Isothermal Vapor Pressures of Three Binary Systems: n-Tetradecane+

Article pubs.acs.org/jced

Isothermal Vapor Pressures of Three Binary Systems: n‑Tetradecane + Methyl Dodecanoate, Methyl Tetradecanoate, or Methyl Hexadecanoate between 353.15 and 453.15 K Lakhdar Sahraoui,†,‡,∥ Kamel Khimeche,‡ Ilham Mokbel,*,†,§ Mokhtar Benziane,‡ and Jacques Jose† †

Laboratoire Multimatériaux et Interfaces, Univ Lyon, Université Claude Bernard Lyon 1, UMR 5615, F-69622 Lyon, France Ecole Militaire Polytechnique EMP, BP 17 Bordj-El-Bahri, Alger 16111, Algérie § Univ Lyon, Université Jean Monnet, F-42023 Saint-Etienne, France ∥ Ecole Nationale Préparatoire aux Etudes d’Ingéniorat-Rouiba,Alger 16013, Algérie ‡

ABSTRACT: Isothermal vapor pressures of three binary systems, methyl dodecanoate (1) + n-tetradecane (2); methyl tetradecanoate (1) + n-tetradecane (2); and methyl hexadecanoate (1) + n-tetradecane (2), were measured by means of a static apparatus at temperatures between 353.15 and 453.15 K. The data of the pure components were correlated by the Antoine equation. A maximum azeotropic behavior is observed for the binary mixture, methyl dodecanoate (1) + n-tetradecane (2). The molar excess Gibbs energies GE were deduced from Barker’s method by fitting the experimental points through Redlich−Kister equation. The NRTL and UNIQUAC models were applied to regress the experimental vapor liquid equilibrium (VLE). The investigated systems were successfully represented by the two models.

■

INTRODUCTION Due to the depletion of oil resources in combination with increasing energy consumption and the negative environmental impact of fossil fuel use, there is great demand for alternative sources of energy.1−4 In this context, biodiesel is gaining more and more importance as an alternative to replace fossil fuels in terms of nontoxicity, biodegradability, renewability, sulfur content, and low emission of greenhouse-gases effect.5 From a chemical point of view, biodiesel, based principally on fatty acid methyl esters (FAMES) or fatty acid ethyl esters (FAEEs), is produced from vegetable oils or animal fats by transesterification with an alcohol (ethanol or methanol) in alkaline acid or enzymatic catalysis.6,7 Biodiesel can also be used blended with petrodiesel in any percentage without affecting the performance of most diesel equipment. On the other hand, by blending biodiesel with diesel fuel, the combustion efficiency is enhanced and a cost-reduction in the distribution system is obtained.8 Vapor liquid equilibrium (VLE) study is very important to accurately characterize diesel/biodiesel blended fuel to optimize the injection and ignition steps of the engine. In our knowledge, only few researchers have published some experimental data of systems containing fatty acid ester and nonvolatile alkanes (above pentane).9−12 Hao Li et al.9 have reported the isobaric vapor−liquid equilibrium data of n-C14 + methyltetradecanoate at 5.00 kPa using ebulliometry method. The studied temperature range is small, between 425 and 465 K. The present work is a continuation of a research program concerning the investigation of the thermodynamic properties of biodiesel/diesel mixtures.10−12 Experimental measurements of © XXXX American Chemical Society

VLE are presented for the binary mixtures of methyl dodecanoate, methyl tetradecanoate, and methyl hexadecanoate with n-tetradecane at a large temperature range, between 253.15 and 433.15 (or 453.15) K. From Barker’s method and Redlich−Kister equation, the composition of the vapor phase was deduced. The VLE data were satisfactorily correlated by NRTL and UNIQUAC models.

2. EXPERIMENTAL PROCEDURES 2.1. Chemicals. The suppliers and the purities of the three saturated FAMEs and n-tetradecane are reported in Table 1.These compounds were used without further purification. 2.2. Apparatus. Vapor pressures of pure compounds and binary systems were measured using a static apparatus described Table 1. Source and Purity of Compounds chemical name

synonym

methyl methyl dodecanoate laurate methyl methyl tetradecanoate myristate methyl methyl hexadecanoate palmitate n-tetradecane

CAS no.

source

supplier GC purity purity mass mass fraction fraction

111-82-0 Sigma-Aldrich

≥0.98

>0.99


≥0.98

>0.99


≥0.97

>0.99


≥0.99

>0.99

Received: January 30, 2017 Accepted: May 2, 2017

A

DOI: 10.1021/acs.jced.7b00099 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 4. Experimental Vapor Pressures of n-Tetradecane T/K

Pexp/Paa

δP/Pb (%)

351.75 361.80 361.89 371.91 381.93 382.07 391.95 392.00 402.74 412.69 422.55 432.39 442.49 452.49

124 232 232 422 717 716 1186 1186 1947 3029 4545 6661 9461 13460

−0.1 0.1 −0.5 1.2 0.1 −0.7 0.2 −0.1 −0.7 0.1 0.3 0.6 −1.0 0.1

a

Combined expanded uncertainty (0.95 level of confidence, k = 2) in the vapor pressure measurements is Uc (P/Pa) = 0.1 Pa + 0.03*P for P < 600 Pa, Uc (P/Pa) = 0.01*P for P in the range (600 to 1300) Pa, Uc (P/Pa) = 0.003*P for P > 1300 Pa, and the standard uncertainty of the temperature measurement is u (T) = 0.02 K. bδP/P = (Pexp − Pcal)/Pexp where Pcal corresponds to the pressure calculated using Antoine parameters (Table 3).

Figure 1. Sample degassing system.

Table 2. Analytical GC Conditions for the Mole Fraction Determination of Methylesters and n-Tetradecane Mixtures column type

HP-5, length 30 m; internal diameter = 0.32 mm; film thickness = 0.25 μm

injector type injection volume detector type oven temperature carrier gas

split; flow = 21 mL/min, 300 °C 1 μL FID; 300 °C From 50 to 290 °C, rate 30 °C/min H2: 2.1 mL/min

Figure 2. Vapor pressures of tetradecane. Comparison between experimental and literature data: ⧫, this work; ◊, ref 15; •, ref 16; ▲, ref 17; × , ref 18.

616A) where the measurement side is connected to a sample cell via a high-vacuum valve. The reference side of the pressure gauge is submitted to a permanent dynamic pumping. The cell equilibrium temperature is obtained using a type J thermocouple calibrated against a 25 Ω platinum resistance standard thermometer (±0.001 K, ITS 90) and a Leeds and Northrup bridge. Prior to VLE measurements, the sample is degassed. The mixture is charged into the preparation bulb by weighing in the

in detail elsewhere.13,14 The experimental procedure for VLE measurement can be found in our previous paper.12 Only a short description is given herein. The apparatus comprises a differential pressure sensor (MKS Instruments, USA, type 670, model

Table 3. Coefficients A, B, C of the Antoine Equation and Overall Mean Relative Deviation of the Vapor Pressures

a

compound

temperature (T/K)

A (σA)

B (σB)

C (σC)

ΔP/Pa (%)

n-tetradecane methyl dodecanoate methyl tetradecanoate methyl hexadecanoate

351.75−452.49 342.00−442.50 332.40−452.26 332.32−452.65

9.213 (0.06) 10.35 (0.74) 11.35 (0.13) 13.87 (0.14)

1791 (35) 2552 (50) 3355 (96) 5806 (127)

−100.2 (1.8) −54.45 (3.2) −25.15 (5.2) 84.85 (5.1)

0.40 0.39 0.88 0.49

ΔP/P =

1 N

∑

|P exp − P cal| P exp

B



Article

Table 5. Experimental and Calculated VLE Data for the Binary System Methyl Dodecanoate (1) + n-Tetradecane (2)a P/Pa x1

experimental

NRTL

γ1

y1(calculated) UNIQUAC

0.0000 0.1331 0.2567 0.3888 0.5172 0.6987 0.8519 1.0000

135.5 137.6 134.7 128.5 119.5 103.0 84.1 64.4

136.5 136.6 133.3 127.5 119.6 103.1 84.1 61.5

136.5 137.8 134.7 128.9 120.4 103.0 83.6 61.5

0.0000 0.1331 0.2567 0.3888 0.5172 0.6987 0.8519 1.0000

251.7 250.2 251.2 234.9 219.6 191.6 157.5 121.7

250.7 251.7 245.9 235.5 220.8 190.9 157.0 117.7

250.7 253.2 247.5 236.8 221.5 190.4 156.3 117.7

0.0000 0.1331 0.2567 0.3888 0.5172 0.6987 0.8519 1.0000

446.9 448.8 439.1 416.8 387.4 340.6 282.7 221.2

441.9 444.9 435.0 416.8 391.0 338.8 281.0 216.0

441.9 446.2 436.4 417.8 391.2 338.1 280.4 216.0

0.0000 0.1331 0.2567 0.3888 0.5172 0.6987 0.8519 1.0000

762 756 751 710 659 581 488 388

750 757 741 710 666 579 484.5 381.0

750 758 741 710 666 579 484.7 381.0

0.0000 0.1331 0.2567 0.3888 0.5172 0.6987 0.8519 1.0000

1254 1257 1222 1168 1084 957 813 657

1231 1244 1219 1169 1097 956 807 648

1231 1243 1217 1167 1096 957 810 648

0.0000 0.1331 0.2567 0.3888 0.5172 0.6987 0.8519 1.0000

1998 1995 1959 1858 1731 1525 1313 1080

1957 1982 1942 1863 1749 1529 1303 1068

1957 1977 1936 1858 1747 1534 1311 1068

0.0000 0.1331 0.2567 0.3888 0.5172 0.6987

3090 3105 3028 2869 2689 2358

3024 3066 3005 2884 2709 2376

3024 3054 2993 2875 2709 2391

Redlich−Kister T 0.0000 0.1133 0.1680 0.2281 0.2991 0.4405 0.6486 1.0000 T 0.0000 0.1105 0.1711 0.2363 0.3098 0.4501 0.6545 1.0000 T 0.0000 0.1083 0.1699 0.2409 0.3197 0.4598 0.6612 1.0000 T 0.0000 0.1097 0.1750 0.2458 0.3259 0.4756 0.6759 1.0000 T 0.0000 0.1088 0.1747 0.2497 0.3349 0.4883 0.6872 1.0000 T 0.0000 0.1103 0.1767 0.2518 0.3405 0.5050 0.7036 1.0000 T 0.0000 0.1109 0.1769 0.2536 0.3469 0.5201

γ2

GE/J mol−1

NRTL

UNIQUAC

Redlich−Kister

0.0000 0.1109 0.1722 0.2303 0.2955 0.4294 0.6261 1.0000

0.0000 0.1129 0.1688 0.2240 0.2892 0.4273 0.6291 1.0000

3.3519 1.8217 1.3682 1.1694 1.0748 1.0085 0.9943 1.0000

1.0000 1.0401 1.1121 1.1965 1.2820 1.4115 1.4728 1.3178

0.0 334.4 468.3 500.6 461.7 322.4 154.2 0.0

0.0000 0.1130 0.1752 0.2351 0.3031 0.4423 0.6418 1.0000

0.0000 0.1140 0.1725 0.2307 0.2992 0.4416 0.6442 1.0000

2.9184 1.7298 1.3526 1.1755 1.0831 1.0119 0.9948 1.0000

1.0000 1.0342 1.0956 1.1698 1.2512 1.3877 1.4618 1.3125

0.0 308.3 438.9 479.3 451.3 322.9 156.3 0.0

0.0000 0.1149 0.1780 0.2398 0.3106 0.4552 0.6570 1.0000

0.0000 0.1151 0.1761 0.2374 0.3089 0.4555 0.6584 1.0000

2.9399 1.6551 1.3095 1.1645 1.0852 1.0117 0.9921 1.0000

1.0000 1.0367 1.0946 1.1561 1.2254 1.3654 1.4488 1.2360

0.0 305.1 423.2 458.7 435.7 316.3 149.4 0.0

0.0000 0.1165 0.1805 0.2443 0.3180 0.4679 0.6716 1.0000

0.0000 0.1162 0.1796 0.2439 0.3185 0.4688 0.6717 1.0000

2.5359 1.6223 1.3068 1.1547 1.0769 1.0176 0.9996 1.0000

1.0000 1.0293 1.0829 1.1473 1.2148 1.3245 1.4033 1.3626

0.0 285.0 407.4 445.7 421.3 308.6 158.8 0.0

0.0000 0.1179 0.1828 0.2486 0.3254 0.4804 0.6856 1.0000

0.0000 0.1172 0.1831 0.2502 0.3277 0.4816 0.6842 1.0000

2.5278 1.5622 1.2654 1.1357 1.0708 1.0163 0.9985 1.0000

1.0000 1.0311 1.0830 1.1388 1.1951 1.2953 1.3712 1.3037

0.0 280.9 391.2 421.4 397.0 291.7 148.5 0.0

0.0000 0.1190 0.1848 0.2527 0.3325 0.4926 0.6989 1.0000

0.0000 0.1182 0.1864 0.2563 0.3366 0.4938 0.6958 1.0000

2.3956 1.5332 1.2404 1.1110 1.0553 1.0180 1.0033 1.0000

1.0000 1.0293 1.0816 1.1382 1.1868 1.2538 1.3174 1.3631

0.0 274.7 380.9 402.5 370.5 270.2 146.2 0.0

0.0000 0.1198 0.1866 0.2566 0.3396 0.5044

0.0000 0.1192 0.1897 0.2623 0.3452 0.5054

2.3835 1.4934 1.2024 1.0831 1.0394 1.0153

1.0000 1.0307 1.0841 1.1376 1.1759 1.2184

0.0 273.4 368.7 377.1 337.3 241.0

= 353.15

= 363.15

= 373.15

= 383.15

= 393.15

= 403.15

= 413.15

C



Article

Table 5. continued P/Pa

γ1

y1(calculated)

x1

experimental

NRTL

UNIQUAC

0.8519 1.0000

2058 1728

2042 1706

2060 1706

0.0000 0.1331 0.2567 0.3888 0.5172 0.6987 0.8519 1.0000

4652 4710 4563 4315 4072 3550 3143 2694

4547 4614 4525 4342 4080 3591 3114 2647

4547 4593 4504 4330 4086 3626 3151 2647

0.0000 0.1331 0.2567 0.3888 0.5172 0.6987 0.8519 1.0000

6836 6951 6716 6389 6007 5256 4685 4104

6685 6787 6657 6388 6006 5305 4640 4009

6685 6752 6625 6375 6028 5375 4710 4009

Redlich−Kister

NRTL

0.7189 0.7115 1.0000 1.0000 T = 423.15 0.0000 0.0000 0.1118 0.1205 0.1766 0.1882 0.2547 0.2603 0.3526 0.3463 0.5349 0.5159 0.7347 0.7234 1.0000 1.0000 T = 433.15 0.0000 0.0000 0.1137 0.1209 0.1786 0.1896 0.2572 0.2639 0.3572 0.3529 0.5456 0.5271 0.7488 0.7346 1.0000 1.0000

UNIQUAC

γ2

GE/J mol−1

Redlich−Kister

0.7066 1.0000

1.0041 1.0000

1.2667 1.3342

132.3 0.0

0.0000 0.1201 0.1927 0.2679 0.3535 0.5164 0.7167 1.0000

2.4006 1.4559 1.1626 1.0524 1.0206 1.0103 1.0040 1.0000

1.0000 1.0328 1.0882 1.1388 1.1668 1.1844 1.2123 1.2800

0.0 274.2 357.1 349.4 299.2 204.6 112.1 0.0

0.0000 0.1210 0.1957 0.2734 0.3614 0.5269 0.7261 1.0000

2.3848 1.4321 1.1379 1.0295 1.0021 1.0009 1.0013 1.0000

1.0000 1.0334 1.0902 1.1410 1.1653 1.1660 1.1654 1.1900

0.0 274.9 350.5 331.2 270.0 168.9 85.7 0.0

a

Combined expanded uncertainty (0.95 level of confidence, k = 2) in the vapor pressure measurements is Uc (P/Pa) = 0.1 Pa + 0.03*P for P < 600 Pa, Uc (P/Pa) = 0.01*P for P in the range (600 to 1300) Pa, Uc (P/Pa) = 0.003*P for P > 1300 Pa, and the standard uncertainty of the composition is u (x1) = 0.0002; u (T) = 0.02 K.

Table 6. Experimental and Calculated VLE Data for the Binary System Methyl Tetradecanoate (1) + n-Tetradecane (2)a P/Pa x1

experimental

NRTL

γ1

y1(calculated) UNIQUAC

0.0000 0.1260 0.2520 0.3834 0.5099 0.6834 0.8615 1.0000

135.4 116.4 103.4 92.4 78.4 59.0 36.4 13.3

136.5 121.6 107.3 92.6 78.5 58.3 34.8 12.5

136.5 121.5 107.0 92.3 78.5 59.2 36.6 12.5

0.0000 0.1260 0.2520 0.3834 0.5099 0.6834 0.8615 1.0000

251.7 216.0 191.8 171.9 145.6 109.9 69.7 26.7

250.7 223.9 198.0 171.6 146.2 109.9 67.2 25.7

250.7 223.7 197.4 170.9 145.9 111.0 69.7 25.7

0.0000 0.1260 0.2520 0.3834 0.5099 0.6834 0.8615 1.0000

447.2 384.0 341.5 306.6 259.8 196.8 127.8 51.6

441.9 395.5 350.7 305.0 261.2 198.6 124.4 50.5

441.9 395.1 349.7 303.7 260.3 199.6 127.6 50.5

0.0000 0.1260 0.2520 0.3834 0.5099

763 658 585 526 447.0

750 673 598 522 449.3

750 672 597 520 447.6

Redlich−Kister T= 0.0000 0.0182 0.0427 0.0670 0.0951 0.1652 0.3243 1.000 T= 0.0000 0.0195 0.0462 0.0725 0.1032 0.1799 0.3423 1.000 T= 0.0000 0.0210 0.0499 0.0784 0.1120 0.1952 0.3614 1.000 T= 0.0000 0.0228 0.0539 0.0847 0.1213

γ2

GE/J mol−1

NRTL

UNIQUAC

Redlich−Kister

0.0000 0.0160 0.03469 0.05839 0.08803 0.15183 0.31105 1.000

0.0000 0.0164 0.0358 0.0606 0.0908 0.1525 0.2980 1.000

0.8440 1.279 1.312 1.196 1.111 1.067 1.030 1.000

1.000 0.9786 0.9762 1.020 1.082 1.145 1.314 2.151

0.0 35.6 148.2 238.1 271.1 256.6 186.5 0.0

0.0000 0.0182 0.0392 0.0656 0.0981 0.1667 0.3322 1.000

0.0000 0.0183 0.0401 0.0675 0.1008 0.1678 0.3220 1.000

0.7905 1.262 1.311 1.198 1.116 1.077 1.036 1.000

1.000 0.976 0.971 1.013 1.072 1.127 1.316 2.364

0.0 24.0 139.4 234.4 272.3 267.9 207.0 0.0

0.000 0.0204 0.0439 0.0731 0.1087 0.1820 0.3534 1.000

0.0000 0.0205 0.0446 0.0748 0.1112 0.1835 0.3458 1.000

0.7717 1.255 1.308 1.197 1.119 1.085 1.040 1.000

1.000 0.975 0.969 1.011 1.066 1.115 1.320 2.520

0.0 19.7 137.5 235.4 276.3 279.1 223.9 0.0

0.0000 0.0227 0.0488 0.0810 0.1197

0.0000 0.0227 0.0493 0.0824 0.1219

0.7785 1.254 1.304 1.195 1.121

1.000 0.975 0.970 1.011 1.064

0.0 21.5 140.9 239.8 282.1

353.15 K

363.15 K

373.15 K

383.15 K

D



Article


γ1

y1(calculated)

γ2

GE/J mol−1

x1

experimental

NRTL

UNIQUAC

Redlich−Kister

NRTL

UNIQUAC

0.6834 0.8615 1.0000

340.1 225.6 95.9

345.2 221.3 95.2

346.0 225.3 95.2

0.1979 0.3746 1.000

0.1995 0.3691 1.000

1.089 1.042 1.000

1.108 1.323 2.615

289.4 237.0 0.0

0.0000 0.1260 0.2520 0.3834 0.5099 0.6834 0.8615 1.0000

1255 1088 970 873 744 569 384.7 172.3

1231 1107 986 864 747 580 379.7 172.3

1231 1106 984 861 744 580 384.3 172.3

0.0000 0.0251 0.0538 0.0891 0.1311 0.2141 0.3956 1.000

0.0000 0.0250 0.0542 0.0903 0.1329 0.2157 0.3919 1.000

0.8059 1.257 1.296 1.191 1.121 1.092 1.043 1.000

1.000 0.977 0.974 1.014 1.063 1.104 1.326 2.649

0.0 28.4 148.6 246.6 288.8 298.4 246.3 0.0

0.0000 0.1260 0.2520 0.3834 0.5099 0.6834 0.8615 1.0000

1998 1744 1558 1403 1201 924 636 300.3

1957 1764 1576 1385 1202 943 631 301.0

1957 1763 1574 1381 1199 943 635 301.0

0.0000 0.0275 0.0590 0.0975 0.1428 0.2306 0.4164 1.000

0.0000 0.0274 0.0593 0.0983 0.1442 0.2319 0.4140 1.000

0.8514 1.264 1.287 1.185 1.119 1.092 1.042 1.000

1.000 0.980 0.979 1.018 1.064 1.104 1.327 2.624

0.0 39.4 159.6 254.8 295.6 305.3 251.5 0.0

0.0000 0.1260 0.2520 0.3834 0.5099 0.6834 0.8615 1.0000

3086 2717 2434 2193 1887 1460 1020 509

3022 2730 2445 2156 1880 1488 1016 508

3022 2728 2443 2152 1877 1488 1020 508

0.0000 0.0300 0.0643 0.1061 0.1547 0.2472 0.4366 1.000

0.000 0.0300 0.0645 0.1066 0.1556 0.2480 0.4353 1.000

0.9138 1.271 1.275 1.177 1.116 1.090 1.041 1.000

1.000 0.984 0.986 1.024 1.067 1.105 1.326 2.545

0.0 53.9 172.9 263.7 301.8 309.6 252.4 0.0

0.0000 0.1260 0.2520 0.3834 0.5099 0.6834 0.8615 1.0000

4642 4127 3706 3340 2890 2250 1596 839

4551 4121 3701 3274 2867 2290 1594 833

4551 4121 3701 3273 2867 2291 1597 833

0.0000 0.0326 0.0698 0.1148 0.1668 0.2639 0.4565 1.0000

0.0000 0.0326 0.0699 0.1150 0.1671 0.2641 0.4558 1.000

0.9927 1.280 1.2618 1.167 1.112 1.085 1.038 1.000

1.000 0.987 0.993 1.030 1.070 1.108 1.322 2.419

0.0 71.1 187.9 272.5 306.7 310.8 248.6 0.0

0.0000 0.1260 0.2520 0.3834 0.5099 0.6834 0.8615 1.0000

6812 6120 5511 4966 4325 3388 2435 1350

6685 6068 5464 4849 4264 3436 2436 1325

6685 6069 5468 4855 4271 3442 2437 1325

0.0000 0.0351 0.0752 0.1236 0.1790 0.2805 0.4757 1.0000

0.0000 0.0352 0.0753 0.1235 0.1786 0.2799 0.4753 1.000

1.088 1.288 1.245 1.155 1.105 1.080 1.034 1.000

1.000 0.992 1.002 1.037 1.074 1.113 1.314 2.255

0.0 90.5 203.7 280.6 309.6 308.2 239.9 0.0

0.0000 0.1260 0.2520 0.3834 0.5099 0.6834 0.8615 1.0000

9776 8881 8019 7225 6335 4997 3634 2123

9603 8737 7889 7024 6201 5041 3637 2054

9603 8744 7903 7045 6225 5058 3636 2054

0.0000 0.0376 0.0807 0.1324 0.1911 0.2970 0.4942 1.000

0.0000 0.0380 0.0809 0.1321 0.1901 0.2953 0.4939 1.000

1.201 1.295 1.226 1.141 1.096 1.070 1.029 1.000

1.000 0.997 1.011 1.045 1.079 1.118 1.302 2.061

0.0 111.6 219.9 287.3 310.0 301.3 225.7 0.0

0.0000 0.1260 0.2520

13746 12633 11439

13514 12325 11158

13514 12341 11191

0.2110 0.3815 1.000 T= 0.0000 0.0249 0.0582 0.0914 0.1313 0.2272 0.4025 1.000 T= 0.0000 0.0273 0.0627 0.0985 0.1418 0.2438 0.4245 1.000 T= 0.0000 0.0300 0.0675 0.1060 0.1529 0.2608 0.4472 1.000 T= 0.0000 0.0330 0.0724 0.1138 0.1645 0.2780 0.4707 1.000 T= 0.0000 0.0362 0.0774 0.1218 0.1765 0.2953 0.4949 1.000 T= 0.0000 0.0396 0.0826 0.1302 0.1889 0.3127 0.5196 1.000 T= 0.0000 0.0433 0.0878

0.0000 0.0402 0.0861

0.0000 0.0407 0.0865

1.332 1.300 1.204

1.000 1.003 1.021

0.0 134.0 235.8

Redlich−Kister

393.15 K

403.15 K

413.15 K

423.15 K

433.15 K

443.15 K

453.15 K

E



Article


γ1

y1(calculated)

x1

experimental

NRTL

UNIQUAC

Redlich−Kister

NRTL

UNIQUAC

0.3834 0.5099 0.6834 0.8615 1.0000

10304 9100 7226 5312 3270

9966 8834 7241 5312 3107

10014 8888 7279 5310 3107

0.1387 0.2016 0.3299 0.5448 1.000

0.1412 0.2032 0.3132 0.5120 1.000

0.1406 0.2015 0.3105 0.5115 1.000

γ2

GE/J mol−1

Redlich−Kister 1.126 1.086 1.060 1.023 1.000

1.053 1.084 1.124 1.286 1.848

292.2 307.5 289.5 205.7 0.0

a Combined expanded uncertainty (0.95 level of confidence, k = 2) in the vapor pressure measurements is Uc (P/Pa) = 0.1 Pa + 0.03*P for P < 600 Pa, Uc (P/Pa) = 0.01*P for P in the range (600 to 1300) Pa, Uc (P/Pa) = 0.003*P for P > 1300 Pa, and the standard uncertainty of the composition is u (x1) = 0.0002; u (T) = 0.02 K.

Table 7. Experimental and Calculated VLE Data for the Binary System Methyl Hexadecanoate (1) + n-Tetradecane (2) P/Pa

γ1

y1 (calculated)

x1

experimental

NRTL

UNIQUAC

0.0000 0.1374 0.2630 0.4045 0.5283 0.7023 0.8526 1.0000

135.4 115.1 100.6 87.4 75.5 51.6 28.2 4.2*

136.5 119.2 104.2 87.4 71.9 48.5 26.3 2.6

136.5 119.4 104.5 87.5 71.8 48.1 25.9 2.6

0.0000 0.1374 0.2630 0.4045 0.5283 0.7023 0.8526 1.0000

251.7 213.6 185.9 161.6 137.5 93.4 51.1 8.2*

250.7 219.2 192.2 161.5 133.3 90.4 49.5 5.8

250.7 219.5 192.6 161.7 133.1 89.6 48.7 5.8

0.0000 0.1374 0.2630 0.4045 0.5283 0.7023 0.8526 1.0000

447.2 379.9 329.8 286.6 241.2 163.5 90.0 15.8

441.9 387.0 340.0 286.5 237.2 161.7 89.4 12.1

441.9 387.5 340.6 286.7 236.7 160.4 88.3 12.1

0.0000 0.1374 0.2630 0.4045 0.5283 0.7023 0.8526 1.0000

763 651 564 489.6 409.1 277.6 154.2 29.4

750 658 579 489.6 406.5 278.5 155.7 24.4

750 659 580 489.7 405.5 276.6 154.2 24.4

0.0000 0.1374 0.2630 0.4045 0.5283 0.7023 0.8526 1.0000

1255 1076 931 809 673 458.4 258.0 53.5

1231 1082 954 809 673 463.7 262.4 47.0

1231 1083 955 809 672 461.2 260.6 47.0

0.0000

1998

1957

1957

Redlich−Kister T 0.0000 0.0068 0.0144 0.0221 0.0308 0.0576 0.1272 1.0000 T 0.0000 0.0069 0.0149 0.0233 0.0330 0.0629 0.1389 1.0000 T 0.0000 0.0072 0.0157 0.0249 0.0358 0.0690 0.1514 1.0000 T 0.0000 0.0077 0.0168 0.0271 0.0393 0.0759 0.1648 1.0000 T 0.0000 0.0085 0.0182 0.0297 0.0435 0.0837 0.1791 1.0000 T 0.0000

γ2

GE/J mol−1

NRTL

UNIQUAC

Redlich−Kister

0.0000 0.0037 0.0076 0.0130 0.0199 0.0381 0.0843 1.0000

0.0000 0.0037 0.0074 0.0129 0.0198 0.0383 0.0857 1.0000

0.9398 1.3639 1.3216 1.1519 1.0562 1.0177 1.0121 1.0000

1.0000 0.9805 0.9914 1.0631 1.1453 1.2083 1.2354 1.5268

0.0 75.4 196.7 274.9 272.7 201.6 121.6 0.0

0.0000 0.0046 0.0092 0.0157 0.0239 0.0454 0.0995 1.0000

0.0000 0.0045 0.0090 0.0155 0.0238 0.0457 0.1009 1.0000

0.8829 1.3023 1.2781 1.1290 1.0457 1.0167 1.0130 1.0000

1.0000 0.9794 0.9871 1.0513 1.1226 1.1679 1.1876 1.4919

0.0 55.3 166.0 238.1 236.1 174.7 109.8 0.0

0.0000 0.0055 0.0110 0.0187 0.0283 0.0535 0.1161 1.0000

0.0000 0.0055 0.0108 0.0185 0.0282 0.0539 0.1175 1.0000

0.8699 1.2640 1.2462 1.1132 1.0395 1.0164 1.0133 1.0000

1.0000 0.9801 0.9865 1.0447 1.1077 1.1427 1.1599 1.4625

0.0 46.1 148.6 215.4 213.3 158.5 102.7 0.0

0.0000 0.0066 0.0130 0.0220 0.0333 0.0625 0.1341 1.0000

0.0000 0.0065 0.0129 0.0219 0.0332 0.0629 0.1354 1.0000

0.8904 1.2433 1.2234 1.1029 1.0369 1.0165 1.0130 1.0000

1.0000 0.9823 0.9889 1.0423 1.0988 1.1291 1.1479 1.4382

0.0 46.3 142.8 204.8 202.5 151.8 99.9 0.0

0.0000 0.0078 0.0153 0.0257 0.0387 0.0723 0.1532 1.0000

0.0000 0.0077 0.0151 0.0256 0.0387 0.0727 0.1543 1.0000

0.9394 1.2361 1.2077 1.0971 1.0371 1.0172 1.0124 1.0000

1.0000 0.9857 0.9937 1.0432 1.0946 1.1246 1.1482 1.4184

0.0 54.6 147.0 204.8 202.2 153.5 100.9 0.0

0.0000

0.0000

1.0148

1.0000

0.0

= 353.15

= 363.15

= 373.15

= 383.15

= 393.15

= 403.15

F



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γ1

y1 (calculated)

γ2

GE/J mol−1

x1

experimental

NRTL

UNIQUAC

Redlich−Kister

NRTL

UNIQUAC

0.1374 0.2630 0.4045 0.5283 0.7023 0.8526 1.0000

1725 1492 1296 1075 738 422 95

1723 1524 1295 1081 749 429 87

1725 1525 1294 1078 746 427 87

0.0091 0.0178 0.0298 0.0447 0.0829 0.1735 1.0000

0.0090 0.0177 0.0297 0.0447 0.0832 0.1742 1.0000

1.2394 1.1975 1.0950 1.0397 1.0183 1.0115 1.0000

0.9900 1.0004 1.0465 1.0940 1.1275 1.1586 1.4027

69.8 159.8 213.9 211.1 162.4 105.3 0.0

0.0000 0.1374 0.2630 0.4045 0.5283 0.7023 0.8526 1.0000

3086 2687 2325 2019 1674 1160 675 164.4

3022 2666 2362 2013 1685 1174 682 155.1

3022 2667 2363 2011 1682 1172 681 155.1

0.0000 0.0105 0.0205 0.0342 0.0510 0.0942 0.1946 1.0000

0.0000 0.0105 0.0204 0.0342 0.0512 0.0945 0.1947 1.0000

1.1163 1.2509 1.1918 1.0960 1.0444 1.0198 1.0103 1.0000

1.0000 0.9950 1.0084 1.0518 1.0963 1.1361 1.1772 1.3904

0.0 90.9 179.8 230.7 227.8 177.8 112.7 0.0

0.0000 0.1374 0.2630 0.4045 0.5283 0.7023 0.8526 1.0000

4642 4079 3531 3067 2545 1783 1058 278.9

4551 4024 3573 3053 2564 1798 1058 267.7

4551 4025 3573 3051 2560 1797 1061 267.7

0.0000 0.0121 0.0234 0.0389 0.0579 0.1061 0.2164 1.0000

0.0000 0.0121 0.0234 0.0390 0.0581 0.1064 0.2160 1.0000

1.2447 1.2688 1.1895 1.0994 1.0507 1.0217 1.0090 1.0000

1.0000 1.0006 1.0176 1.0585 1.1006 1.1492 1.2027 1.3811

0.0 117.0 205.9 254.0 251.1 198.6 122.7 0.0

0.0000 0.1374 0.2630 0.4045 0.5283 0.7023 0.8526 1.0000

6812 6046 5239 4552 3786 2685 1628 463.5

6685 5923 5272 4518 3805 2686 1602 447.4

6685 5924 5271 4515 3802 2689 1612 447.4

0.0000 0.0139 0.0266 0.0440 0.0652 0.1187 0.2387 1.0000

0.0000 0.0139 0.0267 0.0442 0.0655 0.1188 0.2375 1.0000

1.4008 1.2915 1.1898 1.1048 1.0585 1.0238 1.0076 1.0000

1.0000 1.0066 1.0275 1.0661 1.1064 1.1659 1.2340 1.3743

0.0 146.9 236.7 282.5 279.9 224.2 135.0 0.0

0.0000 0.1374 0.2630 0.4045 0.5283 0.7023 0.8526 1.0000

9776 8769 7609 6611 5518 3967 2461 756

9603 8529 7609 6540 5525 3925 2376 726

9603 8529 7606 6535 5523 3938 2397 726

0.0000 0.0157 0.0300 0.0493 0.0729 0.1318 0.2612 1.0000

0.0000 0.0157 0.0301 0.0496 0.0733 0.1318 0.2592 1.0000

1.5856 1.3173 1.1918 1.1118 1.0674 1.0263 1.0062 1.0000

1.0000 1.0128 1.0379 1.0742 1.1129 1.1851 1.2700 1.3694

0.0 179.9 271.1 315.0 313.0 253.5 149.2 0.0

0.0000 0.1374 0.2630 0.4045 0.5283 0.7023 0.8526 1.0000

13746 12467 10834 9414 7894 5759 3659 1210

13514 12032 10760 9277 7860 5623 3454 1147

13514 12031 10755 9271 7864 5653 3495 1147

0.0095 0.0200 0.0329 0.0484 0.0924 0.1942 1.0000 T 0.0000 0.0107 0.0222 0.0367 0.0542 0.1021 0.2103 1.0000 T 0.0000 0.0122 0.0248 0.0412 0.0610 0.1130 0.2274 1.0000 T 0.0000 0.0140 0.0278 0.0464 0.0689 0.1251 0.2455 1.0000 T 0.0000 0.0161 0.0314 0.0526 0.0781 0.1385 0.2647 1.0000 T 0.0000 0.0187 0.0355 0.0597 0.0886 0.1535 0.2851 1.0000

0.0000 0.0177 0.0335 0.0549 0.0809 0.1453 0.2838 1.0000

0.0000 0.0178 0.0338 0.0554 0.0814 0.1451 0.2809 1.0000

1.7991 1.3448 1.1949 1.1200 1.0774 1.0290 1.0047 1.0000

1.0000 1.0191 1.0485 1.0823 1.1197 1.2061 1.3098 1.3660

0.0 214.8 307.9 350.2 349.3 285.9 164.9 0.0

Redlich−Kister

= 413.15

= 423.15

= 433.15

= 443.15

= 453.15

a

Extrapolated vapor pressure. Combined expanded uncertainty (0.95 level of confidence, k = 2) in the vapor pressure measurements is Uc (P/Pa) = 0.1 Pa + 0.03*P for P < 600 Pa, Uc (P/Pa) = 0.01*P for P in the range (600 to 1300) Pa, Uc (P/Pa) = 0.003*P for P > 1300 Pa, and the standard uncertainty of the composition is u (x1) = 0.0002; u (T) = 0.02 K.

1 s each 2 min during 30 min by means of the temporized electrovalve so as the dissolved air is removed from the sample. The condenser, cooled down to 0 °C, limits the loss of the volatile compound. The liquid is then transferred to the measurement cell which is plunged in liquid bath. The mixture is stirred during

components, Figure 1. The uncertainty in the weight is 0.0001 g. The preparation bulb is then connected to the apparatus which is entirely submitted to vacuum during several hours. Later, the liquid is transferred to the degassing bulb. The degassing process is carried out by boiling and submitting the liquid to vacuum for G



Article

The overall mean relative deviation in pressure is expressed: 100 δP %= P N

the experiment. The total pressure of the solution is recorded once the thermodynamic equilibrium is obtained (constant temperature and pressure). At the end of the experiments, the composition of the sample is checked by gas chromatography. The chromatographic conditions are resumed in Table 2. The uncertainty in the mole fraction is estimated to be xi = ± 0.0005. 2.3. Uncertainty of the Vapor Pressure and Temperature. The combined expanded (0.95 level of confidence, k = 2) uncertainty of the measurements is estimated to be Uc (P/Pa) = 0.1 Pa + 0.03*P for pressures lower than 600 Pa; Uc (P/Pa) = 0.01*P for P in the range (600 to 1300) Pa; Uc (P/Pa) = 0.003*P for pressures over 1300 Pa and the standard uncertainty of the sample temperature measurements is u(T) = 0.02 K (temperature range 353.15 ≤ T/K ≤ 463.15).

(3)

n−1

(4)

where x1 is the molar fraction of FAME. The coefficients Ai, Table 8, were determined by regression through minimization of the sum of deviations in vapor pressures (eq 3). Molar fraction of the vapor phases, yi, was calculated from eq 5 assuming an ideal behavior of the vapor phase:

(1)

The values of constants A, B, and C and the standard deviations are given in Table 3. The minimized objective function Q is as follows:

yi =

xiγi P

Pi

(5)

where P is the total equilibrium pressure, Pi is the vapor pressure of pure component i, xi is the mole fraction in the liquid phase of component i; and γi is the activity coefficient of component i in the liquid phase.

2

⎛ Pcalc − Pexp ⎞ ⎟ Q = ∑ ⎜⎜ Pexp ⎟⎠ ⎝

Pexp

GE = x1(1 − x1) ∑ Ai (2x1 − 1)i RT i=0

3. RESULTS AND DISCUSSION The experimental temperature and pressure values of the pure compounds were fitted to the Antoine eq (eq 1): B C + T /K

Pexp − Pcal

where N is the total number of experimental values. In our previous work,12 we have presented the vapor pressures of the pure esters. In Table 4, vapor pressures of pure n-tetradecane are reported. As shown in Figure 2, our experimental values of tetradecane are in a very good agreement with literature data obtained using different methods: saturation, direct and DSC techniques.15−18 The mean relative deviation is less than 3%. A comparison of vapor pressure of pure methyl tertradecanoate was attempted by extrapolating our experimental measurements from 453 to 465 K in order to compare with the sole value from Hao et al.9 A relative deviation of 7% is obtained some of which discrepancy is certainly due to the effect of the extrapolation. The experimental VLE data and the phase diagram (P-x-y) of the binary systems are shown in Tables 5, 6, and 7 and Figures 3, 4, and 5. In Figure 6 is plotted experimental and literature data9 showing the variation of the temperature versus the mole fraction of the system tetradecane (1) + methyl tetradecanoate (2) at P = 5 kPa. A good agreement is observed between the ebulliometric points from Hao et al.9 and those from the present study. From the experimental results the activity coefficients, γ1 and γ2, along with the excess molar Gibbs energies,GE, were calculated by Barker’s method19 using the Redlich−Kister eq (eq 4), Tables 5−7:

Figure 3. Experimental and calculated P-x-y of the binary system methyl dodecanoate (1) + n-tetradecane (2): ⧫, x1 experimental at 353.15 K; ▲, x1 experimental at 373.15 K; , y1 calculated using Redlich−Kister equation.

log10P /Pa = A −

∑

(2)

Figure 4. Experimental and calculated P-x-y of the binary system methyl tetradecanoate (1) + n-tetradecane (2): (a) ⧫, x1 at 353.15 K; ▲, x1 at 373.15 K; •, x1 at 393.15 K. (b) ◊, x1 at 413.15 K; Δ, x1 at 433.15 K; ○, x1 at 453.15; , y1 calculated values using Redlich−Kister equation. H



Article

Figure 5. Experimental and calculated P-x-y of the binary system methyl hexadecanoate (1) + n-tetradecane (2): (a) ⧫, 353.15 K; ▲, 373.15 K; •, 393.15 K. (b) ◊, 413.15 K; Δ, 433.15 K; ○, 453.15; , y1 calculated values using Redlich−Kister equation.

Table 8. Coefficients Ai of Redlich-Kister Equation T/K

A1

353.15 363.15 373.15 383.15 393.15 403.15 413.15 423.15 433.15 353.15 363.15 373.15 383.15 393.15 403.15 413.15 423.15 433.15 44315 453.15

Figure 6. Isobaric vapor−liquid equilibria (P = 5.00 kPa) of the system tetradecane (1) + methyl tetradecanoate (2). Comparison between literature data and the experimental results: ▲, the present work; ○, from ref 9.

The binary mixture (methyl dodecanoate (1) + n-tetradecane (2)) exhibits maximum azeotropic behavior at the mole fraction x1 < 0.1, Figure 3. The azeotropic coordinates at each temperature were determined by progressive approximation until obtaining the equalities of values between xi and yi (using Redlich−Kister equation). The composition and the vapor pressure of the azeotrope at different temperatures are reported in Table 9. The uncertainties indicated at the bottom of Table 9 take into account the experimental uncertainty and the deviation of the fitting of Redlich−Kister parameters. Excess Gibbs free energy, GE, function of the mole fraction x1 of the three binary systems (methyl dodecanoate (1) + n-tetradecane (2), methyl tetradecanoate (1) + n-tetradecane (2), and methyl hexadecanoate (1) + n-tetradecane (2)) show positive deviations for all temperatures investigated and over the whole composition. An example of the variation of GE is illustrated in Figure 7. Positive deviations of GE show that the molecules have less affinity for one another in the mixture than within the pure components, it also follows that the activity coefficients are greater than unity, Tables 5−7. Since no excess enthalpy data, HE, are available in the literature and since Gibbs−Duhem relation is used to calculate the composition of the vapor phase, yi, the test of the thermodynamic consistency of the measurements could not be performed.

A2

A3

methyl dodecanoate (1) + n-tetradecane (2) 0.640 −0.316 0.102 0.607 −0.252 0.064 0.569 −0.209 0.076 0.537 −0.210 0.083 0.493 −0.193 0.103 0.450 −0.214 0.142 0.401 −0.232 0.177 0.349 −0.259 0.212 0.310 −0.296 0.211 methyl tetradecanoate (1) + n-tetradecane (2) 0.371 0.071 −0.089 0.362 0.097 −0.065 0.357 0.112 −0.041 0.355 0.120 −0.016 0.354 0.120 0.008 0.354 0.114 0.031 0.352 0.102 0.052 0.350 0.086 0.070 0.345 0.066 0.085 0.338 0.042 0.096 0.329 0.014 0.102 methyl hexadecanoate (1) + n-tetradecane (2) 0.379 −0.101 −0.198 0.319 −0.090 −0.182 0.281 −0.081 −0.161 0.260 −0.075 −0.136 0.253 −0.070 −0.109 0.257 −0.067 −0.080 0.270 −0.063 −0.050 0.290 −0.059 −0.019 0.315 −0.055 0.013 0.344 −0.050 0.044 0.374 −0.043 0.075

353.15 363.15 373.15 383.15 393.15 403.15 413.15 423.15 433.15 44315 453.15

A4 −0.151 −0.148 −0.224 −0.100 −0.138 −0.068 −0.058 −0.055 −0.052 0.446 0.500 0.529 0.536 0.525 0.499 0.460 0.410 0.349 0.279 0.200 0.343 0.352 0.341 0.315 0.276 0.228 0.173 0.111 0.046 −0.023 −0.095

In a second step, the nonrandom two liquid (NRTL)20 and universal quasi-chemical (UNIQUAC)21,22 models were used to correlate the experimental data. The activity coefficients were correlated with 2 models, the NRTL model given by eq 6: n

lnγi =

∑ j = 1 Gjixj n

∑k = 1 Gkixk

n

+

∑ j=1

n ⎛ ∑k = 1 xkτkjGkj ⎞ ⎜ ⎟ τij − n n ∑k = 1 Gkjxk ⎟⎠ ∑k = 1 Gkjxk ⎜⎝

xjGij

(6) I



Article

αij = α0ij + αTij (T − 273.15) with α0ij fixed to 0.2 for the three systems and αTij = 0, and the UNIQUAC model, eq 7:

Table 9. Coordinates of the Azeotropic Point of the System Methyl Dodecanoate (1) + n-Tetradecane (2)a

a

T/K

x1

P/Pa

353.15 363.15 373.15 383.15 393.15 403.15 413.15 423.15 433.15

0.088 0.073 0.071 0.063 0.063 0.064 0.068 0.079 0.079

138 254 452 767 1265 2014 3119 4622 6929

lnγi = lnγiC + lnγi R

(7)

in which ⎛ ϕ ϕ θ z lnγi = ⎜⎜ln i + qi ln i + li − i xi 2 ϕi ⎝ xi

n

⎞

j=1

⎠

∑ xjlj⎟⎟

n n ⎛ θj′τij ⎞ ⎟ ′ q + ⎜⎜qi′ − qi′ln(∑ θτ ) − ∑ j ji n i ⎟ ′ ∑ θ τ j=1 j=1 k k kj ⎠ ⎝

u(x) = ± 0.005 u(P) = ± 2 Pa.

li =

(8)

Z (ri − qi) − (ri − 1) 2

Where ri and qi are molecular volume and area respectively, called van der Waals volume and area, which are estimated using the group contribution values of Bondi,23 Table 10. The coordination number Z is equal to 10. xiq xr ϕi = n i i θi = n i ∑ j = 1 xjrj ∑ j = 1 xjqj The interaction parameters are as follows: τij = exp −

E

Figure 7. Plot of G against x1 calculated values using Redlich−Kister equation for the binary system methyl dodecanoate (1) + n-tetradecane (2): ⧫, 353.15 K; ▲, 373.15 K; •, 393.15 K; ×, 413.15 K; ■, 433.15 K.

uij − ujj = (uij − ujj)0 + (uij − ujj)T T

Table 10. Structural Parameters r and q for UNIQUAC Model compounds

tetradecane

methyl dodecanoate

methyl tetradecanoate

methyl hexadecanoate

ri qi

9.90 8.18

9.55 7.98

10.9 9.06

12.3 10.1

⎛ C 0 + C T *T ⎞ ij ij ⎟ τij = exp − ⎜⎜ ⎟ RT ⎝ ⎠

The objective function, OF, used was the following, eq 9: n

OF =

where τij =

⎛ uij − ujj ⎞ ⎜ ⎟τ = τ = 1 jj ⎝ RT ⎠ ii

∑ 1

gij − gjj

P cal − P exp P exp

(9)

The obtained energy parameters, the deviation of the vapor phase composition, and the mean relative deviation for the two activity coefficient models are given in Table 11. Both models present well our experimental results.

RT

τii = τjj = 0

■

αii = αjj = 0

CONCLUSION In this work, we studied the liquid−vapor equilibrium of three binary mixtures (n-tetradecane + methyl dodecanoate, methyl tetradecanoate, or methyl hexadecanoate) as a function of composition and temperature. The experimental results show that the binary mixture (methyl dodecanoate (1) + n-tetradecane

Gij = exp( −αijτij)

Gii = Gjj = 1 gij − gjj = Cij0 + CijT(T − 273.15)

Table 11. NRTL and UNIQUAC Parameters and Mean Relative Deviation, ΔP/P %, for the Three Binary Systemsa system methyl dodecanoate (1) + tetradecane(2) methyl tetradecanoate (1) + tetradecane (2) methyl hexadecanoate (1) + tetradecane (2)

a ΔP

P

=

1 n

n

∑i = 1

model

C°ij [J mol−1]

C°ji [J mol−1]

CTij [J mol−1 K−1]

CTji [J mol−1 K−1]

ΔP/P %

NRTL UNIQUAC NRTL UNIQUAC NRTL UNIQUAC

150.48 149.60 −890.34 −167.20 −803.77 −166.56

1885.18 470.70 646.23 76.490 1097.1 34.157

−31.98 −4.193 41.01 4.631 −14.51 −1.554

48.79 4.62 −23.78 −3.242 27.00 2.515

1.0 6.4 1.5 1.3 2.6 2.6

|Pexp − Pcalc| Pexp

J



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2,6-Dimethylpiperidine in the Range between 0.2 Pa and 75 kPa. J. Chem. Eng. Data 2009, 54, 819−822. (15) 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. (16) Morgan, D. L.; Kobayashi, R. Direct vapor pressure measurements of ten n-alkanes in the C10-C28 range. Fluid Phase Equilib. 1994, 97, 211−242. (17) Allemand, N.; Jose, J.; Michou-Saucet, C. Réalisation d’un ensemble destine à la mesure de faibles pressions de vapeur (domaine: 3−1000 Pa). Thermochim. Acta 1986, 98, 237−253. (18) Casserino, M.; Blevins, D. R.; Sanders, R. N. An improved method for measuring vapor pressure by DSC with automated pressure control. Thermochim. Acta 1996, 284, 145−152. (19) Barker, J. A. Determination of activity coefficients from total pressure measurements. Aust. J. Chem. 1953, 6, 207−210. (20) Renon, H.; Prausnitz, J. M. Local compositions in thermodynamic excess functions for liquid mixtures. AIChE J. 1968, 14 (3), 135−144. (21) Abrams, D. S.; Prausnitz, J. M. Statistical thermodynamics of liquid mixtures: a new expression for the excess Gibbs energy of partly or complete miscible systems. AIChE J. 1975, 21 (3), 116−128. (22) Anderson, T. F.; Prausnitz, J. M. Application of the UNIQUAC equation to calculation of multicomponent phase-equilibria. 1-Vaporliquid equilibria. Ind. Eng. Chem. Process Des. Dev. 1978, 17 (4), 552− 560. (23) Bondi, A. Physical Properties of Molecular Crystals, Liquids and Gases; Wiley and Sons, 1968.

(2)) exhibits a maximum azeotropic behavior. The binary mixtures exhibit positive deviations from ideality (γi > 1.0). The experimental results for all three systems were well correlated (mean relative deviation of about 2%) using the NRTL and UNIQUAC models. A slightly greater deviation (6%) is observed for the system tetradecane + methyl dodecanoate with the UNIQUAC correlation.

■

AUTHOR INFORMATION

Corresponding Author

*Phone: + 33 472 43 19 16; E-mail: [email protected]. ORCID

Lakhdar Sahraoui: 0000-0003-3829-0464 Ilham Mokbel: 0000-0003-2384-900X Notes

The authors declare no competing financial interest.

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REFERENCES

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Isothermal Vapor Pressures of Three Binary Systems: n-Tetradecane+

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