanoate (1) + heptane (2) and those from literature. y1−x1 vs x1: ○, experimental; ●, ref 8; T vs x1: △, experimental; ▲, ref 8; T vs y1: □, experimental; ■, ref 8. 3221



Article

Figure 7. Plots of experimental VLE values for binaries: a, methyl butanoate (1) + heptane (2), b, methyl butanoate (1) + nonane (2), c, ethyl butanoate (1) + heptane (2), d, ethyl butanoate (1) + nonane (2). ○, gE/RT vs x1; △, γ1 vs x1; □, γ2 vs y1; , correlation curves; − − −, prediction by UNIFAC.19

confirming in this case the multiobjective optimization procedure with the function established in eq 17. Prediction by UNIFAC. The UNIFAC group contribution model was used in the version proposed by Gmehling et al.19 to predict the characteristic properties of isobaric VLE presented here, the enthalpies of the mixtures, and the excess thermal capacities, using the same set of interaction parameters. Estimates of γi and the excess Gibbs function can be considered to be acceptable, with the exception of the methyl butanoate + heptanes system, as in Figure 7a, which presents important differences compared with experimental values. This difference also affects the estimation of the azeotropic point and the γ∞ 1 coefficients for the same mixture; see Table 7. On the other hand, estimation of the T−x−y properties, Figure 5a−d, confirms the previous observation. Figure 8 compares the experimental values of hE with those estimated by the method, which produces lower values in all cases; this fact has already been demonstrated by the authors in previous works, suggesting that the method begins to fail as the ester chain length increases. The curves estimated by the model for the entropic term TsE are also much lower. Therefore, the method seems to predict the excess heat capacities of the binary mixture methyl butanoate + heptane with values

Table 7. Parameters of eqs 8 and 9 Obtained by a Simultaneous Correlation of Different Quantities (VLE Data, hE, and cEp ), and Standard Deviations, s, for Each of the Properties methyl butanoate (1) + G00 G01 G02 G10 G11 G12 G20 G21 G22 kg kh kcp s (γ1) s (γ2) s(gE/RT) s(hE) (T = 298 K) s(hE) (T = 318 K) s(cEp ) (T = 298 K)


heptane (2)

nonane (2)

heptane (2)

nonane (2)

1.49·105 2674.9 −2.2607 −2.50·105 2817.8 −6.966 3.46·105 −933.88 0.9259 1.105 0.713 1.613 0.035 0.051 0.007 6 4 0.01

−7.91·105 8552.6 −13.634 3.84·106 −24524 41.562 −4.68·106 35488 −63.333 1.152 0.607

1.91·105 1767.4 0.5522 −9.94·105 5428.0 −14.533 1.57·106 −6195.6 8.4393 1.652 0.579

−8.96·105 8718.7 −11.009 3.03·106 −18037 20.020 −1.77·106 13263 −18.458 1.850 0.692

0.018 0.013 0.004 7 12

0.011 0.012 0.004 10 9

0.033 0.039 0.005 10 7

3222



Article

Figure 8. Plots of experimental hE values (○, at 298.15 K; △, at 318.15 K), correlation curves () by eq 8 and curves (·) by UNIFAC19 of the binaries: a, methyl butanoate (1) + heptane (2), b, methyl butanoate (1) + nonane (2), c, ethyl butanoate (1) + heptane (2), d, ethyl butanoate (1) + nonane (2). In red, curves estimating TsE: solid line; by eq 8: dashed line.

Table 8. Activity Coefficients at Infinite Dilution Obtained by eqs 18 and 19 for the Binaries of an Alkyl Butanoate (1) + an Alkane (2) and Comparison with Those Estimated by UNIFAC19 methyl butanoate (1) + γ∞ 1 γ∞ 2 a


heptane (2)

nonane (2)

heptane (2)

nonane (2)

1.926 1.706a 2.096 1.698a

1.251 1.428a 1.815 1.928a

1.629 1.612a 1.360 1.450a

1.347 1.380a 1.538 1.580a

Reference 19.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

cEp

Figure 9. Plots of vs x1 for the mixture methyl butanoate (1) + hepane (2) at 298.15 K: ●, experimental from ref 14;  obtained by eq 8, and − − −, by UNIFAC.19

Funding

The authors would like to thank the Ministry of Economy and Competitiveness for funding project CTQ2009-12482. Two of the authors (L.F. and R.R.) thank the FULP for the assistance received as part of the INNOVA program.

which are contrary to experimental ones, as can be seen in Figure 9. 3223



Article

Notes

(18) Ortega, J.; Espiau, F.; Wisniak, J. New Parametric Model To Correlate the Gibbs Excess Function and Other Thermodynamic Properties of Multicomponent Systems. Aplication to Binary Systems. Ind. Eng. Chem. Res. 2010, 49, 406−421. (19) Gmehling, J.; Li, J.; Schiller, M. A Modified UNIFAC model. 2. Present parameter matrix and results for different thermodynamic properties. Ind. Eng. Chem. Res. 1993, 32, 178−193. (20) Hernández, P.; Ortega, J. Vapor-liquid equilibria and densities for ethyl esters (ethanoate to butanoate) and alkan-2-ol (C3-C4) at 101.32 kPa. J. Chem. Eng. Data 1997, 42, 1090−1100. (21) Ortega, J.; Susial, P.; de Alfonso, C. Isobaric vapor-liquid equilibrium of methyl butanoate with ethanol and 1-propanol binary systems. J. Chem. Eng. Data 1990, 35, 216−219. (22) Riddick, J. A.; Bunger, W. B.; Sakano, T. K. Organic Solvents. Physical Properties and Methods of Purification, 4th ed.; WileyInterscience: New York, 1986. (23) Ortega, J.; Peña, J. A.; De Alfonso, C. Isobaric vapor-liquid equilibria of ethyl acetate + ethanol mixtures at 760 ± 0.5 mmHg. J. Chem. Eng. Data 1986, 31, 339−342. (24) Bondi, A. Physical Properties of Molecular Crystals, Liquids and Glasses; Wiley: New York, 1968. (25) Ortega, J.; Toledo-Marante, F. Thermodynamic properties of (an ethyl ester + a branched alkane). XV. HEm and VEm values for (an ester + an alkane). J. Chem. Thermodyn. 2002, 34, 1439−1459. (26) Ortega, J.; Espiau, F.; Toledo, F. Thermodynamic properties of (an ester + an alkane). XVI. Experimental HEm and VEm values and a new correlation method for (an alkyl ethanoate + an n-alkane) at 318.15 K. J. Chem. Thermodyn. 2004, 36, 193−209. (27) Constantinescu, D.; Wichterle, I. Isothermal vapour−liquid equilibria and excess molar volumes in the binary ethanol + methyl propanoate or methyl butanoate systems. Fluid Phase Equilib. 2002, 203, 71−82. (28) Fárková, J.; Wichterle, I. Vapour pressures of some ethyl and propyl esters of fatty acids. Fluid Phase Equilib. 1993, 90, 143−148. (29) Lee, B. I.; Kesler, M. G. A generalized thermodynamic correlation based on three-parameter corresponding states. AIChE J. 1975, 21, 510−527. (30) Pitzer, K. S. The Volumetric and Thermodynamic Properties of Fluids. I. Theoretical Basis and Virial Coeficients. J. Am. Chem. Soc. 1955, 77, 3427−3433. (31) Spencer, C. F.; Danner, R. P. Improved equation for prediction of saturated liquid density. J. Chem. Eng. Data 1972, 17, 236−241. (32) Yamada, T.; Gunn, R. D. Saturated liquid molar volumes. Rackett equation. J. Chem. Eng. Data 1973, 18, 234−236. (33) Tsonopoulos, C. Second virial coefficients of water pollutants. AIChE J. 1978, 24, 1112−1115. (34) Fredenslund, A.; Gmehling, J.; Rasmussen, P. Vapor-Liquid Equilibria Using UNIFAC: A group Contribution Method; Elsevier: Amsterdam, 1977. (35) Gmehling, J.; Menke, J.; Krafczyk, J.; Fischer, K. Azeotropic Data, 2nd ed.; Wiley-VCH: Oldënburg, 2004.

The authors declare no competing financial interest.

■

REFERENCES

(1) Fernandez, L.; Perez, E.; Ortega, J.; Canosa, J.; Wisniak, J. Measurements of the Excess Properties and Vapor-Liquid Equilibria at 101.32 kPa for Mixtures of Ethyl Ethanoate + Alkanes (from C5 to C10). J. Chem. Eng. Data 2010, 55, 5519−5533. (2) Ortega, J.; Sabater, G.; de la Nuez, I.; Quintana, J. J.; Wisniak, J. Isobaric Vapor-Liquid Equilibrium Data and Excess Properties of Binary Systems Comprised of Alkyl Methanoates + Hexane. J. Chem. Eng. Data 2007, 52, 215−225. (3) Sabater, G.; Ortega, J. Excess properties and isobaric vapor-liquid equilibria for four binary systems of alkyl (methyl to butyl) methanoates with decane. Fluid Phase Equilib. 2010, 291, 18−31. (4) Ortega, J.; Legido, J. L.; Fernandez, J.; Pias, L.; Paz Andrade, M. I. Measurements and analysis of excess enthalpies of ester+n-alkane using the UNIFAC model. Ber. Bunsenges Phys. Chem. 1991, 95, 128− 135. (5) Ortega, J.; Matos, S.; Peña, J. A. Excess molar enthalpies of methyl alkanoates + n-nonane at 298.15 K. Thermochim. Acta 1990, 160, 337−342. (6) Ortega, J.; Navas, A.; Sabater, G.; Ascanio, M.; Placido, J. Thermodyamic properties of (an ester and an alkane). XVIII. Experimental HEm and VEm values for (an alkyl butanoate + an alkane) at T = 318.15 K. J. Chem. Thermodyn. 2007, 39, 1514−1529. (7) Vidal, M.; Ortega, J.; Placido, J. Thermodynamic properties of ( a n e t h y l e s t e r + n - a l k a n e ) . I X . - H mE a n d V mE f o r {xCH3(CH2)uCOOCH2CH3+(1-x)CH3(CH2)2v+1CH3} with u = 0 to 5, and v = 1 to 7. J. Chem. Thermodyn. 1997, 29, 47−74. (8) 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. (9) Postigo, M. A.; Garcia, P. H.; Ortega, J.; Tardajos, G. Excess molar volumes of binary mixtures containing a methyl ester (ethanoate to tetradecanoate) with odd n-alkanes at 298.15 K. J. Chem. Eng. Data 1995, 40, 283−289. (10) Dusart, O.; Piekarski, S.; Grolier. Int. DATA Ser., Sel. Data Mixtures, Ser. A 1983, 3, 244. (11) Ilic, P. V.; Jiménez, E.; Legido, J. L.; Fernández, J.; Paz Andrade, M. I. Excess molar volumes of (methyl butanoate + n-heptane, + n-decane) and of (butyl butanoate + n-heptane + n-decane) at 298.15 K. J. Chem. Thermodyn. 1990, 22, 865−871. (12) Matos, J. S.; Trenzado, J. L.; González, E.; Alcalde, R. Volumetric properties and viscosities of the methyl butanoate + nheptane, + n-octane ternary system and its binary constituents in the temperature range from 283.15 to 313.15 K. Fluid Phase Equilib. 2001, 186, 207−234. (13) Matos, J. S.; Trenzado, J. L.; Caro, M. N.; Romano, E.; Pérez, E. Volumetric study of (an aliphatic methyl ester + heptane or nonane) at the temperature 298.15 K. J. Chem. Thermodyn. 1994, 26, 857−862. (14) Pintos, M.; Bravo, R.; Baluja, M. C.; Paz Andrade, M. I.; RouxDesgranges, G.; Grolier, J.-P. E. Thermodynamics of alkanoate + alkane binary mixtures. Concentration dependence of excess heat capacities and volumes. Can. J. Chem. 1988, 66, 1179−1186. (15) Sastry, N. V.; George, A.; Jain, N. J.; Bahadur, P. Densities, Relative Permittivities, Excess Volumes, and Excess Molar Polarizations for Alkyl Ester (Methyl Propanoate, Methyl Butanoate, Ethyl Propanoate, and Ethyl Butanoate) + Hydrocarbons (n-Heptane, Benzene, Chlorobenzene, and 1,1,2,2-Tetrachloroethane) at 308.15 and 318.15 K. J. Chem. Eng. Data 1999, 44, 456−464. (16) Scheller, W. A.; Torres-Soto, A. R.; Daphtary, K. J. Isothermal Vapor-Liquid Equilibrium Data for the System Heptane-Ethyl Butyrate at 74.7° and 100°. J. Chem. Eng. Data 1969, 14, 439−441. (17) Ortega, J.; Espiau, F. A New Correlation Method for VaporLiquid Equilibria and Excess Enthalpies for Nonideal Solutions Using a Genetic Algorithm. Application to Ethanol + Alkane Mixtures. Ind. Eng. Chem. Res. 2003, 42, 4978−4992. 3224


Measurements and Correlations of the Isobaric ... - ACS Publications

Recommend Documents