294
J. Chem. Eng. Data 2003, 48, 294-301
Vapor Liquid Equilibrium between (278.15 and 323.15) K and Excess Functions at T ) 298.15 K for 1-Bromobutane with 2-Methyl-1-propanol or 2-Butanol Santiago Martı´nez, Rosa Garriga, Pascual Pe´ rez, and Mariano Gracia* Departamento de Quı´mica Orga´nica y Quı´mica Fı´sica (A Ä rea de Quı´mica Fı´sica), Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain
Vapor pressures of (1-bromobutane + 2-methyl-1-propanol or 2-butanol) at 10 temperatures between (278.15 and 323.15) K were measured by a static method. Excess molar enthalpies and volumes were also measured at 298.15 K. The reduction of the vapor pressures to obtain activity coefficients and excess molar Gibbs energies was carried out by fitting the vapor pressure data to the Wilson equation according to Barker’s method. Azeotropic mixtures with a minimum boiling temperature were observed over the whole temperature range.
Introduction Hydrogen bonding plays an important role in both fundamental science and in industrial applications.1 Although many experimental and theoretical studies have been directed toward understanding hydrogen bonding, it remains an area of active research. In previous papers, we have reported vapor-liquid equilibrium (VLE) measurements at several temperatures as well as excess enthalpies and excess volumes, at T ) 298.15 K, for binary mixtures of 1-chlorobutane + butanol isomers,2,3 + ethanol, or + 1-hexanol4 and 1-bromobutane + 1-butanol or + 2-methyl2-propanol.5 We report here vapor pressures at 10 temperatures for (1-bromobutane + 2-methyl-1-propanol) and for (1-bromobutane + 2-butanol). We have also measured excess enthalpies and excess volumes at T ) 298.15 K. Experimental Section Chemicals. All of the chemicals were supplied by Aldrich. All of the chemicals had low water content, were stored over molecular sieve (3A), and were used without further purification. The mass fraction purity was checked by gas-liquid chromatography and found to be 0.996 for 1-bromobutane, 0.998 for 2-methyl-1-propanol, and 0.999 for 2-butanol. Apparatus and Procedures. The vapor pressure measurements were performed by a static method. The apparatus is similar to that of Marsh,6 except for some experimental details which have been described previously.7,8 Each liquid was degassed by magnetic stirring under its own vapor pressure before mixing, with the vapor + air being pumped away periodically. The mixture cell containing a known mass of the first component was immersed in liquid nitrogen, and a known mass of the second component was added by gravity. The mixture cell, filled with 8-10 cm3 of sample in each experiment, was connected to the manometric system, which was evacuated, and then the liquid sample was introduced by gravity into the vapor-pressure cell which is connected to one of the branches of the manometer. To prevent condensation * To whom correspondence should be addressed.
effects on the mercury meniscus, the temperatures of the manometer and the connecting tube containing the vapor phase were maintained at 325.0 ( 0.1 K by circulating water from a thermostat. Uncertainties in the mole fractions are estimated to be less than 0.0003. The temperature of the liquid sample was controlled to within (10 mK. Manometric levels were read with a cathetometer to within (0.01 mm, and the pressure reproducibility was 10 Pa. A calorimeter Thermometric 2277, together with two Shimadzu (model LC-10AD) variable speed piston pumps, were used to determine HE at T ) 298.15 K. The precision of the HE measurements is better than (2%. The accuracy of the method was verified with a test on (benzene + cyclohexane).9 The experimental results agreed with the literature data to within (10 J, in the worst case. A densimeter (Anton Paar DMA 60/DMA 602) was used for density measurements on the pure liquids and mixtures. The densimeter works at 298.15 K, and sample density is calculated from the vibration period with an uncertainty of (0.000 02 g‚cm-3. The accuracy for VE is estimated to be 0.002 cm3‚mol-1. Results The molar volumes of the pure components used in the Barker analysis together with the experimental and calculated vapor pressures are presented in Table 1. The second virial coefficient, at T ) 325.0 K, of 1-bromobutane (B11 ) -1200 cm3 ‚ mol-1) was taken from Velasco et al.,14 that of 2-methyl-1-propanol (B22 ) -3260 cm3‚mol-1) was calculated by interpolation of values taken from the TRC tables,15 and that of 2-butanol (B22 ) -2640 cm3‚mol-1) was obtained by extrapolation from the Dymond and Smith16 data compilation. The interaction virial coefficient was estimated with a cubic combination rule
B12 )
1 (B 1/3+ B221/3)3 8 11
(1)
Table 2 shows our vapor pressure measurements along with the activity coefficients γ1 and γ2, and the excess molar Gibbs free energy GE values fitted by Barker’s method17 to
10.1021/je020110g CCC: $25.00 © 2003 American Chemical Society Published on Web 01/29/2003
Journal of Chemical and Engineering Data, Vol. 48, No. 2, 2003 295 Table 1. Molar Volumes V0 and Vapor Pressures P0 of the Pure Compounds Used in Barker Analysis 1-bromobutane T
V0 a
K
cm3‚mol-1
b
278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15
105.6f 106.2f 106.8 107.4 108.0 108.7 109.3f 109.9f 110.5f 111.2f
1.860 2.480 3.265 4.261 5.506 7.039 8.899 11.148 13.872 17.092
a
Timmermans.10
b
2-methyl-1-propanol
P0/kPa
V0 d c
cm3‚mol-1
b
1.855 2.477 3.269 4.264 5.502 7.027 8.889 11.143 13.851 17.077
91.2 91.6 92.0 92.5 92.9 93.4 93.9 94.3 94.8 95.3
0.335 0.505 0.739 1.057 1.501 2.133 2.956 4.026 5.444 7.237
This work. c Riddick.11
d
TRC.12
e
2-butanol
P0/kPa
Ambrose and Ghiassee.13
f
V0 d
P0/kPa
e
cm3‚mol-1
b
e
0.325 0.488 0.719 1.044 1.491 2.099 2.913 3.988 5.392 7.203
90.5 90.9 91.4 91.9 92.4 92.8 93.3 93.9 94.4 94.9
0.519 0.780 1.137 1.648 2.324 3.256 4.462 6.048 8.105 10.706
0.503 0.755 1.110 1.606 2.284 3.198 4.412 6.003 8.062 10.691
Interpolated values.
Table 2. Values of the Vapor Pressure P, Deviations ∆P ) P - Pcalc, Activity Coefficients γ1 and γ2, and Excess Molar Gibbs Energies GE x2
P/kPa
∆P/Pa
γ1
0.0513 0.1003 0.1992 0.3031 0.3865 0.4782
1.944 1.967 1.933 1.901 1.857 1.817
12 30 11 2 -16 -13
1.0170 1.0520 1.1535 1.2968 1.4423 1.6417
0.0513 0.1003 0.1992 0.3031 0.3865 0.4783
2.606 2.642 2.606 2.560 2.513 2.440
13 37 16 0 -11 -26
1.0168 1.0515 1.1520 1.2935 1.4367 1.6321
0.0512 0.1003 0.1993 0.3031 0.3866 0.4783
3.440 3.498 3.452 3.397 3.326 3.232
14 50 20 5 -18 -36
1.0156 1.0486 1.1458 1.2841 1.4243 1.6156
0.0512 0.1003 0.1993 0.3031 0.3866 0.4784
4.496 4.576 4.514 4.437 4.360 4.246
22 64 19 -6 -22 -36
1.0139 1.0444 1.1368 1.2705 1.4072 1.5944
0.0512 0.1003 0.1993 0.3032 0.3867 0.4784
5.818 5.933 5.872 5.774 5.666 5.521
27 80 31 0 -28 -46
1.0127 1.0412 1.1296 1.2591 1.3921 1.5746
0.0511 0.1003 0.1993 0.3032 0.3867 0.4785
7.461 7.629 7.554 7.459 7.311 7.118
32 101 26 11 -35 -64
1.0117 1.0388 1.1237 1.2491 1.3782 1.5552
0.0510 0.1002 0.1993 0.3033 0.3868 0.4786
9.470 9.685 9.627 9.507 9.346 9.133
36 100 20 -6 -40 -44
1.0114 1.0378 1.1210 1.2439 1.3700 1.5422
0.0509 0.1002 0.1993 0.3033 0.3869 0.4788
11.899 12.204 12.148 12.015 11.814 11.576
52 136 18 -11 -59 -41
1.0105 1.0353 1.1149 1.2341 1.3572 1.5257
γ2
GE/(J‚mol-1)
x2
P/kPa
1-Bromobutane (1) + 2-Methyl-1-propanol (2) 278.15 K 7.9790 283 0.5834 1.731 5.2368 490 0.6959 1.615 3.0600 780 0.7947 1.387 2.1490 955 0.8393 1.280 1.7543 1022 0.9219 0.877 1.4791 1031 283.15 K 7.7530 284 0.5835 2.333 5.1092 491 0.6959 2.172 2.9994 782 0.7948 1.883 2.1138 956 0.8394 1.689 1.7300 1022 0.9219 1.219 1.4626 1030 288.15 K 7.3638 280 0.5835 3.090 4.9504 487 0.6960 2.888 2.9520 778 0.7949 2.513 2.0933 954 0.8394 2.246 1.7177 1021 0.9220 1.652 1.4550 1029 293.15 K 6.8865 273 0.5836 4.060 4.7698 477 0.6961 3.802 2.9128 769 0.7949 3.318 2.0831 949 0.8395 2.989 1.7142 1018 0.9220 2.221 1.4542 1030 298.15 K 6.4746 267 0.5837 5.285 4.5885 469 0.6962 4.938 2.8590 761 0.7950 4.337 2.0616 942 0.8396 3.921 1.7023 1013 0.9221 2.981 1.4475 1026 303.15 K 6.0998 261 0.5838 6.823 4.4016 461 0.6964 6.385 2.7908 751 0.7952 5.625 2.0290 931 0.8397 5.113 1.6821 1003 0.9222 3.934 1.4349 1016 308.15 K 5.8643 259 0.5840 8.721 4.2615 458 0.6965 8.177 2.7248 746 0.7953 7.225 1.9918 925 0.8398 6.498 1.6569 995 0.9222 5.150 1.4180 1007 313.15 K 5.5713 253 0.5841 11.055 4.1241 451 0.6968 10.383 2.6848 739 0.7955 9.206 1.9776 920 0.8400 8.423 1.6501 992 0.9224 6.681 1.4148 1006
∆P/Pa
γ1
γ2
GE/(J‚mol-1)
-21 6 -8 25 -10
1.9392 2.3753 2.9134 3.2248 3.9645
1.2761 1.1381 1.0614 1.0376 1.0090
967 817 617 507 268
-25 8 7 -2 8
1.9212 2.3404 2.8505 3.1421 3.8255
1.2657 1.1323 1.0585 1.0357 1.0085
964 812 612 502 265
-36 16 15 -12 12
1.8982 2.3068 2.8013 3.0829 3.7398
1.2613 1.1300 1.0574 1.0350 1.0083
964 812 613 502 265
-43 23 14 -11 11
1.8721 2.2746 2.7631 3.0417 3.6930
1.2615 1.1303 1.0576 1.0351 1.0083
967 816 616 506 267
-52 13 14 -18 36
1.8453 2.2372 2.7114 2.9812 3.6098
1.2578 1.1284 1.0568 1.0346 1.0082
964 815 616 505 267
-65 19 17 -15 38
1.8169 2.1935 2.6453 2.9005 3.4903
1.2503 1.1245 1.0549 1.0334 1.0079
955 807 609 500 263
-78 44 45 -84 78
1.7948 2.1544 2.5797 2.8170 3.3589
1.2399 1.1187 1.0521 1.0316 1.0074
945 797 600 492 259
-103 37 21 -32 69
1.7735 2.1270 2.5451 2.7785 3.3114
1.2385 1.1181 1.0519 1.0315 1.0074
946 798 602 494 260
296
Journal of Chemical and Engineering Data, Vol. 48, No. 2, 2003
Table 2 (Continued) 1-Bromobutane (1) + 2-Methyl-1-propanol (2) 318.15 K 5.2649 247 0.5844 13.891 3.9567 442 0.6971 13.072 2.6186 728 0.7958 11.619 1.9452 908 0.8402 10.691 1.6298 980 0.9225 8.595 1.4021 994
0.0508 0.1001 0.1992 0.3034 0.3870 0.4790
14.784 15.225 15.204 15.177 14.824 14.536
13 140 0 87 -80 -54
1.0097 1.0332 1.1096 1.2249 1.3441 1.5072
0.0506 0.1001 0.1992 0.3034 0.3872 0.4792
18.240 18.809 18.876 18.708 18.441 18.003
48 187 49 -3 -51 -115
1.0086 1.0302 1.1016 1.2115 1.3262 1.4839
4.9010 3.7711 2.5589 1.9229 1.6189 1.3969
323.15 K 238 0.5847 429 0.6975 711 0.7961 892 0.8405 966 0.9227 983
-132 48 12 -33 86
1.7464 2.0856 2.4834 2.7038 3.2035
1.2311 1.1142 1.0500 1.0303 1.0071
934 788 594 487 256
17.311 16.280 14.613 13.484 10.975
-131 28 47 -33 94
1.7160 2.0462 2.4336 2.6483 3.1356
1.2288 1.1133 1.0497 1.0301 1.0070
926 783 591 484 255
-20 -23 -19 -21 -13 47
1.6858 1.6953 2.0356 2.5479 2.9885 3.8303
1.4580 1.4495 1.2466 1.1131 1.0590 1.0141
1044 1042 958 775 613 332
0.0953 0.0976 0.1500 0.2111 0.3087 0.3852
2.068 2.066 2.061 2.056 2.048 2.020
22 20 9 8 14 5
1.0512 1.0532 1.1040 1.1755 1.3164 1.4531
1-Bromobutane (1) + 2-Butanol (2) 278.15 K 5.6042 484 0.4889 1.953 5.5058 493 0.4926 1.948 3.9298 669 0.6049 1.868 2.9493 823 0.7247 1.703 2.1297 979 0.7997 1.540 1.7669 1038 0.9024 1.217
0.0952 0.0976 0.1500 0.2111 0.3087 0.3852
2.788 2.774 2.782 2.781 2.772 2.742
21 7 5 6 14 11
1.0522 1.0542 1.1053 1.1767 1.3162 1.4505
5.4502 5.3534 3.8148 2.8646 2.0749 1.7268
283.15 K 489 0.4889 497 0.4927 673 0.6050 825 0.7247 978 0.7997 1034 0.9024
2.657 2.641 2.529 2.314 2.100 1.620
-15 -28 -23 -11 5 26
1.6766 1.6859 2.0112 2.4905 2.8931 3.6402
1.4317 1.4235 1.2307 1.1048 1.0543 1.0128
1035 1033 945 761 601 324
0.0952 0.0975 0.1500 0.2111 0.3087 0.3852
3.700 3.668 3.698 3.690 3.674 3.645
33 0 11 3 9 13
1.0485 1.0504 1.0994 1.1684 1.3042 1.4351
5.2360 5.1470 3.7157 2.8118 2.0493 1.7105
288.15 K 480 0.4889 489 0.4927 664 0.6051 817 0.7248 970 0.7998 1027 0.9025
3.533 3.526 3.372 3.093 2.813 2.196
-22 -25 -27 -11 5 30
1.6552 1.6643 1.9801 2.4425 2.8282 3.5379
1.4222 1.4141 1.2253 1.1021 1.0528 1.0124
1029 1028 941 758 597 322
0.0952 0.0975 0.1499 0.2111 0.3087 0.3853
4.838 4.824 4.846 4.858 4.850 4.825
24 7 -5 2 19 36
1.0450 1.0468 1.0935 1.1600 1.2914 1.4182
4.9851 4.9040 3.5893 2.7399 2.0124 1.6861
293.15 K 470 0.4889 479 0.4928 652 0.6051 804 0.7249 957 0.7998 1014 0.9025
4.668 4.649 4.454 4.092 3.733 2.953
-21 -35 -31 -14 6 35
1.6305 1.6395 1.9424 2.3816 2.7438 3.4013
1.4076 1.3996 1.2170 1.0980 1.0506 1.0118
1016 1015 929 747 589 317
0.0951 0.0975 0.1499 0.2111 0.3087 0.3853
6.271 6.274 6.305 6.325 6.330 6.285
21 19 -8 -2 30 37
1.0417 1.0434 1.0879 1.1519 1.2791 1.4022
4.7712 4.6971 3.4857 2.6842 1.9859 1.6695
298.15 K 460 0.4889 469 0.4928 642 0.6052 793 0.7250 947 0.7999 1005 0.9026
6.098 6.070 5.826 5.368 4.910 3.941
-23 -45 -37 -16 4 46
1.6082 1.6170 1.9103 2.3333 2.6798 3.3040
1.3982 1.3903 1.2118 1.0954 1.0492 1.0115
1008 1007 922 741 584 314
0.0950 0.0974 0.1499 0.2111 0.3087 0.3854
8.061 8.053 8.123 8.161 8.186 8.141
17 2 -20 -12 38 57
1.0394 1.0411 1.0839 1.1458 1.2692 1.3886
4.5667 4.4977 3.3727 2.6161 1.9491 1.6448
303.15 K 452 0.4889 461 0.4929 632 0.6053 782 0.7252 935 0.8000 992 0.9027
7.921 7.879 7.553 6.969 6.415 5.188
-5 -38 -46 -25 17 34
1.5875 1.5962 1.8775 2.2788 2.6035 3.1807
1.3833 1.3755 1.2033 1.0912 1.0469 1.0109
995 994 909 730 575 308
0.0949 0.0973 0.1498 0.2110 0.3087 0.3854
10.230 10.212 10.339 10.414 10.467 10.427
13 -15 -34 -16 53 85
1.0362 1.0378 1.0781 1.1374 1.2566 1.3726
4.3834 4.3201 3.2879 2.5746 1.9329 1.6361
308.15 K 442 0.4890 451 0.4930 621 0.6055 771 0.7254 926 0.8002 985 0.9028
10.139 10.111 9.735 8.989 8.290 6.827
-14 -32 -24 -35 -8 49
1.5663 1.5750 1.8497 2.2418 2.5588 3.1215
1.3793 1.3715 1.2014 1.0904 1.0465 1.0108
990 989 906 729 574 308
0.0947 0.0972 0.1497 0.2109 0.3087 0.3855
12.851 12.847 13.055 13.174 13.264 13.228
-9 -29 -37 -14 75 119
1.0337 1.0353 1.0737 1.1306 1.2459 1.3582
4.1965 4.1378 3.1871 2.5165 1.9038 1.6175
313.15 K 432 0.4890 441 0.4931 609 0.6057 759 0.7256 913 0.8004 972 0.9029
12.883 12.843 12.382 11.432 10.623 8.877
-3 -30 -25 -80 -10 72
1.5455 1.5540 1.8190 2.1949 2.4965 3.0274
1.3688 1.3610 1.1956 1.0876 1.0449 1.0104
979 977 896 720 567 304
Journal of Chemical and Engineering Data, Vol. 48, No. 2, 2003 297 Table 2 (Continued)
0.0948 0.0973 0.1497 0.2110 0.3087 0.3853
16.045 16.048 16.356 16.531 16.663 16.641
-14 -33 -38 -15 84 146
1.0314 1.0329 1.0692 1.1236 1.2343 1.3425
1-Bromobutane (1) + 2-Butanol (2) 318.15 K 3.9979 422 0.4889 16.273 3.9450 430 0.4929 16.183 3.0800 596 0.6055 15.556 2.4556 745 0.7259 14.531 1.8745 898 0.8006 13.526 1.5994 958 0.9031 11.430
0.0945 0.0971 0.1496 0.2108 0.3086 0.3854
19.857 19.836 20.257 20.520 20.760 20.777
1 -52 -77 -50 102 197
1.0289 1.0303 1.0646 1.1164 1.2228 1.3275
3.8325 3.7834 2.9933 2.4088 1.8540 1.5876
39 -38 -108 -56 -8 74
1.5232 1.5310 1.7857 2.1468 2.4334 2.9342
1.3584 1.3512 1.1903 1.0849 1.0435 1.0100
965 964 884 710 559 300
323.15 K 411 0.4890 420 0.4930 584 0.6057 731 0.7255 886 0.8009 946 0.9033
13 -26 -33 -79 -51 80
1.5026 1.5104 1.7578 2.1064 2.3867 2.8710
1.3527 1.3455 1.1875 1.0840 1.0428 1.0099
956 955 877 707 555 298
20.302 20.246 19.593 18.288 17.064 14.621
Table 3. Wilson Parameters and Standard Deviations, σ(P), of eq 9 1-bromobutane (1) + 2-methyl-1-propanol (2)
1-bromobutane (1) + 2-butanol (2)
T/K
Λ12
Λ21
σ/Pa
Λ12
Λ21
σ/Pa
278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15
0.4956 0.5193 0.5280 0.5244 0.5302 0.5455 0.5707 0.5701 0.5857 0.5845
0.1030 0.1046 0.1152 0.1333 0.1485 0.1613 0.1661 0.1817 0.1951 0.2193
17 18 26 31 39 49 62 67 81 93
0.4918 0.5329 0.5459 0.5673 0.5799 0.6034 0.6053 0.6201 0.6341 0.6380
0.0913 0.0875 0.0996 0.1124 0.1264 0.1364 0.1537 0.1675 0.1834 0.2018
22 17 20 24 29 32 40 57 70 84
Table 4. Experimental Molar Excess Enthalpies and Excess Volumes at T ) 298.15 K HE x2
J‚mol-1
HE x2
J‚mol-1
VE
VE
cm3‚mol-1
x2
x2
cm3‚mol-1
0.0421 0.0942 0.1932 0.2938 0.3468 0.3957 0.4476
1-Bromobutane (1) + 2-Methyl-1-propanol (2) 530 0.4990 1207 0.0576 0.077 0.5655 851 0.6000 1081 0.1063 0.124 0.6332 1125 0.7021 891 0.1475 0.146 0.6772 1248 0.8052 636 0.2348 0.190 0.7160 1271 0.9060 330 0.2586 0.198 0.8210 1272 0.9587 159 0.3910 0.221 0.8385 1245 0.4368 0.219 0.8690 0.5451 0.198 0.9469
0.186 0.157 0.126 0.102 0.051 0.044 0.025 0.007
0.0424 0.0948 0.1942 0.2951 0.3482 0.3973 0.4492
520 924 1282 1465 1519 1542 1532
1-Bromobutane (1) + 2-Butanol (2) 0.5006 1508 0.0408 0.151 0.5140 0.6015 1395 0.0848 0.223 0.5484 0.7035 1191 0.1407 0.293 0.6292 0.8062 887 0.2281 0.374 0.6450 0.9066 489 0.2864 0.408 0.7188 0.9590 246 0.3642 0.440 0.7739 0.3923 0.448 0.8388 0.4098 0.451 0.8639 0.4148 0.448 0.9284
0.449 0.440 0.397 0.382 0.325 0.260 0.186 0.150 0.076
the Wilson18 correlation. The activity coefficients are given by
ln γ1 ) -ln(x1 + Λ12x2) + x2
[
]
ln γ2 ) -ln(x2 + Λ21x1) - x1
[
]
Λ21 Λ12 x1 + Λ12x2 Λ21x1 + x2 (2) Λ21 Λ12 x1 + Λ12x2 Λ21x1 + x2 (3)
with
(
)
V0j λij - λii Λij ) 0exp RT Vi
(4)
Figure 1. Vapor pressures plotted against liquid-phase composition of alcohol, at 10 temperatures between 278.15 and 323.15 K: (a) {x1 1-bromobutane + x2 2-methyl-1-propanol} and (b) {x1 1-bromobutane + x2 2-butanol}.
298
Journal of Chemical and Engineering Data, Vol. 48, No. 2, 2003
Figure 2. Excess molar Gibbs energies GE at 278.15 K and 323.15 K: (a) {x1 1-bromobutane + x2 2-methyl-1-propanol} and (b) {x1 1-bromobutane + x2 2-butanol}, plotted as a function of mole fraction of alcohol.
where the subscripts 1 and 2 stand for 1-bromobutane and alcohol, respectively. V0 is the molar volume, and λ’s are negative interaction constants between the molecules designated in the subscripts. The vapor pressure is then given by
Pcalc ) x1 γ1 P01R1 + x2 γ2 P02R2
(5)
where the nonideality of the vapor phase is taken into account with the corrections
R1 ) exp{[(V01 - B11) (P - P01) - P δ12 y22]/RT} (6) R2 ) exp{[(V02 - B22) (P - P02) - P δ12 y12]/RT} (7) where y1 and y2 are the vapor phase mole fractions of 1-bromobutane and alcohol, respectively, and δ12
δ12 ) 2B12 - B11 - B22
(8)
For a given composition in Table 2, when the sample temperature is changed, a slight variation of the true liquid mole fraction is observed, because of an enrichment of the most volatile component in the vapor phase. In Table 3, the Wilson parameters Λ12 and Λ21 are collected, together with the standard deviations defined by N
σ(P) ) {
∑(∆P)
2 i
/(N-2)}
1/2
(9)
Figure 3. Thermal excess molar functions at T ) 298.15 K: (a) {x1 1-bromobutane + x2 2-methyl-1-propanol}; O, experimental HE; (b) {x1 1-bromobutane + x2 2-butanol}; 0, experimental HE; b and 9, Artigas et al.;19 ‚‚‚, Gibbs-Helmholtz HE; and s, GE and TSE.
Experimental excess molar enthalpies and volumes, at 298.15 K, are given in Table 4 and plotted in Figures 3 and 4. The results were fitted with a polynomial
i)1
m
∆P’s are the residual pressures according to Barker’s method, and N is the number of experimental points. Vapor pressure-liquid composition curves are shown in Figure 1, parts a and b. For both systems, Figure 2 shows the analytical equations for GE at the lowest and highest temperatures. A negative temperature coefficient was observed in both cases.
QE ) x1x2
∑ Cx
j/2 j 2
(10)
j)0
where QE denotes HE or VE and x1 and x2 denote the mole fractions of 1-bromobutane and alcohol, respectively. For alcoholic mixtures, this polynomial21,22 represents the experimental behavior better than the classical Redlich-
Journal of Chemical and Engineering Data, Vol. 48, No. 2, 2003 299 Table 5. Coefficients Cj and Standard Deviations σ(QE) for Least-Squares Representation by eq 10 of HE and VE, at T ) 298.15 K QE
mixture
HE/(J‚mol-1)
x1 1-bromobutane + x2 2-methyl-1-propanol
VE/(cm3‚mol-1) HE/(J‚mol-1) VE/(cm3‚mol-1)
x1 1-bromobutane + x2 2-butanol
C0
C1
C2
C3
σ(QE)
22057 2.542 21005 6.863
-56464 -6.793 -46452 -21.131
63289 11.045 46733 30.807
-25312 -6.880 -15552 -15.603
9 0.003 10 0.003
Table 6. Azeotropic Presures and Mole Fractions 1-bromobutane + 2-methyl-1-propanol
1-bromobutane + 2-butanol
z2
Pz/kPa
z2
Pz/kPa
z2
Pz/kPa
z2
Pz/kPa
T/K
exptl.
exptl.
calcd. eq 11
calcd. eq 13
exptl.
exptl.
calcd. eq 11
calcd. eq 13
278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15
0.0869 0.0990 0.1092 0.1187 0.1293 0.1425 0.1549 0.1687 0.1816 0.1951
1.937 2.606 3.449 4.514 5.859 7.545 9.620 12.138 15.207 18.827
0.0850 0.0969 0.1089 0.1208 0.1328 0.1447 0.1567 0.1686 0.1806 0.1925
1.952 2.605 3.442 4.504 5.841 7.510 9.578 12.121 15.225 18.990
0.1488 0.1631 0.1776 0.1930 0.2076 0.2232 0.2407 0.2573 0.2743 0.2931
2.052 2.778 3.689 4.857 6.327 8.173 10.435 13.205 16.587 20.659
0.1452 0.1611 0.1771 0.1930 0.2090 0.2249 0.2409 0.2568 0.2728 0.2887
2.072 2.776 3.683 4.837 6.297 8.125 10.398 13.203 16.638 20.818
Table 7. Thermodynamic Excess Functions for 0.5 Butanol Isomer + 0.5 Butanenitrile, or 0.5 Butanone, or 0.5 1-Bromobutane, or 0. 5 1-Chlorobutane, or 0.5 n-Hexane, at 298.15 K butanol isomer 1-butanol 2-methyl-1-propanol 2-butanol 2-methyl-2-propanol
excess functions
butanenitrile (µ ) 4.1 D)a
butanone (µ ) 3.4 D)a
1-bromobutane (µ ) 2.2 D)a
1-chlorobutane (µ ) 2.1 D)a
n-hexane
HE/(J‚mol-1) TSE/(J‚mol-1) VE/(cm3‚mol-1) HE/(J‚mol-1) TSE/(J‚mol-1) VE/(cm3‚mol-1) HE/(J‚mol-1) TSE/(J‚mol-1) VE/(cm3‚mol-1) HE/(J‚mol-1) TSE/(J‚mol-1) VE/(cm3‚mol-1)
1588b 801b 0.105b 1810i 1017i 0.137n 1985p 1223p 0.349n 1851i 1158i 0.422i
1325c 815g 0.010c 1488j 1036j 0.091j 1630q 1174q 0.352q 1571c 1203j 0.481c
956d -3d 0.141d 1206k 187k 0.207k 1507k 503k 0.452k 1560d 649d 0.728d
873e -65h 0.061e 1124l 179l 0.144l 1415l 513l 0.398l 1548e 705h 0.675e
510f -630f 0.08f 658f -488m 0.184o 858f -213m 0.439r 847f -17m 0.921r
a McClelland.24 b Garriga et al.25 c In ˜ arrea et al.26 d Garriga et al.5 e Pe´rez et al.27 f Brown et al.28 g Garriga et al.29 h Garriga et al.2 Garriga et al.30 j Garriga et al.31 k This work. l Garriga et al.3 m Calculated from GE data from Rodrı´guez et al.32 n Martı´nez et al.33 o Berro et al.34 p Garriga et al.35 q Garriga et al.36 r Pardo et al.,37 at T ) 303.15 K. i
Kister equation. Table 5 gives the Cj coefficients along with the standard deviations. We test the consistency of the enthalpies and free energies by means of the Gibbs-Helmholtz equation. The coefficients ∂Λij/∂T have been obtained by fitting the Wilson parameters as a linear function of the temperature. The HE-calculated values, at T ) 298.15 K, are shown as curves in Figure 3 together with the HE-experimental data found in the literature. The agreement is reasonable considering that the quantitative evaluation of HE from vapor pressures involves considerably uncertainty.23 In the same figure and at the same temperature, TSE curves, obtained from TSE ) HE - GE, are also plotted. For both systems, azeotropic mixtures with a minimum boiling temperature were observed over the whole range of temperature. Azeotropic mole fractions z2 were graphically calculated, assuming ideal behavior of the vapor, from the well-known equation, γ1/γ2 ) P02/P01. Azeotropic compositions show a linear relation with the temperature according to the equation
z2 ) a + b(T/K)
(11)
For 1-bromobutane + 2-mehtyl-1-propanol, a ) -0.5798 and b ) 2.390 × 10-3 K-1, and for 1-bromobutane + 2-butanol, a ) -0.7421 and b ) 3.190 × 10-3 K-1.
Along the azeotropic line, assuming both ideal behavior of the vapor phase and negligible volume of the liquid phase, the Clausius-Clapeyron equation
d ln Pz/dT ) ∆vapHz/RT2
(12)
is satisfied. If we accept that the enthalpy of azeotropic vaporization is constant, the azeotropic pressure is related to the temperature in a similar way to that shown by a pure substance
ln(Pz/Pa) ) A + B(T/K)-1
(13)
For 1-bromobutane + 2-mehtyl-1-propanol, A ) 23.91 and B ) - 4544 K, and for 1-bromobutane + 2-butanol, A ) 24.20 and B ) - 4608 K. Experimental and calculated (from eqs 11 and 13) azeotropic compositions and pressures are compared in Table 6. In Table 7, experimental values of thermodynamic properties are briefly summarized at T ) 298.15 K for butanol isomers with solvents of different polarity including n-hexane as an inert solvent. In mixtures of an alcohol with a polar solvent, solventsolvent and OH-group-solvent interactions come into play, and the excess molar entropies and enthalpies are much more positive than those with n-hexane in place of the polar
300
Journal of Chemical and Engineering Data, Vol. 48, No. 2, 2003 resultant of structural and interaction effects that are not easy to evaluate. Acknowledgment The authors are grateful for the financial support of Spanish Ministry of Science and Technology (Project BQU2000-1154). Literature Cited
Figure 4. Excess molar volumes at T ) 298.15 K: O, {x1 1-bromobutane + x2 2-methyl-1-propanol}; 0, {x1 1-bromobutane + x2 2-butanol}; b and 9, Artigas et al.20
Figure 5. Excess molar entropies, at T ) 298.15 K, for mixtures {0.5 butanol isomer + 0.5 solvent} with solvent: O, 1-bromobutane; b, 1-chlorobutane; 0, butanone; 9, butanenitrile; 4, nhexane.
solvent, as shown in Figure 5 and Table 7. By increasing the solvent polarity, both properties increase as more hydrogen bonds are broken at a given mole fraction because of the stronger hydroxyl group-solvent interaction. With the same solvent, all excess functions increase on going from 1-butanol to 2-methyl-2-propanol, which suggests an increase of the liquid butanol structure with the branching and shielding of the OH group. For these systems, a theoretical analysis of the volumetric behavior is a very complicated question, as VE is the
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