Isothermal Vapor–Liquid Equilibria of n-Tetradecane+ Ethyl

Article pubs.acs.org/jced

Isothermal Vapor−Liquid Equilibria of n‑Tetradecane + Ethyl Hexanoate, Ethyl Decanoate, and Ethyl Tetradecanoate Mokhtar Benziane,† Kamel Khimeche,*,† Ilham Mokbel,‡ Abdallah Dahmani,§ and Jacques Jose‡ †

Ecole Militaire Polytechnique EMP, BP 17 Bordj-El-Bahri, Alger, Algérie Laboratoire des Sciences Analytiques UMR 5280, Université de Lyon-UCB Lyon 1, 43 Bd du 11 Novembre 1918, 69622 Villeurbanne, France § Laboratoire de Thermodynamique et Modélisation Moléculaire, Faculté de Chimie, USTHB, BP. 32 El-Alia, 16111 Bab-Ezzouar, Alger, Algérie ‡

ABSTRACT: The vapor pressures of three binary systems, (ethyl hexanoate (1) + n-tetradecane (2)), (ethyl decanoate (1) + n-tetradecane (2)), and (ethyl tetradecanoate (1) + n-tetradecane (2)), were measured by means of a static apparatus at temperatures between (373.15 and 453.15) K. We correlated the data with the Antoine equation. The molar excess Gibbs energies GE obtained from these data by using Barker’s method were fitted to the Redlich−Kister equation. A maximum azeotropic behavior is observed for the binary mixture {ethyl decanoate (1) + n-tetradecane (2)}. Positive values of the excess Gibbs energy are obtained for all of the investigated temperatures and compositions. The data were also correlated by using Wilson equation. The predicted GE obtained by using group contribution model, UNIFAC (Gmehling version), are different to the experimental values. These deviations are more important for systems {ethyl decanoate (1) + n-tetradecane (2)} and {ethyl tetradecanoate (1) + n-tetradecane (2)}.

1. INTRODUCTION Biodiesel (alkyl esters of fatty acids), produced by transesterification process,1−4 is becoming a promising alternative to fossil fuels. Biodiesel can also be used blended with petrodiesel (paraffinic fuel) in any percentage without affecting the performance of most diesel equipment. On the other hand, by blending biofuel with fossil fuels, the combustion efficiency is enhanced, and a cost-reduction in the distribution system is obtained.5−7 The knowledge of vapor−liquid equilibria of mixtures containing fatty acid ethyl esters (biodiesel) and alkane (paraffinic fuel) is essential in industrial scale operations and allows an understanding of the problems of volatility, stability, and security during the exploitation, transport, and storage of diesel/biodiesel blends. Such data are scarce in the literature for these systems. In a previous work, we studied vapor pressures of pure saturated fatty acid ethyl ester (FAEE).8 Continuing this research line, we present a complete set of data on vapor pressures for (FAEE + n-tetradecane) mixtures for temperatures from (373.15 to 453.15) K. The excess molar Gibbs energies GE evaluated by Barker’s method are examined on the basis of the modified universal functional activity coefficient (UNIFAC) model.

Table 1. Source and Purity of Products chemical name

CAS no.

source

purity

123-66-0 110-38-3 124-06-1 629-59-4

SAFC Aldrich Chem Aldrich Chem Janssem Chimica

≥ 98 % ≥ 99 % ≥ 99 % > 99 %

2.2. Apparatus. A static method was used to measure the vapor pressures. The experimental procedure and the apparatus are described in the literature.9,10 The vapor and the sublimation pressures of water and naphthalene were measured to check the calibration the apparatus.11 2.3. Uncertainty on the Vapor Pressure System Temperature and Molar Fraction. The measurements were done with the following estimated uncertainties: u(P) = 0.03 P/Pa for P < 600 Pa; u(P) = 0.01 P/Pa for pressure: 600 < P/Pa < 1300; u(P) = 0.003 P/Pa for pressure ranging from (1.3 to 200) kPa; u(T) = 0.02 K for temperatures from (253.15 to 463.15) K; u (xi) = 0.0002.

3. RESULTS AND DISCUSSION The vapor pressures of the systems (ethyl hexanoate (1) + n-tetradecane (2)), (ethyl decanoate (1) + n-tetradecane (2)),

2. EXPERIMENTAL PROCEDURES 2.1. Chemicals. The suppliers and the purities of the three saturated FAEEs and n-tetradecane are reported in Table 1. These compounds were used without any further purification. © 2013 American Chemical Society

synonym

ethyl hexanoate ethyl caproate ethyl decanoate ethyl caprate ethyl tetradecanoate ethyl myristate n-tetradecane

Received: December 7, 2012 Accepted: January 17, 2013 Published: February 4, 2013 492

dx.doi.org/10.1021/je301294a | J. Chem. Eng. Data 2013, 58, 492−498

Journal of Chemical & Engineering Data

Article

Table 2. Values of the Vapor Pressure P, Standard Deviations δP/P (%), Activity Coefficients γ1 and γ2, and Excess Molar Gibbs Functions GE for the Binary System Ethyl Hexanoate (1) + Tetradecane (2)a x1

y1,cal

0.0000 0.1262 0.3053 0.4945 0.6985 0.9003 1.0000

0.0000 0.8187 0.9294 0.9657 0.9825 0.9930 1.0000

0.0000 0.1262 0.3053 0.4945 0.6985 0.9003 1.0000

0.0000 0.7926 0.9184 0.9598 0.9796 0.9923 1.0000

0.0000 0.1262 0.3053 0.4945 0.6985 0.9003 1.0000

0.0000 0.7660 0.9064 0.9534 0.9766 0.9916 1.0000

0.0000 0.1262 0.3053 0.4945 0.6985 0.9003 1.0000

0.0000 0.7391 0.8934 0.9464 0.9733 0.9908 1.0000

0.0000 0.1262 0.3053 0.4945

0.0000 0.7122 0.8792 0.9389

a

P/Pa T 444.0 2158.2 4461.1 6817.4 8891.4 10459.3 11349.4 T 751.6 3191.7 6530.5 9889.0 12903.5 15337.0 16688.0 T 1230.4 4631.8 9330.7 14019.4 18317.7 21957.3 23941.7 T 1953.6 6604.8 13041.3 19463.9 25485.3 30759.1 33590.2 T 3017.1 9265.4 17866.6 26511.7

δP/P (%) = 373.15 K 0.00 −0.14 0.54 −0.91 0.79 −0.02 0.00 = 383.15 K 0.00 −0.08 0.30 −0.51 0.44 −0.03 0.00 = 393.15 K 0.00 −0.02 0.09 −0.16 0.15 −0.05 0.00 = 403.15 K 0.00 0.03 −0.09 0.15 −0.11 −0.07 0.00 = 413.15 K 0.00 0.08 −0.27 0.44

γ1

γ2

GE

x1

y1,cal

1.3495 1.2434 1.2036 1.1776 1.1042 1.0172 1.0000

1.0000 1.0047 1.0127 1.0289 1.1413 1.6290 2.2957

0.0 98.1 202.7 295.5 338.5 198.5 0.0

0.6985 0.9003 1.0000

0.9699 0.9900 1.0000

1.2748 1.2139 1.1865 1.1563 1.0876 1.0140 1.0000

1.0000 1.0028 1.0087 1.0277 1.1330 1.5311 2.0244

0.0 85.8 185.5 272.7 306.7 175.2 0.0

0.0000 0.1262 0.3053 0.4945 0.6985 0.9003 1.0000

0.0000 0.6854 0.8639 0.9307 0.9663 0.9891 1.0000

1.2267 1.1906 1.1692 1.1370 1.0739 1.0115 1.0000

1.0000 1.0017 1.0067 1.0270 1.1238 1.4512 1.8253

0.0 76.9 171.1 251.5 277.8 155.1 0.0

0.0000 0.1262 0.3053 0.4945 0.6985 0.9003 1.0000

0.0000 0.6589 0.8474 0.9219 0.9625 0.9881 1.0000

1.1995 1.1722 1.1514 1.1192 1.0628 1.0097 1.0000

1.0000 1.0014 1.0063 1.0268 1.1137 1.3853 1.6779

0.0 71.2 159.0 231.6 251.4 137.9 0.0

0.0000 0.1262 0.3053 0.4945 0.6985 0.9003 1.0000

0.0000 0.6328 0.8296 0.9125 0.9586 0.9870 1.0000

1.1897 1.1579 1.1333 1.1028

1.0000 1.0016 1.0075 1.0271

0.0 68.5 149.2 212.6

0.0000 0.1262 0.3053 0.4945 0.6985 0.9003 1.0000

0.0000 0.6072 0.8106 0.9025 0.9546 0.9859 1.0000

P/Pa

δP/P (%)

T 34810.2 42243.8 46179.6 T 4543.0 12801.0 24034.8 35484.6 46749.7 56976.6 62321.5 T 6683.9 17435.5 31798.2 46736.2 61815.4 75584.9 82691.3 T 9626.9 23433.1 41431.9 60649.2 80572.3 98758.0 108024.6 T 13597.2 31102.0 53233.4 77632.3 103638.1 127244.3 139113.8

= 413.15 K −0.33 −0.10 0.00 = 423.15 K 0.00 0.12 −0.42 0.69 −0.52 −0.14 0.00 = 433.15 K 0.00 0.17 −0.57 0.93 −0.69 −0.19 0.00 = 443.15 K 0.00 0.22 −0.72 1.16 −0.84 −0.25 0.00 = 453.15 K 0.00 0.27 −0.87 1.37 −0.97 −0.32 0.00

γ1

γ2

GE

1.0538 1.0083 1.0000

1.1027 1.3307 1.5688

227.1 123.4 0.0

1.1950 1.1471 1.1148 1.0875 1.0468 1.0074 1.0000

1.0000 1.0025 1.0101 1.0276 1.0909 1.2851 1.4889

0.0 68.6 141.3 194.3 204.7 111.3 0.0

1.2140 1.1391 1.0958 1.0731 1.0414 1.0069 1.0000

1.0000 1.0039 1.0139 1.0284 1.0783 1.2469 1.4320

0.0 71.4 135.1 176.5 183.8 101.5 0.0

1.2462 1.1335 1.0762 1.0594 1.0374 1.0068 1.0000

1.0000 1.0057 1.0189 1.0293 1.0647 1.2146 1.3938

0.0 76.7 130.5 158.9 164.2 93.9 0.0

1.2913 1.1299 1.0560 1.0462 1.0347 1.0070 1.0000

1.0000 1.0081 1.0249 1.0304 1.0503 1.1873 1.3710

0.0 84.6 127.1 141.2 145.6 88.3 0.0

u(T) = 0.02 K, u(P) = 0.03 P/Pa for P < 600 Pa; 0.01 P/Pa for 600 < P/Pa < 1300; 0.003 P/Pa for 1.3 < P/kPa < 200, u(x1) = 0.0002, u(y1) = 0.001, u(γ1) = u(γ2) = 0.05.

Figure 1. Relative deviation of the experimental vapor pressures of n-tetradecane from values obtained with Antoine equation as a function of temperature T/K: △, this work; ×, Mokbel et al.;12 +, Morgan et al.;13 ○, Vargaftik (Handbook of the Thermal Properties of Gases and Liquids).14

Figure 2. Experimental and calculated P-x(y) behavior of the system ethyl hexanoate (1) + n-tetradecane (2) at different temperatures: ■, 373.15 K; ▲, 393.15 K; ◆, 413.15 K; ●, 433.15 K; ○, 453.15 K; , calculated values using Barker’s method. 493



Article

Table 3. Values of the Vapor Pressure P, Standard Deviations δP/P (%), Activity Coefficients γ1 and γ2, and Excess Molar Gibbs Functions GE for the Binary System Ethyl Decanoate (1) + Tetradecane (2)a x1

y1,cal

0.0000 0.1211 0.3046 0.5027 0.6916 0.8931 1.0000

0.0000 0.3220 0.5530 0.6172 0.6339 0.7466 1.0000

444.0 574.1 713.5 772.5 771.1 705.1 582.7

0.0000 0.1211 0.3046 0.5027 0.6916 0.8931 1.0000

0.0000 0.2866 0.4984 0.5955 0.6580 0.7954 1.0000

751.6 929.4 1113.2 1172.8 1184.6 1119.8 977.1

0.0000 0.1211 0.3046 0.5027 0.6916 0.8931 1.0000

0.0000 0.2569 0.4516 0.5763 0.6776 0.8324 1.0000

1230.4 1466.1 1705.1 1759.8 1795.3 1741.7 1585.7

0.0000 0.1211 0.3046 0.5027 0.6916 0.8931 1.0000

0.0000 0.2325 0.4151 0.5616 0.6931 0.8585 1.0000

1953.6 2258.1 2567.2 2611.6 2686.0 2656.8 2497.8

0.0000 0.1211 0.3046 0.5027

0.0000 0.2130 0.3895 0.5521

3017.1 3402.0 3803.1 3834.5

a

P/Pa

δP/P (%) T = 373.15 0.00 0.19 −1.21 1.22 0.89 −0.85 0.00 T = 383.15 0.00 −0.11 0.46 −0.46 −0.18 0.29 0.00 T = 393.15 0.00 −0.46 1.45 −1.23 −0.45 0.84 0.00 T = 403.15 0.00 −0.74 1.93 −1.50 −0.35 0.96 0.00 T = 413.15 0.00 −0.92 2.07 −1.56

γ1

γ2

GE

x1

y1,cal

P/Pa

2.3397 2.6153 2.2495 1.6071 1.2017 1.0198 1.0000

1.0000 0.9953 1.0446 1.3220 2.0413 3.7938 5.3076

0.0 348.2 860.3 1170.5 1077.0 496.5 0.0

0.6916 0.8931 1.0000

0.7044 0.8757 1.0000

3969.5 3979.6 3829.0

2.3708 2.2540 1.8549 1.4275 1.1549 1.0174 1.0000

1.0000 1.0043 1.0624 1.2737 1.7488 2.8399 3.8465

0.0 325.6 733.6 953.2 866.4 404.5 0.0

0.0000 0.1211 0.3046 0.5027 0.6916 0.8931 1.0000

0.0000 0.1980 0.3740 0.5474 0.7120 0.8861 1.0000

4543.0 5021.8 5548.8 5572.7 5797.7 5860.3 5726.1

2.3530 1.9712 1.5708 1.2874 1.1137 1.0147 1.0000

1.0000 1.0115 1.0757 1.2320 1.5303 2.1977 2.8611

0.0 301.4 615.6 754.3 672.5 317.9 0.0

0.0000 0.1211 0.3046 0.5027 0.6916 0.8931 1.0000

0.0000 0.1870 0.3670 0.5469 0.7162 0.8913 1.0000

6683.9 7273.8 7980.1 8019.6 8373.5 8492.9 8371.0

2.2707 1.7495 1.3734 1.1854 1.0811 1.0123 1.0000

1.0000 1.0162 1.0825 1.1944 1.3711 1.7803 2.2310

0.0 274.2 508.8 582.8 507.0 243.3 0.0

0.0000 0.1211 0.3046 0.5027 0.6916 0.8931 1.0000

0.0000 0.1794 0.3668 0.5500 0.7179 0.8923 1.0000

9626.9 10352.4 11321.9 11432.3 11964.4 12124.5 11985.4

2.1257 1.5781 1.2438 1.1169

1.0000 1.0181 1.0821 1.1608

0.0 244.1 416.7 445.7

0.0000 0.1211 0.3046 0.5027 0.6916 0.8931 1.0000

0.0000 0.1747 0.3721 0.5560 0.7176 0.8898 1.0000

13597.2 14494.8 15858.5 16150.0 16920.4 17066.2 16835.0

K

K

K

K

K

δP/P (%) T = 413.15 −0.15 0.85 0.00 T = 423.15 0.00 −0.98 2.03 −1.54 0.05 0.68 0.00 T = 433.15 0.00 −0.97 1.91 −1.50 0.21 0.52 0.00 T = 443.15 0.00 −0.89 1.73 −1.44 0.31 0.40 0.00 T = 453.15 0.00 −0.77 1.50 −1.36 0.37 0.30 0.00

γ1

γ2

GE

1.0572 1.0102 1.0000

1.2604 1.5177 1.8363

377.4 184.2 0.0

1.9428 1.4494 1.1660 1.0763 1.0417 1.0084 1.0000

1.0000 1.0177 1.0752 1.1316 1.1887 1.3616 1.5976

0.0 212.4 342.0 346.5 286.8 142.4 0.0

1.7526 1.3568 1.1273 1.0585 1.0338 1.0072 1.0000

1.0000 1.0154 1.0639 1.1072 1.1473 1.2813 1.4694

0.0 181.5 286.5 285.3 235.4 118.4 0.0

1.5757 1.2940 1.1189 1.0595 1.0331 1.0066 1.0000

1.0000 1.0119 1.0497 1.0872 1.1295 1.2589 1.4262

0.0 153.2 250.4 260.2 221.3 112.2 0.0

1.4204 1.2555 1.1349 1.0764 1.0388 1.0067 1.0000

1.0000 1.0075 1.0340 1.0711 1.1303 1.2842 1.4551

0.0 128.5 232.9 268.1 241.6 123.2 0.0

K

K

K

K

K


Figure 3. Experimental and calculated P−x(y) behavior of the system ethyl decanoate (1) + n-tetradecane (2) at different temperatures: ■, 373.15 K; ▲, 383.15 K; ◆, 393.15 K; ●, 403.15 K; ○, 413.15 K; , calculated values using Barker’s method.

Figure 4. Experimental and calculated P−x(y) behavior of the system ethyl tetradecanoate (1) + n-tetradecane (2) at different temperatures: ■, 373.15 K; ▲, 393.15 K; ◆, 413.15 K; ●, 433.15 K; ○, 453.15 K; , calculated values using Barker’s method. 494



Article

Table 4. Values of the Vapor Pressure P, Standard Deviations δP/P (%), Activity Coefficients γ1 and γ2, and Excess Molar Gibbs Functions GE for the Binary System Ethyl Tetradecanoate (1) + Tetradecane (2)a x1

y1,cal

0.0000 0.1006 0.3006 0.4978 0.7003 0.8908 1.0000

0.0000 0.0146 0.0454 0.0762 0.1145 0.2157 1.0000

0.0000 0.1006 0.3006 0.4978 0.7003 0.8908 1.0000

0.0000 0.0162 0.0477 0.0804 0.1280 0.2602 1.0000

0.0000 0.1006 0.3006 0.4978 0.7003 0.8908 1.0000

0.0000 0.0177 0.0503 0.0854 0.1422 0.3053 1.0000

0.0000 0.1006 0.3006 0.4978 0.7003 0.8908 1.0000

0.0000 0.0190 0.0532 0.0912 0.1574 0.3495 1.0000

0.0000 0.1006 0.3006 0.4978

0.0000 0.0203 0.0565 0.0978

a

P/Pa

δP/P (%)

T = 373.15 0.00 0.03 0.34 −0.39 0.21 −0.05 0.00 T = 383.15 751.6 0.00 690.8 0.03 583.4 0.27 482.1 −0.32 374.0 0.17 216.2 −0.04 62.3 0.00 T = 393.15 1230.4 0.00 1134.3 0.04 964.1 0.23 795.8 −0.28 602.4 0.15 336.5 −0.04 114.3 0.00 T = 403.15 1953.6 0.00 1805.1 0.05 1540.3 0.21 1269.2 −0.26 943.6 0.14 517.6 −0.04 201.9 0.00 T = 413.15 3017.1 0.00 2792.1 0.06 2387.0 0.19 1962.5 −0.24

γ1

γ2

GE

x1

y1,cal

1.9011 1.8083 1.5658 1.3217 1.1247 1.0181 1.0000

1.0000 1.0029 1.0420 1.1697 1.4963 2.2232 3.0530

0.0 192.9 507.6 675.0 630.0 320.3 0.0

0.7003 0.8908 1.0000

0.1735 0.3917 1.0000

1.9611 1.7802 1.4771 1.2512 1.0930 1.0131 1.0000

1.0000 1.0052 1.0544 1.1789 1.4463 1.9520 2.4549

0.0 199.8 491.6 618.7 550.8 269.7 0.0

0.0000 0.1006 0.3006 0.4978 0.7003 0.8908 1.0000

0.0000 0.0214 0.0601 0.1055 0.1907 0.4306 1.0000

1.9700 1.7368 1.4037 1.1950 1.0671 1.0089 1.0000

1.0000 1.0067 1.0621 1.1821 1.4006 1.7434 2.0327

0.0 201.2 470.8 564.6 478.6 224.1 0.0

0.0000 0.1006 0.3006 0.4978 0.7003 0.8908 1.0000

0.0000 0.0225 0.0639 0.1142 0.2092 0.4657 1.0000

1.9382 1.6823 1.3422 1.1505 1.0462 1.0054 1.0000

1.0000 1.0075 1.0658 1.1799 1.3581 1.5823 1.7328

0.0 197.9 445.9 512.5 413.7 183.9 0.0

0.0000 0.1006 0.3006 0.4978 0.7003 0.8908 1.0000

0.0000 0.0235 0.0681 0.1242 0.2292 0.4963 1.0000

1.8773 1.6205 1.2905 1.1158

1.0000 1.0078 1.0662 1.1730

0.0 190.7 417.4 462.7

0.0000 0.1006 0.3006 0.4978 0.7003 0.8908 1.0000

0.0000 0.0244 0.0725 0.1356 0.2511 0.5222 1.0000

K

444.0 406.5 340.0 281.1 225.2 137.3 32.6

K

K

K

K

P/Pa

δP/P (%)

T = 413.15 0.14 −0.04 0.00 T = 423.15 4543.0 0.00 4208.5 0.07 3598.5 0.16 2950.7 −0.21 2149.7 0.12 1184.1 −0.04 571.2 0.00 T = 433.15 6683.9 0.00 6195.4 0.06 5290.5 0.12 4325.4 −0.16 3138.9 0.10 1762.8 −0.03 919.8 0.00 T = 443.15 9626.9 0.00 8924.9 0.05 7602.4 0.05 6195.9 −0.08 4493.3 0.05 2598.0 −0.02 1443.3 0.00 T = 453.15 13597.2 0.00 12604.0 0.01 10699.0 −0.04 8690.5 0.05 6315.7 −0.03 3792.1 0.01 2211.3 0.00

γ1

γ2

GE

1.0303 1.0027 1.0000

1.3183 1.4585 1.5220

356.3 149.8 0.0

1.7980 1.5545 1.2466 1.0897 1.0191 1.0009 1.0000

1.0000 1.0077 1.0641 1.1618 1.2802 1.3654 1.3798

0.0 180.3 385.9 415.4 307.1 122.4 0.0

1.7097 1.4866 1.2090 1.0714 1.0128 1.0001 1.0000

1.0000 1.0073 1.0599 1.1466 1.2432 1.2985 1.2940

0.0 167.3 351.9 371.1 267.1 102.9 0.0

1.6196 1.4187 1.1766 1.0604 1.0116 1.0004 1.0000

1.0000 1.0069 1.0540 1.1276 1.2066 1.2549 1.2586

0.0 152.5 315.7 329.8 237.2 92.5 0.0

1.5329 1.3519 1.1482 1.0562 1.0157 1.0019 1.0000

1.0000 1.0065 1.0470 1.1051 1.1698 1.2326 1.2727

0.0 136.2 277.5 291.7 218.2 92.3 0.0

K

1441.0 787.1 344.8

K

K

K

K


Figure 5. GE against x1 for the ethyl hexanoate (1) + tetradecane (2) system at different temperatures: ■, 373.15 K; ○, 453.15 K; solid line, calculated with modified UNIFAC (Gmehling) for GE at 373.15 K; ···, calculated with modified UNIFAC (Gmehling) for GE at 453.15 K.

Figure 6. GE against x1 for the ethyl decanoate (1) + tetradecane (2) system at different temperatures: ■, 373.15 K; ○, 453.15 K; solid line, calculated with modified UNIFAC (Gmehling) for GE at 373.15 K; ···, calculated with modified UNIFAC (Gmehling) for GE at 453.15 K. 495



Article

and (ethyl tetradecanoate (1) + n-tetradecane (2)) at different temperatures are given in Tables 2 to 4. In a previous work, we have presented the vapor pressures of the pure quoted esters, FAEE.8 Regarding the vapor pressures of n-tetradecane, the agreement is about 2 % between the values obtained in the present study and the data given in the literature12−14 (Figure 1). From the experimental results, the activity coefficients, γ1 and γ2, along with the excess molar Gibbs energies, GE, were calculated by Barker’s method,15 using the Redlich−Kister eq 1:

with the virial coefficients are presented in Table 7. The virial coefficients of the pure compounds were obtained from Pitzer correlation,17 whereas the mixed virial coefficients were calculated by using Lorentz−Berthelot combining rules. The experimental temperature and pressure values of the pure compounds were fitted to the Antoine eq 3. The values of constants A, B, and C and the standard deviations are given in Table 8. log10 P /Pa = A −

n−1

GE /RT = x1(1 − x1) ∑ Ai (2x1 − 1)i

where x1 is the molar fraction of FAEE. In Table 5 the values of the parameters Ai and the standard deviation for the pressure are reported. The Wilson equation16 was also used: GE /RT = −x1 ln[x1 + Λ12(1 − x1)] − (1 − x1)ln[(1 − x1) + Λ 21x1]

(3)

The experimental values of the vapor pressures are plotted in Figures 2 to 4. As shown in Figure 3, the binary mixture (ethyl decanoate (1) + tetradecane (2)) exhibits maximum azeotropic behavior. The azeotropic compositions vary from 0.6 (at 373.15 K) to 0.8 (at 453.15 K). Positive deviations in GE are observed for all of the systems investigated in this work, and the GE values decrease with increasing temperature. The lower values of GE for the system (ethyl hexanoate + tetradecane) result probably from an order/disorder phenomenon known as the Patterson effect, which is influenced by the difference between chain lengths of the compounds. As reported in the literature,18 high positive values for the entropy of mixing are a consequence of disorder caused by short or spherical solvents which are able to destroy the conformational order in liquid long-chain hydrocarbons. The equimolar GE of (ethyl hexanoate + tetradecane)

(1)

i=0

B C + t /°C

(2)

where x1 is the mole fraction of the FAEE. The parameters Λij and the corresponding standard deviations σ (Pa) are reported in Table 6. The small values of σ (Pa) confirm the consistency of the model with the experimental data. The molar volumes of the pure compounds (FAEE and n-tetradecane) estimated with the Rackett correlation together

Table 5. Coefficients Ai and Standard Deviations σ for Least-Squares Representations by eq 1 T/K

A1

373.15 383.15 393.15 403.15 413.15 423.15 433.15 443.15 453.15

0.38393 0.34502 0.31000 0.27823 0.24911 0.22218 0.19698 0.17313 0.15023

373.15 383.15 393.15 403.15 413.15 423.15 433.15 443.15 453.15

1.50698 1.19558 0.92251 0.69553 0.51942 0.39448 0.31735 0.28270 0.28452

373.15 383.15 393.15 403.15 413.15 423.15 433.15 443.15 453.15

0.87131 0.77741 0.69091 0.61130 0.53830 0.47175 0.41154 0.35749 0.30925

σ

A2

σ

Ethyl Hexanoate (1) + Tetradecane (2) 0.26565 0.024 0.23125 0.013 0.19873 0.004 0.16782 0.004 0.13831 0.012 0.10997 0.019 0.08258 0.026 0.05596 0.033 0.02995 0.040 Ethyl Decanoate (1) + Tetradecane (2) −0.029 0.40955 0.067 0.011 0.24198 0.025 0.038 0.09775 0.081 0.052 −0.00883 0.107 0.057 −0.07317 0.115 0.058 −0.09779 0.115 0.056 −0.08812 0.110 0.052 −0.04982 0.103 0.046 0.01209 0.093 Ethyl Tetradecanoate (1) + Tetradecane (2) 0.005 0.23684 0.010 0.004 0.11227 0.009 0.004 0.01568 0.008 0.004 −0.05600 0.007 0.004 −0.10488 0.007 0.003 −0.13236 0.006 0.003 −0.13928 0.005 0.001 −0.12608 0.003 0.001 −0.09302 0.002 0.012 0.007 0.002 0.002 0.006 0.010 0.013 0.017 0.020

496

A3

σ

0.18145 0.12901 0.09301 0.07150 0.06289 0.06592 0.07954 0.10292 0.13539

0.047 0.026 0.009 0.008 0.023 0.037 0.050 0.063 0.077

−0.24739 −0.09040 0.03096 0.11574 0.16149 0.17184 0.15565 0.12217 0.07849

0.132 0.053 0.174 0.236 0.258 0.257 0.246 0.227 0.203

0.00797 0.00839 0.00279 −0.00554 −0.01336 −0.01743 −0.01451 −0.00142 0.02489

0.019 0.016 0.014 0.013 0.013 0.011 0.009 0.005 0.003



Article

Table 6. Coefficients Λij and Pressure Standard Deviations σ/Pa for Least-Squares Representation by eq 2 All Binary Mixtures Esters + n-Tetradecane ethyl hexanoate (1) + n-tetradecane (2)

ethyl decanoate (1) + n-tetradecane (2)

ethyl tetradecanoate (1) + n-tetradecane (2)

T/K

Λ12

Λ21

σ/Pa

Λ12

Λ21

σ/Pa

Λ12

Λ21

σ/Pa

373.15 383.15 393.15 403.15 413.15 423.15 433.15 443.15 453.15

1.78871 1.78078 1.76389 1.73733 1.69961 1.64871 1.57977 1.48269 1.32793

0.18122 0.20990 0.24000 0.27227 0.30814 0.34949 0.40026 0.46848 0.57892

0.00514 0.00206 0.00376 0.00583 0.00728 0.00822 0.00875 0.00896 0.00897

0.66964 0.74236 0.73915 0.65046 0.51665 0.42668 0.42540 0.55187 0.93139

0.16663 0.28077 0.45056 0.69850 1.01308 1.27903 1.37331 1.22009 0.78629

0.02373 0.00690 0.00871 0.01097 0.01128 0.01156 0.01115 0.01029 0.00892

0.99960 0.86632 0.71780 0.58168 0.47933 0.41534 0.38693 0.39326 0.44801

0.30117 0.45553 0.64944 0.86556 1.07190 1.24163 1.35789 1.40857 1.36721

0.02045 0.01340 0.00978 0.00787 0.00717 0.00640 0.00507 0.00312 0.00058

Table 7. Molar Volumes V* and the Virial Coefficient Bij for {FAEE (1) + Tetradecane (2)} ethyl hexanoate

ethyl decanoate

ethyl tetradecanoate

tetradecane

V*

−B11

−B12

V*

−B11

−B12

V*

−B11

−B12

V*

−B22

T/K

cm3·mol−1

cm3·mol−1

cm3·mol−1

cm3·mol−1

cm3·mol−1

cm3·mol−1

cm3·mol−1

cm3·mol−1

cm3·mol−1

cm3·mol−1

cm3·mol−1

373.15 383.15 393.15 403.15 413.15 423.15 433.15 443.15 453.15

174.52 176.82 179.23 181.77 184.43 187.23 190.20 193.34 196.68

2463 2285 2128 1987 1861 1747 1644 1549 1462

4471 4111 3797 3520 3275 3055 2858 2680 2519

217.27 219.67 222.15 224.72 227.39 230.17 233.06 236.07 239.21

7998 7241 6595 6038 5554 5129 4755 4422 4124

8681 7861 7161 6558 6034 5575 5169 4809 4487

241.44 243.97 246.58 249.27 252.05 254.93 257.91 261.00 264.21

17003 15156 13606 12293 11171 10203 9361 8625 7975

10454 9451 8599 7868 7236 6684 6198 5768 5384

268.27 271.11 274.04 277.08 280.23 283.49 286.89 290.42 294.10

9542 8637 7866 7203 6627 6123 5678 5283 4930

Table 8. Antoine Equation Parameters A, B, and C and Mean Relative Deviation da temperature range

a

parameters of the Antoine equation

FAEE

T/K

A (σA)

ethyl hexanoate ethyl decanoate ethyl tetradecanoate tetradecane

253.41 to 462.44 303.1 to 462.37 333.22 to 462.3 303.14 to 462.26

9.106 (0.028) 9.850 (0.065) 10.153 (0.096) 9.705 (0.035)

B (σB) 1476 2169 2571 2033

(14) (42) (61) (21)

C (σC) 192.2 205.7 197.6 193.2

(1.2) (2.9) (3.7) (1.5)

100 d 0.9 0.9 0.75 0.84

d = 1/n∑(|Pexp − Pcal|/Pexp).

decreases with increasing temperature from 297.8 J·mol−1 at T = 373.15 K to 141.5 J·mol−1 at T = 453.15 K. For the (ethyl decanoate + tetradecane) mixture the equimolar GE decreases with increasing temperature from 1210.2 J·mol −1 at T = 373.15 K to 272.0 J·mol−1 at T = 453.15 K. The equimolar GE of (ethyl tetradecanoate + tetradecane) decreases with increasing temperature from 684.3 J·mol−1 at T = 373.15 K to 293.8 J·mol−1 at T = 453.15 K. The GE(x1 = 0.5)/T data were fitted with a second degree polynomial in 1/T; the derivative at 373.15 K gives HE = 1266.2 J·mol−1, 9254.2 J·mol−1, and 2790.4 J·mol−1 respectively, for (ethyl hexanoate (1) + n-tetradecane (2)), (ethyl decanoate (1) + n-tetradecane (2)) and (ethyl tetradecanoate (1) + n-tetradecane (2)) systems. The UNIFAC group contribution method is widely used in chemical engineering.19 In the modified UNIFAC, the modifications concern the combinatorial term and the group interaction parameters which become dependent on temperature. Using the parameters of modified UNIFAC (Gmehling version),20 we calculated GE. Figures 5 to 7 show the experimental and theoretical curves of GE at 373.15 and 453.15 K for the different binary systems.

Figure 7. GE against x1 for the ethyl tetradecanoate (1) + tetradecane (2) system at different temperatures: ■, 373.15 K; ○, 453.15 K; solid line, calculated with modified UNIFAC (Gmehling) for GE at 373.15 K; ···, calculated with modified UNIFAC (Gmehling) for GE at 453.15 K.

As can be seen from Figures 5 to 7, the GE curves are asymmetrical, and important deviations are obtained between experimental values of GE and those predicted using modified UNIFAC (Gmehling version) model. This can be explained by 497



Article

(12) Mokbel, I.; Blondel-Telouk, A.; Vellut, D.; Jose, J. Vapor−liquid equilibria of two binary mixtures: benzene + n-tetradecane and benzene + squalane. Fluid Phase Equilib. 1998, 149, 287−308. (13) Morgan, D. L.; Kobayashi, R. Direct vapor pressure measurements of ten n-alkanes in the C10-C28 range. Fluid Phase Equilib. 1994, 97, 21 l−242. (14) Vargaftik, N. B. Spravochnik po teplofizicheskim svoistvam gazov i zhidkostei (the Thermal Properties of Gases and Liquids); Fizmatgiz: Moscow, 1963. (15) Barker, J. A. Determination of activity coefficients from total pressure measurements. Aust. J. Chem. 1953, 6, 207−210. (16) Wilson, G. M. Vapor-Liquid Equilibrium. XI. A New Expression for the Excess Free Energy of Mixing. J. Am. Chem. Soc. 1964, 86 (2), 127−130. (17) Pitzer, K. S.; Curl, R. F. The volumetric and thermodynamic properties of fluids. III. Empirical equation for the second virial coefficient. J. Am. Chem. Soc. 1957, 79, 2369−2370. (18) Kniaź, K. Influence of size and shape effects on the solubility of hydrocarbons: the role of the combinatorial entropy. Fluid Phase Equilib. 1991, 68, 35−46. (19) Khimeche, K.; Dahmani, A. Determination by DSC of solid− liquid diagrams for polyaromatic−4,4′diaminodiphenylmethane binary systems. J. Therm. Anal. Calorim. 2006, 84, 47−52. (20) 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. (21) Khimeche, K.; Dahmani, A. Solid−Liquid Equilibria of Naphthalene + Alkanediamine Mixtures. J. Chem. Eng. Data 2006, 51, 382−385.

the complexity of the systems, attributed to intramolecular effects, especially the proximity effect.19,21

4. SUMMARY Vapor−liquid equilibrium data for the three binary mixtures of (ethyl hexanoate (1) + n-tetradecane (2)), (ethyl decanoate (1) + n-tetradecane (2)), and (ethyl tetradecanoate (1) + n-tetradecane (2)) were measured, using a static method between T = (373.15 and 453.15) K. The molar excess Gibbs energies GE were obtained with Barker’s method and fitted to the Redlich−Kister equation. The experimental results have been carefully analyzed and compared with the group contribution model (UNIFAC). The binary mixture (ethyl decanoate (1) + tetradecane (2)) exhibits maximum azeotropic behavior. The modified UNIFAC (Gmehling version) model is not capable of correlating accurately GE.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

REFERENCES

(1) Antolin, G.; Tinaut, F.; Briceno, Y. Optimization of biodiesel production by sunflower oil transesterification. Bioresour. Technol. 2002, 83, 111−114. (2) Al-Widyan, M. I.; Al-Shyoukh, A. O. Experimental evaluation of the transesterifation of waste palm oil into biodiesel. Bioresour. Technol. 2002, 85, 253−256. (3) Tashtoush, G. M.; Al-Widyan, M. I.; Al-Shyoukh, A. O. Experimental study on evaluation and optimization of conversion of waste animal fat into biodiesel. Energy Convers. Manage. 2004, 45, 2697−2711. (4) Hoekman, S. K.; Broch, A.; Robbins, C.; Ceniceros, E.; Natarajan, M. Review of biodiesel composition, properties, and specifications. Renewable Sustainable Energy Rev. 2012, 16, 143−169. (5) Alleman, T. L.; Fouts, L.; McCormick, R. L. Quality analysis of wintertime B6-B20 biodiesel blend samples collected in the United States. Fuel Process. Technol. 2011, 92, 1297−1304. (6) Bueno, A. V.; Velásquez, J. A.; Milanez, L. F. Heat release and engine performance effects of soybean oil ethyl ester blending into diesel fuel. Energy 2011, 36, 3907−3916. (7) Lin, Y.-C.; Wu, T.-Y.; Ou-Yang, W.-C.; Chen, C.-B. Characterization of particle size distribution from diesel engines fueled with palm-biodiesel blends and paraffinic fuel blends. Atmos. Environ. 2009, 43, 2642−2647. (8) Benziane, M.; Khimeche, K.; Mokbel, I.; Sawaya, T.; Dahmani, A.; Jose, J. Experimental Vapor Pressures of Five Saturated Fatty Acid Ethyl Ester (FAEE) Components of Biodiesel. J. Chem. Eng. Data 2011, 56, 4736−4740. (9) Mokbel, I.; Rauzy, E.; Loiseleur, H.; Berro, C.; Jose, J. Vapor pressures of 12 alkycyclohexanes, cyclopentane, butylcyclopentane and transdecahydronaphthalene down to 0.5 Pa, experimental results, correlation and prediction by an equation of state. Fluid Phase Equilib. 1995, 108, 103−120. (10) Chiali-Baba Ahmed, N.; Negadi, L.; Mokbel, I.; Ait Kaci, A.; Jose, J. Experimental determination of the isothermal (vapour + liquid) equilibria of binary aqueous solutions of sec-butylamine and cyclohexylamine at several temperatures. J. Chem. Thermodyn. 2012, 44, 116−120. (11) Mokbel, I.; Razzouk, A.; Sawaya, T.; Jose, J. Experimental Vapor Pressures of 2-Phenylethylamine, Benzylamine, Triethylamine, and cis2,6-Dimethylpiperidine in the Range between 0.2 Pa and 75 kPa. J. Chem. Eng. Data 2009, 54, 819−822. 498


Isothermal Vapor–Liquid Equilibria of n-Tetradecane+ Ethyl

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