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Excess molar volumes of the ternary system {methylcyclohexane (1) + cyclohexane (2) + n-alkanes (3)} at T = 298.15 K
J. Chem. Thermodynamics 37 (2005) 1151–1161 www.elsevier.com/locate/jct
Excess molar volumes of the ternary system {methylcyclohexane (1) + cyclohexane (2) + n-alkanes (3)} at T = 298.15 K Hossein Iloukhani *, Mahdi Rezaei-Sameti Department of Chemistry, Faculty of Science, Bu-Ali Sina University, Hamadan, Iran Received 21 October 2004; received in revised form 7 February 2005; accepted 8 February 2005 Available online 10 March 2005
Abstract Densities were experimentally determined in the whole range of composition at T = 298.15 K for the ternary system {methylcyclohexane (1) + cyclohexane (2) + n-alkanes (3)} and for the seven corresponding binary systems. The n-alkanes include n-hexane, nheptane, and n-octane. Excess molar volumes, VE, were calculated for the binaries and ternaries systems. The V E123 data are positive over the entire range of composition for the systems {methylcyclohexane (1) + cyclohexane (2) + n-heptane (3) or n-octane (3)} at three fixed compositions (fm = X1/X2). For the system {methylcyclohexane (1) + cyclohexane (2) + n-hexane (3)}, the VE values showed positive for fm = 0.3 and negative for fm = 3. The VE data exhibit, an inversion in sign in the mixture containing fm = 1 for later ternary system. Several empirical expressions are used to predict and correlate the ternary excess molar volumes from experimental results on the constituted binaries and analyzed to gain insight about liquid mixture interactions. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Ternary system; Excess molar volumes; n-alkanes; Interactions
1. Introduction This paper, as part of a continuing study in our laboratory [1–4], presents experimental densities for the ternaries systems formed by {methylcyclohexane (1) + cyclohexane (2) + n-hexane (3), n-heptane (3), or n-octane (3)}, and constituted binary mixtures. Our results are compared with values of VE for the binary mixtures (methylcyclohexane + cyclohexane, cyclohexane + n-hexane, cyclohexane + n-heptane, cyclohexane + n-octane) which were reported earlier [5–7]. Experimental data for these properties allow us to test various fitting and predictive equations appearing in the literature. As computer design of chemical prop*
Corresponding author. Tel.: +98 811 8271541; fax: +98 811 8271061. E-mail address: [email protected] (H. Iloukhani). 0021-9614/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2005.02.006
erties requires mathematical models to predict or describe transport properties of pure liquids and their mixtures over the entire range of composition engineering. The excess properties are analyzed because of their importance for inferring which type of interactions predominates in liquid mixtures.
2. Experimental The solvents used in the present study, suppliers, and their purities are listed in table 1. Methylcyclohexane and cyclohexane were purified by the standard method described by Perrin and Armarego [8]. n-Alkanes, namely n-hexane, n-hepatne, and n-octane used were purified by distillation using a 1 m fractionation column. The purified compounds were stored in brown glass
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TABLE 1 Source, purity grades, density, q, refractive indices, nD, and normal boiling points, Tb, of the pure components at T = 298.15 K Compound
Methylcyclohexane Cyclohexane N-Hexane N-Heptane N-Octane a
Source
Merck Merck Merck Merck Merck
Purity/(mass %)
>99 99 99 99 >99
q/(kg Æ m3)
nD a
Tb/K a
Exp.
Ref.
Exp.
Ref.
Exp.
Ref.a
764.97 773.93 655.07 679.69 698.59
765.06a 773.89 654.81a 679.51a 698.49a
1.4207 1.4232 1.3720 1.3848 1.3950
1.42058 1.42354 1.37226 1.38511 1.39503
373.9 353.7 341.8 371.5 398.6
374.1 353.9 341.9 371.6 398.8
Reference [9].
bottles and fractionally distilled immediately before use. Purity of each compounds were ascertained by the accuracy of their boiling points and also from their density and refractive index values, which agreed as shown in table 1 with the literature values [9]. The boiling points at atmospheric pressure were measured using a Swietoslawski-type ebulimeter, which gave an accuracy of ±0.2 K. The density of the compounds and their binary and ternary mixtures were measured with Anton Paar DMA 4500 oscillating U-tube densitometer, provided with automatic viscosity correction. The density measurements accuracy was ±1 Æ 102 kg Æ m3. The temperature in the cell was regulated to ±0.01 K with solid state thermostat. The apparatus was calibrated once a day with dry air and double distilled freshly degassed water. Air tight stoppered bottles were used for the preparation of the mixtures. The mass of the dry bottle was first determined. The less volatile component of the mixture was introduced in the bottle and the total mass was recorded. Subsequently, the other component was introduced and the mass of the bottle along with the two components was determined. Ternary mixtures were prepared by mixing a measured binary mixtures (methylcyclohexane + cyclohexane at known composition) with pure liquids (n-hexane, n-heptane, and n-octane, as a third component). Each mixture was immediately used after it was well mixed by shaking. All the weightings were preformed on an electronic balance (AB 204-N Mettler) accurate to 0.1 mg. The uncertainly in the mole fraction is estimated to be lower than ±2 Æ 104. Refractive indices were measured at T = 298.15 K with an Abbe refractometer. Water was circulated to the refractometer from a constant-temperature both at T = 298.15 K. The accuracy of the refractive index measured is on the order of ±0.0002.
3.1. Excess molar volumes Molar volumes of the mixtures were calculated from the equation n X ðX i M i Þ=q; ð1Þ V ¼ i¼1
where Xi and Mi are the mole fraction and molar mass of component i and q is the measured density of the solution. The excess molar volumes VE for the seven binary systems and the corresponding ternary system were evaluated using the following equation: n X ðX i M i =qi Þ; ð2Þ VE ¼V i¼1
where Mi, V, and qi are the pure-component molar mass, molar volume, and density, respectively. The excess molar volumes are accurate to ±0.0003 cm3 Æ mol1. 3.2. Fitting equations 3.2.1. Binary systems VE for the binary systems were fitted by the leastsquares method to the Redlich–Kister [10] equation n X k Ak ðX i X j Þ ; ð3Þ V Eij ¼ X i X j k¼0 E ij
where V denotes the excess molar volume for the binary system with mole fractions Xi and Xj. Fitting parameters, Ak, and root mean deviations, r, are presented in table 4.
3. Results and discussion
3.2.2. Ternary systems The dependence of experimental ternary excess molar volumes on the composition is expressed by the polynomial h DV E123 ¼ X 1 X 2 X 3 A þ BX 1 ðX 2 X 3 Þþ i CX 21 ðX 2 X 3 Þ2 þ DX 31 ðX 2 X 3 Þ3 ; ð4Þ
Experimental excess molar volumes for the binary systems are listed in table 2 and for the ternary system in table 3.
where DV E123 is the difference between experimental ternary excess molar volume data and those calculated from binary data using the Redlich–Kister equation.
H. Iloukhani, M. Rezaei-Sameti / J. Chem. Thermodynamics 37 (2005) 1151–1161 TABLE 2 Experimental densities, q, excess molar volumes, VE, for binary system at T = 298.15 K X
0.0399 0.1202 0.2004 0.2820 0.3592 0.4401 0.5183 0.5511 0.6629 0.7551 0.8334 0.9219
q
VE
kg Æ m3
cm3 Æ mol1
{X methylcyclohexane + (1 X) cyclohexane} 773.53 0.0024 772.74 0.0072 771.95 0.0086 771.15 0.0056 770.40 0.0010 769.61 0.0049 768.88 0.0988 767.99 0.0134 767.57 0.0157 766.81 0.0153 766.20 0.0120 765.54 0.0047
0.0506 0.1005 0.1988 0.3015 0.4036 0.5028 0.5945 0.6653 0.7985 0.8508 0.8932 0.9413 0.0507
{X methylcyclohexane + (1 X) n-hexane} 660.68 666.23 677.10 688.42 699.71 710.63 720.68 728.48 742.97 748.76 753.37 758.60 660.68
0.0321 0.0671 0.1146 0.1462 0.1713 0.1769 0.1663 0.1578 0.1014 0.0900 0.0663 0.0380 0.0321
0.0529 0.1038 0.1958 0.3039 0.3993 0.4611 0.5045 0.5680 0.6280 0.7034 0.8172 0.8650 0.9066 0.9575
{X methylcyclohexane + (1 X) n-heptane} 683.71 687.59 694.71 703.31 711.08 716.24 719.91 721.18 728.28 737.24 747.61 749.21 756.00 760.85
0.0134 0.0185 0.0220 0.0253 0.0274 0.0281 0.0274 0.0252 0.0224 0.0175 0.0124 0.0093 0.0081 0.0012
0.0670 0.1001 0.2011 0.2993 0.4001 0.4996 0.6016 0.6983 0.7986 0.8509 0.8998 0.9486
{X methylcyclohexane + (1 X) n-octane} 702.12 703.93 709.48 715.14 721.23 727.56 734.38 741.20 748.63 752.71 756.65 760.66
0.0167 0.0118 0.0261 0.0364 0.0440 0.0464 0.0473 0.0425 0.0402 0.0224 0.0150 0.0060
0.0444 0.1222 0.1996
{X cyclohexane + (1 X) n-hexane} 768.00 762.10 750.57
0.0013 0.0384 0.0533
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TABLE 2 (continued) X
0.2828 0.3558 0.4375 0.5207 0.6007 0.6818 0.7657 0.8378 0.9200 0.9611
q
VE
kg Æ m3
cm3 Æ mol1
740.95 730.14 720.12 710.55 700.91 691.78 683.83 675.11 667.14 659.45
0.0873 0.1020 0.1219 0.1340 0.1411 0.1471 0.1382 0.1237 0.0778 0.0554
0.0516 0.0974 0.2503 0.2982 0.4017 0.4437 0.4881 0.5993 0.7000 0.7490 0.8718 0.8867 0.9479
{X cyclohexane + (1 X) n-heptane} 683.17 686.28 697.41 701.08 709.54 713.02 717.01 727.30 737.45 742.72 757.12 758.74 766.75
0.0328 0.0748 0.1787 0.2131 0.2534 0.2889 0.2853 0.3116 0.3004 0.2814 0.1910 0.1701 0.0931
0.0509 0.0991 0.2498 0.2996 0.3837 0.4467 0.4777 0.6064 0.6981 0.7961 0.8490 0.8996 0.9504
{X cyclohexane + (1 X) n-octane} 700.97 703.37 711.09 713.94 719.01 723.01 725.03 734.47 741.93 750.97 756.28 761.77 767.64
0.0489 0.0801 0.2443 0.2751 0.3247 0.3654 0.3894 0.3991 0.3901 0.3217 0.2710 0.1993 0.1178
X1, X2 and X3 are mole fractions of methylcyclohexane, cyclohexane, and n-alkanes, respectively. A, B, C, and D are ternary constants and their values, obtained by the least-squares method, are given in table 5 along with the root mean deviations.
4. Prediction of excess molar volumes for the ternary system Although prediction of the physical properties of multicomponent mixtures from those of their pure components is generally unreliable because of mixing effects, numerous schemes have been put forward for predictions based on the properties of the binary systems formed by pairs of components of the
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TABLE 3 Experimental densities, q, and excess molar volumes, VE, for the ternary system of {methylcyclohexane (1) + cyclohexane (2) + n-alkanes (3)} at T = 298.15 K X1
X2
X3
q
VE
kg Æ m3
cm Æ mol1
{Methylcyclohexane (1) + cyclohexane (2) + n-hexane (3)} fm = 0.3 0.0413 765.93 0.0831 760.21 0.1598 750.05 0.2356 740.38 0.3161 730.42 0.3926 721.19 0.4796 710.98 0.5520 702.70 0.6361 693.30 0.7108 685.13 0.7931 676.32 0.8753 667.73
0.2165 0.2052 0.1901 0.1728 0.1536 0.1337 0.1148 0.1005 0.0810 0.0645 0.0479 0.0285
0.7423 0.7117 0.6502 0.5916 0.5304 0.4737 0.4055 0.3475 0.2829 0.2247 0.1590 0.0961
0.4385 0.4235 0.3819 0.3492 0.3133 0.2697 0.2377 0.2032 0.1636 0.1286 0.0937 0.0555 0.0188
0.5214 0.4945 0.4580 0.4117 0.3675 0.3218 0.2788 0.2380 0.1952 0.1544 0.1085 0.0768 0.0214
fm = 1 0.0401 0.0820 0.1601 0.2391 0.3192 0.4085 0.4835 0.5588 0.6412 0.7170 0.7979 0.8677 0.9597
764.20 758.88 749.25 739.64 730.11 719.66 711.06 702.55 693.39 685.08 676.34 668.84 659.20
0.0256 0.0281 0.0240 0.0178 0.0070 0.0000 0.0089 0.0159 0.0231 0.0250 0.0207 0.0129 0.0020
0.6848 0.6651 0.6007 0.5528 0.4949 0.4381 0.3804 0.3187 0.2652 0.2074 0.1514 0.0888 0.0323
0.2722 0.2554 0.2413 0.2074 0.1970 0.1687 0.1490 0.1224 0.1037 0.0834 0.0578 0.0350 0.0151
fm = 3 0.0430 0.0795 0.1580 0.2399 0.3082 0.3932 0.4706 0.5589 0.6312 0.7092 0.7908 0.8762 0.9525
762.13 757.80 748.68 739.18 731.38 721.74 713.05 703.21 695.18 686.58 677.67 668.37 660.15
0.0078 0.0173 0.0330 0.0507 0.0613 0.0779 0.0891 0.0961 0.0914 0.0848 0.0709 0.0443 0.0222
{Methylcyclohexane (1) + cyclohexane (2) + n-heptane (3)} fm = 0.3 0.0384 766.61 0.0784 761.79 0.1599 752.35 0.2390 743.61 0.3195 735.32 0.3963 727.86 0.4740 720.66 0.5541 713.60 0.6357 706.73 0.7188 700.04 0.7941 694.34 0.8735 688.53 0.9562 682.76
0.0610 0.1058 0.1633 0.2193 0.2414 0.2439 0.2378 0.2221 0.1991 0.1710 0.1236 0.0749 0.0121
0.2252 0.2051 0.1862 0.1693 0.1511 0.1336 0.1157 0.0988 0.0798 0.0562 0.0464 0.0299 0.0112
0.7364 0.7165 0.6539 0.5918 0.5295 0.4701 0.4102 0.3471 0.2845 0.2250 0.1595 0.0966 0.0326
0.0230 0.0522 0.0778 0.0848 0.0841 0.0790 0.0676 0.0567 0.0428 0.0333 0.0252 0.0140
H. Iloukhani, M. Rezaei-Sameti / J. Chem. Thermodynamics 37 (2005) 1151–1161
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TABLE 3 (continued) X1
X2
X3
q
VE
kg Æ m3
cm Æ mol1
0.4398 0.4232 0.3816 0.3462 0.3140 0.2695 0.2427 0.2080 0.1670 0.1274 0.0922 0.0540 0.0294
0.5187 0.4966 0.4696 0.4281 0.3739 0.3429 0.2829 0.2412 0.1950 0.1518 0.1096 0.0615 0.0386
fm = 1 0.0414 0.0802 0.1489 0.2256 0.3121 0.3876 0.4744 0.5508 0.6381 0.7208 0.7982 0.8845 0.9320
764.53 760.07 752.61 744.60 735.97 728.84 720.96 714.33 707.02 700.34 694.39 688.01 684.61
0.0478 0.0841 0.1240 0.1494 0.1658 0.1680 0.1578 0.1434 0.1267 0.1100 0.0774 0.0332 0.0029
0.7052 0.6950 0.6713 0.6498 0.6181 0.5621 0.5440 0.3716 0.2848 0.2060 0.1493 0.0893 0.0306
0.2770 0.2728 0.2654 0.2546 0.2434 0.2485 0.2210 0.1456 0.1244 0.0801 0.0592 0.0350 0.0142
fm = 3 0.0179 0.0322 0.0633 0.0956 0.1385 0.1894 0.2351 0.4828 0.5908 0.7139 0.7916 0.8757 0.9552
765.20 763.66 760.39 757.05 752.67 747.70 743.19 720.50 711.40 701.40 695.27 688.87 682.94
0.0223 0.0298 0.0421 0.0498 0.0639 0.0744 0.0788 0.0867 0.0598 0.0396 0.0337 0.0156 0.0080
{Methylcyclohexane (1) + cyclohexane (2) + n-octane (3)} fm = 0.3 0.0819 762.49 0.1658 753.89 0.3165 740.53 0.4031 733.70 0.4726 728.68 0.5543 723.20 0.6385 717.92 0.7162 713.23 0.7883 709.13 0.8731 704.68 0.9536 700.83
0.1459 0.2370 0.3267 0.3412 0.3270 0.2941 0.2497 0.2261 0.1974 0.1317 0.0331
0.1897 0.1851 0.1409 0.1305 0.1220 0.1020 0.0812 0.0625 0.0554 0.0318 0.0134
0.7285 0.6491 0.5425 0.4665 0.4054 0.3437 0.2803 0.2213 0.1563 0.0951 0.0329
0.4238 0.3915 0.3513 0.3125 0.2738 0.2376 0.2042 0.1665 0.1389 0.0944 0.0593 0.0205
0.4939 0.4535 0.4089 0.3681 0.3247 0.2801 0.2409 0.1937 0.1646 0.1094 0.0684 0.0227
fm = 1 0.0822 0.1549 0.2398 0.3194 0.4015 0.4822 0.5549 0.6398 0.6964 0.7962 0.8723 0.9568
760.87 754.02 746.55 740.12 733.89 728.20 723.36 718.01 714.66 709.03 705.00 700.65
0.6704 0.6049 0.5488
0.2562 0.2450 0.2155
fm = 3 0.0734 0.1501 0.2357
760.18 753.50 746.43
0.1142 0.1699 0.2241 0.2453 0.2567 0.2470 0.2321 0.2084 0.1796 0.1274 0.0778 0.0401
0.0738 0.1160 0.1423 (continued on next page)
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TABLE 3 (continued) X2
X1 0.5002 0.4365 0.3815 0.3221 0.2633 0.2057 0.1492 0.0901 0.0310
X3
0.1912 0.1697 0.1472 0.1260 0.1031 0.0811 0.0595 0.0351 0.0128
0.3085 0.3938 0.4712 0.5519 0.6335 0.7132 0.7913 0.8748 0.9562
q
VE
kg Æ m3
cm Æ mol1
740.79 734.53 729.15 723.86 718.76 714.01 709.61 705.10 700.81
0.1519 0.1608 0.1594 0.1454 0.1271 0.1059 0.0711 0.0340 0.0140
TABLE 4 Values of parameters, Ak, of equation (3) and standard deviations, r, for binary Systems at T = 298K System
A0
A1
A2
{X Methylcyclohexane + (1 X) n-hexane} {X Methylcyclohexane + (1 X) n-heptane} {X Methylcyclohexane + (1 X) n-octane} {X Cyclohexane + (1 X) n-hexane} {X Cyclohexane + (1 X) n-heptane} {X Cyclohexane + (1 X) n-octane} {X Methylcyclohexane + (1 X) cyclohexane}
0.7084 0.1000 0.1975 0.5203 1.2061 1.5667 0.0365
0.0082 0.0041 0.0240 0.1447 0.5697 0.7205 0.1124
0.0276 0.0420 0.0719 0.2298 0.1955 0.0539 0.0471
A3 0.1285 0.6638
r/(cm3 Æ mol1) 0.0011 0.0025 0.0014 0.0001 0.0003 0.0050 0.0003
TABLE 5 Values of parameters, Ak, of equation (4) and standard deviations, r, for the ternary system at T = 298.15 K A
B
C
D
fm = 0.3 fm = 1 fm = 3
0.2930 0.1986 0.0473
{Methylcyclohexane (1) + cyclohexane (2) + n-hexane (3)} 19.7330 58.260 3.9245 43.633 2.5385 52.774
fm = 0.3 fm = 1 fm = 3
13.097 15.426 24.576
{Methylcyclohexane (1) + cyclohexane 164.750 76.906 87.990
fm = 0.3 fm = 1 fm = 3
1.2848 1.0489 1.0638
{Methylcyclohexane (1) + cyclohexane (2) + n-octane (3)} 20.076 492.72 0.5732 10.305 2.556 3.228
multicomponent system. In this work, we applied the following models [11–18]. 4.1. Tsao–Smith [11] model V E123 ¼ X 2 V E12 =ð1 X 1 Þ þ X 3 V E13 =ð1 X 1 Þ þ ð1 X 1 ÞV E23 : ð5Þ X 0i
Binary contributions were evaluated at ¼ X1 and X 0j ¼ 1 X 0i for 1-2 and 1-3 binaries, and X 02 ¼ X 2 =ðX 2 þ X 3 Þ and X 03 ¼ X 3 =ðX 2 þ X 3 Þ for 2-3 binary (option a in table 6). As this model is asymmetric, we evaluated binary contributions alternatively at
300.260 66.869
(2) + n-heptane (3)} 892.32 279.20 289.80
r/(cm3 Æ mol1) 0.0004 0.0079 0.0064 0.0320 0.0700 0.0050
3223.2 179.65 21.852
0.0065 0.0064 0.0062
X 0i ¼ X 2 and X 0j ¼ 1 X 0i for 2-1 and 2-3 binaries and X 03 ¼ X 3 =ðX 1 þ X 3 Þ and X 01 ¼ X 1 =ðX 1 þ X 3 Þ for the 3-1 binary (option b in table 6). The third alternative (option c in table 6), was using X 0i ¼ X 3 and X 0j ¼ 1 X 0i for 3-1 and 3-2 binaries and X 02 ¼ X 2 =ðX 2 þ X 1 Þ and X 01 ¼ X 1 =ðX 2 þ X 1 Þ for the 1-3 binary. 4.2. Jacob–Fitzner [12] model V E123 ¼ X 1 X 2 V E12 =½ðX 1 þ X 3 =2ÞðX 2 þ X 3 Þ=2þ X 1 X 3 V E13 =½ðX 1 þ X 2 =2ÞðX 3 þ X 2 Þ=2þ X 1 X 3 V E23 =½ðX 2 þ X 1 =2ÞðX 3 þ X 1 Þ=2:
ð6Þ
H. Iloukhani, M. Rezaei-Sameti / J. Chem. Thermodynamics 37 (2005) 1151–1161 TABLE 6 Standard deviations, r, in the predictions, VE with different models for the ternary system at T = 298.15K fm = 0.3
fm = 1
fm = 3
r/(cm3 Æ mol1)
r/(cm3 Æ mol1)
r/(cm3 Æ mol1)
{Methylcyclohexane (1) + cyclohexane (2) + n-hexane (3)} Radojkovic 0.0149 0.0112 0.0050 Rastogi 0.0507 0.0281 0.0458 Kohler 0.0220 0.0320 0.0723 Jacob and Fitzner 0.0613 0.0270 0.0585 Tsao and Smitha 0.0186 0.0267 0.0244 Tsao and Smithb 0.0296 0.0170 0.0159 0.0843 0.0124 0.0898 Tsao and Smithc Colinet 0.0171 0.0206 0.0499 Toopa 0.0080 0.0071 0.0273 Toopb 0.0230 0.0273 0.0200 0.0719 0.0151 0.0981 Toopc Scatcharda 0.0334 0.0581 0.0650 Scatchardb 0.0451 0.0171 0.0148 Scatchardc 0.0990 0.0326 0.0806
1157
Binary contributions were evaluated at mole fraction calculated by X 0i ¼ ð1 X 0j Þ ¼ X i =ðX i þ X j Þ. 4.4. Rastogi [14] model V E123 ¼ ½ðX 1 þ X 2 ÞV E12 þ ðX 1 þ X 3 ÞV E13 þ ðX 2 þ X 3 ÞV E23 =2:
ð8Þ
Binary contributions were evaluated at mole fraction calculated by X 0i ¼ ð1 X 0j Þ ¼ X i =ðX i þ X j Þ. 4.5. Radojkovic [15] model V E123 ¼ V E12 þ V E13 þ V E23 :
ð9Þ E ij
Binary contributions V were evaluated using the ternary mole fraction directly.
{Methylcyclohexane (1) + cyclohexane (2) + n-heptane (3)} Radojkovic 0.0167 0.0183 0.0132 Rastogi 0.0881 0.0458 0.0145 Kohler 0.0575 0.0445 0.0101 Jacob and Fitzner 0.1342 0.0437 0.0672 Tsao and Smitha 0.0201 0.0303 0.0353 0.0831 0.0186 0.0276 Tsao and Smithb Tsao and Smithc 0.2555 0.1284 0.0425 Colinet 0.0478 0.0282 0.0159 Toopa 0.0133 0.0178 0.0192 0.0499 0.0446 0.0391 Toopb Toopc 0.2295 0.1076 0.0404 Scatcharda 0.0501 0.0956 0.1544 Scatchardb 0.1256 0.0353 0.0082 0.2870 0.1644 0.0568 Scatchardc
4.6. Colinet [16] model V E123 ¼ 0:5 X 2 V E12 ðX 1 ; 1 X 1 Þ=ð1 X 1 Þþ X 1 V E12 ð1 X 2 ; X 2 Þ=ð1 X 2 Þþ X 3 V E13 ðX 1 ; 1 X 1 Þ=ð1 X 1 Þ þ 0:5 X 1 V E12 ð1 X 3 ; X 3 Þ=ð1 X 3 Þþ X 3 V E23 ðX 2 ; 1 X 2 Þ=ð1 X 2 Þþ X 2 V E23 ð1 X 3 ; X 3 Þ=ð1 X 3 Þ :
{Methylcyclohexane (1) + cyclohexane (2) + n-octane (3)} Radojkovic 0.0256 0.0268 0.0204 Rastogi 0.1039 0.0640 0.0208 Kohler 0.0663 0.0515 0.0340 Jacob and Fitzner 0.1625 0.0509 0.1095 Tsao and Smitha 0.2280 0.0306 0.0358 Tsao and Smithb 0.0988 0.0026 0.0450 Tsao and Smithc 0.4760 0.0246 0.1411 Colinet 0.0623 0.0501 0.0247 Toopa 0.0272 0.0338 0.0246 Toopb 0.0633 0.0609 0.0621 Toopc 0.4470 0.2200 0.1288 0.0495 0.1112 0.1628 Scatcharda Scatchardb 0.1448 0.0375 0.0123 Scatchardc 0.5116 0.2887 0.1644
ð10Þ
4.7. Toop [17] model The same argument is applied as Section 4.1 V E123 ¼ X 2 V E12 ðX 01 ; X 02 Þ=ð1 X 1 Þþ X 3 V E12 ðX 01 ; X 03 Þ=ð1 X 1 Þþ 2
ð1 X 1 Þ V E23 ðX 02 ; X 03 Þ:
ð11Þ
4.8. Scatchard [18] model Binary contributions were evaluated as Section 4.1 V E123 ¼ X 2 V E12 ðX 01 ; X 02 Þ=ð1 X 1 Þþ X 3 V E12 ðX 01 ; X 03 Þ=ð1 X 1 Þ þ V E23 ðX 02 ; X 03 Þ:
ð12Þ
Binary contributions were evaluated at mole fraction calculated by X 0i ¼ ð1 X 0j Þ ¼ ð1 þ X i X j Þ=2.
Standard deviations r, presented in table 6, were determined for all models as
4.3. Kohler [13] model
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi , u n 2 uX E E t V ðexp Þi V ðcalcÞi r¼ ðn pÞ;
ð13Þ
i¼1
V E123 ¼ ðX 1 þ X 2 Þ2 V E12 þ ðX 1 þ X 3 Þ2 V E13 þ 2
ðX 2 þ X 3 Þ V E23 :
ð7Þ
where p is the number of parameters and n is the number of experimental data.
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Experimental data and fits equation (3) for VE for the nine binary systems are depicted in figures 1 to 3. Comparison of VE for different systems reveals several interesting features. Excess molar volumes for the binary systems formed by cyclohexane with (n-hexane, n-heptane, n-octane) and methylcyclohexane with noctane are positive. This would indicate that molecular interactions between different molecules are weaker than interactions between molecules in the same pure liquid and that repulsive forces dominate the behaviour of the solutions. The negative values of excess molar volumes for the binary systems of methylcyclo-
hexane with n-hexane and n-heptane suggested the specific intermolecular interactions, between different molecules. The negative values of excess molar volumes also means that the mixtures is less compressible than the corresponding ideal mixture. Therefore, in the systems, a compression in free volume is considered to occur, making the mixtures less compressible than the ideal mixture, which ultimately culminates into the negative value of VE. For the binary systems with methylcyclohexane with cyclohexane, an inversion of the sign of VE is observed over some concentration of methylcyclohexane.
0.20 0.15
VE/(cm3· mol-1)
0.10 0.05 0.00 -0.05 -0.10 -0.15 -0.20 0.0
0.2
0.4
0.6
0.8
1.0
X
FIGURE 1. Excess molar volumes of the binary mixtures against mole fraction x at T = 298.15 K. Experimental results: (d) x methylcyclohexane + (1 x) cyclohexane, (,) x methylcyclohexane + (1 x) n-hexane, (n) x cyclohexane + (1 x) n-hexane, (——) calculated with equation (3) using parameters from table 4.
0.35 0.30
VE/(cm3· mol-1)
0.25 0.20 0.15 0.10 0.05 0.00 -0.05 0.0
0.2
0.4
0.6
0.8
1.0
X
FIGURE 2. Excess molar volumes of the binary mixtures against mole fraction x at T = 298.15 K. Experimental results: (d) x methylcyclohexane + (1 x) cyclohexane, (,) x methylcyclohexane + (1 x) n-heptane, (n) x cyclohexane + (1 x) n-heptane, (——) calculated with equation (3) using parameters from table 4.
H. Iloukhani, M. Rezaei-Sameti / J. Chem. Thermodynamics 37 (2005) 1151–1161
1159
0.5
VE/(cm3· mol-1)
0.4
0.3
0.2
0.1
0.0
-0.1 0.0
0.2
0.4
0.6
0.8
1.0
X
FIGURE 3. Excess molar volumes of the binary mixtures against mole fraction x at T = 298.15 K. Experimental results: (d) x methylcyclohexane + (1 x) cyclohexane, (,) x methylcyclohexane + (1 x) n-octane, (n) x cyclohexane + (1 x) n-octane, (——) calculated with equation (3) using parameters from table 4.
0.10 0.08 0.06
E 3 -1 V /(cm . mol )
0.04 0.02 0.00 -0.02 -0.04 -0.06 -0.08 -0.10 -0.12 0.0
0.2
0.4
0.6
0.8
1.0
X3 FIGURE 4. Excess molar volumes of the ternary mixtures formed by addition of n-hexane (3) to the binary mixtures of {methylcyclohexane (1) + cyclohexane (2)} for (d) fm = 0.3, (s) fm = 1 and (.) fm = 3 at T = 298.15 K.
Experimental data for VE of the ternary system at three fixed compositions, fm are shown in figures 4 to 6. Excess molar volumes for the ternary systems of {methylcyclohexane (1) + cyclohexane (2) + n-hexane (3)} is positive at fixed fm = 0.3, whereas at fm = 3 is negative over the whole range of composition of n-hexane. An inversion of the sign of VE is observed at fm = 1 for the above ternary systems (figure 4). For longer nalkanes, i.e., n-heptane and n-octane the VE values are positive over the whole composition range of n-alkanes
at three different fixed fm (figures 5 and 6). As can be seen in table 6, the standard deviations presented by Radojkovic et al. [15], Rastogi et al. [14], Kohler [13], Jacob and Fitzner [12], Taso and Smith [11], Colinet [16], Toop [17], Scatchard et al. [18], fitting equations for VE are similar and, although small, are beyond experimental errors. Thus, it is up to the design engineer to consider, the advantages of relying on these relations for the description of these properties as continuous models for the whole range of ternary compositions.
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0.25
E 3 -1 V /(cm · mol )
0.20
0.15
0.10
0.05
0.00 0.0
0.2
0.4
0.6
0.8
1.0
X3
FIGURE 5. Excess molar volumes of the ternary mixtures formed by addition of n-heptane (3) to the binary mixtures of {methylcyclohexane (1) + cyclohexane (2)} for (d) fm = 0.3, (s) fm = 1 and (.) fm = 3 at T = 298.15 K. 0.4
E 3 -1 V / (cm . mol )
0.3
0.2
0.1
0.0 0.0
0.2
0.4
0.6
0.8
1.0
X3 FIGURE 6. Excess molar volumes of the ternary mixtures formed by addition of n-octane (3) to the binary mixtures of {methylcyclohexane (1) + cyclohexane (2)} for (d) fm = 0.3, (s) fm = 1 and (.) fm = 3 at T = 298.15 K.
Acknowledgements The authors thank the University authorities for providing the necessary facilities to carry out the work. References [1] H. Iloukhani, Z. Rostami, J. Solution Chem. 32 (2003) 451–462. [2] H. Iloukhani, H.A. Zarei, J. Chem. Eng. Data 47 (2002) 195–197.
[3] [4] [5] [6]
H. Iloukhani, J.B. Parsa, J. Solution Chem. 30 (2001) 807–814. H.A. Zarei, H. Iloukhani, Thermochim. Acta 405 (2003) 123–128. A. Saito, R. Tanka, J. Chem. Thermodyn. 20 (1988) 859–865. B.J. Hasted, E.S. Thomoson, J. Chem. Thermodyn. 7 (1975) 369– 376. [7] M.B. Ewing, B.J. Levien, K.N. Marsh, R.H. Stokes, J. Chem. Thermodyn. 2 (1970) 689–695. [8] D.D. Perrin, W.L.F. Armarego, Purification of Laboratory Chemicals, third ed., Pergamon Press, New York, 1970. [9] J.A. Riddick, W.B. Bunger, T.K. Sakano, Organic Solvent, Wiley–Interscience, New York, 1986.
H. Iloukhani, M. Rezaei-Sameti / J. Chem. Thermodynamics 37 (2005) 1151–1161 [10] O.J. Redlich, A.T. Kister, Ind. Eng. Chem. 30 (1948) 345– 348. [11] C.C. Tsao, J.M. Smith, Chem. Eng. Prog. Symp. Ser. 49 (1953) 107–117. [12] K.T. Jacob, K. Fitzner, Thermochim. Acta 18 (1977) 197–206. [13] F. Kohler, Monatsh. Chem. 91 (1960) 738–740. [14] R.P. Rastogi, J. Nath, S.S. Das, J. Chem. Eng. Data 22 (1977) 249–252.
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[15] N. Radojkoric, A. Tasic, D. Grozdanic, B. Djordjevic, M. Malic, J. Chem.Thermodyn. 9 (1977) 349–352. [16] C. Colinet, Ph.D. Thesis, University of Grenoble, France, 1967. [17] G.W. Toop, Trans. TMS-AIME 223 (1965) 850–855. [18] G. Scatchard, L.B. Ticknor, J.R. Goates, E.R. McCartney, J. Am. Chem. Soc. 74 (1952) 3721–3724.
JCT 04-226
Excess molar volumes of the ternary system {methylcyclohexane (1) + cyclohexane (2) + n-alkanes (3)} at T = 298.15 K Hossein Iloukhani *, Mahdi Rezaei-Sameti Department of Chemistry, Faculty of Science, Bu-Ali Sina University, Hamadan, Iran Received 21 October 2004; received in revised form 7 February 2005; accepted 8 February 2005 Available online 10 March 2005
Abstract Densities were experimentally determined in the whole range of composition at T = 298.15 K for the ternary system {methylcyclohexane (1) + cyclohexane (2) + n-alkanes (3)} and for the seven corresponding binary systems. The n-alkanes include n-hexane, nheptane, and n-octane. Excess molar volumes, VE, were calculated for the binaries and ternaries systems. The V E123 data are positive over the entire range of composition for the systems {methylcyclohexane (1) + cyclohexane (2) + n-heptane (3) or n-octane (3)} at three fixed compositions (fm = X1/X2). For the system {methylcyclohexane (1) + cyclohexane (2) + n-hexane (3)}, the VE values showed positive for fm = 0.3 and negative for fm = 3. The VE data exhibit, an inversion in sign in the mixture containing fm = 1 for later ternary system. Several empirical expressions are used to predict and correlate the ternary excess molar volumes from experimental results on the constituted binaries and analyzed to gain insight about liquid mixture interactions. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Ternary system; Excess molar volumes; n-alkanes; Interactions
1. Introduction This paper, as part of a continuing study in our laboratory [1–4], presents experimental densities for the ternaries systems formed by {methylcyclohexane (1) + cyclohexane (2) + n-hexane (3), n-heptane (3), or n-octane (3)}, and constituted binary mixtures. Our results are compared with values of VE for the binary mixtures (methylcyclohexane + cyclohexane, cyclohexane + n-hexane, cyclohexane + n-heptane, cyclohexane + n-octane) which were reported earlier [5–7]. Experimental data for these properties allow us to test various fitting and predictive equations appearing in the literature. As computer design of chemical prop*
Corresponding author. Tel.: +98 811 8271541; fax: +98 811 8271061. E-mail address: [email protected] (H. Iloukhani). 0021-9614/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2005.02.006
erties requires mathematical models to predict or describe transport properties of pure liquids and their mixtures over the entire range of composition engineering. The excess properties are analyzed because of their importance for inferring which type of interactions predominates in liquid mixtures.
2. Experimental The solvents used in the present study, suppliers, and their purities are listed in table 1. Methylcyclohexane and cyclohexane were purified by the standard method described by Perrin and Armarego [8]. n-Alkanes, namely n-hexane, n-hepatne, and n-octane used were purified by distillation using a 1 m fractionation column. The purified compounds were stored in brown glass
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TABLE 1 Source, purity grades, density, q, refractive indices, nD, and normal boiling points, Tb, of the pure components at T = 298.15 K Compound
Methylcyclohexane Cyclohexane N-Hexane N-Heptane N-Octane a
Source
Merck Merck Merck Merck Merck
Purity/(mass %)
>99 99 99 99 >99
q/(kg Æ m3)
nD a
Tb/K a
Exp.
Ref.
Exp.
Ref.
Exp.
Ref.a
764.97 773.93 655.07 679.69 698.59
765.06a 773.89 654.81a 679.51a 698.49a
1.4207 1.4232 1.3720 1.3848 1.3950
1.42058 1.42354 1.37226 1.38511 1.39503
373.9 353.7 341.8 371.5 398.6
374.1 353.9 341.9 371.6 398.8
Reference [9].
bottles and fractionally distilled immediately before use. Purity of each compounds were ascertained by the accuracy of their boiling points and also from their density and refractive index values, which agreed as shown in table 1 with the literature values [9]. The boiling points at atmospheric pressure were measured using a Swietoslawski-type ebulimeter, which gave an accuracy of ±0.2 K. The density of the compounds and their binary and ternary mixtures were measured with Anton Paar DMA 4500 oscillating U-tube densitometer, provided with automatic viscosity correction. The density measurements accuracy was ±1 Æ 102 kg Æ m3. The temperature in the cell was regulated to ±0.01 K with solid state thermostat. The apparatus was calibrated once a day with dry air and double distilled freshly degassed water. Air tight stoppered bottles were used for the preparation of the mixtures. The mass of the dry bottle was first determined. The less volatile component of the mixture was introduced in the bottle and the total mass was recorded. Subsequently, the other component was introduced and the mass of the bottle along with the two components was determined. Ternary mixtures were prepared by mixing a measured binary mixtures (methylcyclohexane + cyclohexane at known composition) with pure liquids (n-hexane, n-heptane, and n-octane, as a third component). Each mixture was immediately used after it was well mixed by shaking. All the weightings were preformed on an electronic balance (AB 204-N Mettler) accurate to 0.1 mg. The uncertainly in the mole fraction is estimated to be lower than ±2 Æ 104. Refractive indices were measured at T = 298.15 K with an Abbe refractometer. Water was circulated to the refractometer from a constant-temperature both at T = 298.15 K. The accuracy of the refractive index measured is on the order of ±0.0002.
3.1. Excess molar volumes Molar volumes of the mixtures were calculated from the equation n X ðX i M i Þ=q; ð1Þ V ¼ i¼1
where Xi and Mi are the mole fraction and molar mass of component i and q is the measured density of the solution. The excess molar volumes VE for the seven binary systems and the corresponding ternary system were evaluated using the following equation: n X ðX i M i =qi Þ; ð2Þ VE ¼V i¼1
where Mi, V, and qi are the pure-component molar mass, molar volume, and density, respectively. The excess molar volumes are accurate to ±0.0003 cm3 Æ mol1. 3.2. Fitting equations 3.2.1. Binary systems VE for the binary systems were fitted by the leastsquares method to the Redlich–Kister [10] equation n X k Ak ðX i X j Þ ; ð3Þ V Eij ¼ X i X j k¼0 E ij
where V denotes the excess molar volume for the binary system with mole fractions Xi and Xj. Fitting parameters, Ak, and root mean deviations, r, are presented in table 4.
3. Results and discussion
3.2.2. Ternary systems The dependence of experimental ternary excess molar volumes on the composition is expressed by the polynomial h DV E123 ¼ X 1 X 2 X 3 A þ BX 1 ðX 2 X 3 Þþ i CX 21 ðX 2 X 3 Þ2 þ DX 31 ðX 2 X 3 Þ3 ; ð4Þ
Experimental excess molar volumes for the binary systems are listed in table 2 and for the ternary system in table 3.
where DV E123 is the difference between experimental ternary excess molar volume data and those calculated from binary data using the Redlich–Kister equation.
H. Iloukhani, M. Rezaei-Sameti / J. Chem. Thermodynamics 37 (2005) 1151–1161 TABLE 2 Experimental densities, q, excess molar volumes, VE, for binary system at T = 298.15 K X
0.0399 0.1202 0.2004 0.2820 0.3592 0.4401 0.5183 0.5511 0.6629 0.7551 0.8334 0.9219
q
VE
kg Æ m3
cm3 Æ mol1
{X methylcyclohexane + (1 X) cyclohexane} 773.53 0.0024 772.74 0.0072 771.95 0.0086 771.15 0.0056 770.40 0.0010 769.61 0.0049 768.88 0.0988 767.99 0.0134 767.57 0.0157 766.81 0.0153 766.20 0.0120 765.54 0.0047
0.0506 0.1005 0.1988 0.3015 0.4036 0.5028 0.5945 0.6653 0.7985 0.8508 0.8932 0.9413 0.0507
{X methylcyclohexane + (1 X) n-hexane} 660.68 666.23 677.10 688.42 699.71 710.63 720.68 728.48 742.97 748.76 753.37 758.60 660.68
0.0321 0.0671 0.1146 0.1462 0.1713 0.1769 0.1663 0.1578 0.1014 0.0900 0.0663 0.0380 0.0321
0.0529 0.1038 0.1958 0.3039 0.3993 0.4611 0.5045 0.5680 0.6280 0.7034 0.8172 0.8650 0.9066 0.9575
{X methylcyclohexane + (1 X) n-heptane} 683.71 687.59 694.71 703.31 711.08 716.24 719.91 721.18 728.28 737.24 747.61 749.21 756.00 760.85
0.0134 0.0185 0.0220 0.0253 0.0274 0.0281 0.0274 0.0252 0.0224 0.0175 0.0124 0.0093 0.0081 0.0012
0.0670 0.1001 0.2011 0.2993 0.4001 0.4996 0.6016 0.6983 0.7986 0.8509 0.8998 0.9486
{X methylcyclohexane + (1 X) n-octane} 702.12 703.93 709.48 715.14 721.23 727.56 734.38 741.20 748.63 752.71 756.65 760.66
0.0167 0.0118 0.0261 0.0364 0.0440 0.0464 0.0473 0.0425 0.0402 0.0224 0.0150 0.0060
0.0444 0.1222 0.1996
{X cyclohexane + (1 X) n-hexane} 768.00 762.10 750.57
0.0013 0.0384 0.0533
1153
TABLE 2 (continued) X
0.2828 0.3558 0.4375 0.5207 0.6007 0.6818 0.7657 0.8378 0.9200 0.9611
q
VE
kg Æ m3
cm3 Æ mol1
740.95 730.14 720.12 710.55 700.91 691.78 683.83 675.11 667.14 659.45
0.0873 0.1020 0.1219 0.1340 0.1411 0.1471 0.1382 0.1237 0.0778 0.0554
0.0516 0.0974 0.2503 0.2982 0.4017 0.4437 0.4881 0.5993 0.7000 0.7490 0.8718 0.8867 0.9479
{X cyclohexane + (1 X) n-heptane} 683.17 686.28 697.41 701.08 709.54 713.02 717.01 727.30 737.45 742.72 757.12 758.74 766.75
0.0328 0.0748 0.1787 0.2131 0.2534 0.2889 0.2853 0.3116 0.3004 0.2814 0.1910 0.1701 0.0931
0.0509 0.0991 0.2498 0.2996 0.3837 0.4467 0.4777 0.6064 0.6981 0.7961 0.8490 0.8996 0.9504
{X cyclohexane + (1 X) n-octane} 700.97 703.37 711.09 713.94 719.01 723.01 725.03 734.47 741.93 750.97 756.28 761.77 767.64
0.0489 0.0801 0.2443 0.2751 0.3247 0.3654 0.3894 0.3991 0.3901 0.3217 0.2710 0.1993 0.1178
X1, X2 and X3 are mole fractions of methylcyclohexane, cyclohexane, and n-alkanes, respectively. A, B, C, and D are ternary constants and their values, obtained by the least-squares method, are given in table 5 along with the root mean deviations.
4. Prediction of excess molar volumes for the ternary system Although prediction of the physical properties of multicomponent mixtures from those of their pure components is generally unreliable because of mixing effects, numerous schemes have been put forward for predictions based on the properties of the binary systems formed by pairs of components of the
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TABLE 3 Experimental densities, q, and excess molar volumes, VE, for the ternary system of {methylcyclohexane (1) + cyclohexane (2) + n-alkanes (3)} at T = 298.15 K X1
X2
X3
q
VE
kg Æ m3
cm Æ mol1
{Methylcyclohexane (1) + cyclohexane (2) + n-hexane (3)} fm = 0.3 0.0413 765.93 0.0831 760.21 0.1598 750.05 0.2356 740.38 0.3161 730.42 0.3926 721.19 0.4796 710.98 0.5520 702.70 0.6361 693.30 0.7108 685.13 0.7931 676.32 0.8753 667.73
0.2165 0.2052 0.1901 0.1728 0.1536 0.1337 0.1148 0.1005 0.0810 0.0645 0.0479 0.0285
0.7423 0.7117 0.6502 0.5916 0.5304 0.4737 0.4055 0.3475 0.2829 0.2247 0.1590 0.0961
0.4385 0.4235 0.3819 0.3492 0.3133 0.2697 0.2377 0.2032 0.1636 0.1286 0.0937 0.0555 0.0188
0.5214 0.4945 0.4580 0.4117 0.3675 0.3218 0.2788 0.2380 0.1952 0.1544 0.1085 0.0768 0.0214
fm = 1 0.0401 0.0820 0.1601 0.2391 0.3192 0.4085 0.4835 0.5588 0.6412 0.7170 0.7979 0.8677 0.9597
764.20 758.88 749.25 739.64 730.11 719.66 711.06 702.55 693.39 685.08 676.34 668.84 659.20
0.0256 0.0281 0.0240 0.0178 0.0070 0.0000 0.0089 0.0159 0.0231 0.0250 0.0207 0.0129 0.0020
0.6848 0.6651 0.6007 0.5528 0.4949 0.4381 0.3804 0.3187 0.2652 0.2074 0.1514 0.0888 0.0323
0.2722 0.2554 0.2413 0.2074 0.1970 0.1687 0.1490 0.1224 0.1037 0.0834 0.0578 0.0350 0.0151
fm = 3 0.0430 0.0795 0.1580 0.2399 0.3082 0.3932 0.4706 0.5589 0.6312 0.7092 0.7908 0.8762 0.9525
762.13 757.80 748.68 739.18 731.38 721.74 713.05 703.21 695.18 686.58 677.67 668.37 660.15
0.0078 0.0173 0.0330 0.0507 0.0613 0.0779 0.0891 0.0961 0.0914 0.0848 0.0709 0.0443 0.0222
{Methylcyclohexane (1) + cyclohexane (2) + n-heptane (3)} fm = 0.3 0.0384 766.61 0.0784 761.79 0.1599 752.35 0.2390 743.61 0.3195 735.32 0.3963 727.86 0.4740 720.66 0.5541 713.60 0.6357 706.73 0.7188 700.04 0.7941 694.34 0.8735 688.53 0.9562 682.76
0.0610 0.1058 0.1633 0.2193 0.2414 0.2439 0.2378 0.2221 0.1991 0.1710 0.1236 0.0749 0.0121
0.2252 0.2051 0.1862 0.1693 0.1511 0.1336 0.1157 0.0988 0.0798 0.0562 0.0464 0.0299 0.0112
0.7364 0.7165 0.6539 0.5918 0.5295 0.4701 0.4102 0.3471 0.2845 0.2250 0.1595 0.0966 0.0326
0.0230 0.0522 0.0778 0.0848 0.0841 0.0790 0.0676 0.0567 0.0428 0.0333 0.0252 0.0140
H. Iloukhani, M. Rezaei-Sameti / J. Chem. Thermodynamics 37 (2005) 1151–1161
1155
TABLE 3 (continued) X1
X2
X3
q
VE
kg Æ m3
cm Æ mol1
0.4398 0.4232 0.3816 0.3462 0.3140 0.2695 0.2427 0.2080 0.1670 0.1274 0.0922 0.0540 0.0294
0.5187 0.4966 0.4696 0.4281 0.3739 0.3429 0.2829 0.2412 0.1950 0.1518 0.1096 0.0615 0.0386
fm = 1 0.0414 0.0802 0.1489 0.2256 0.3121 0.3876 0.4744 0.5508 0.6381 0.7208 0.7982 0.8845 0.9320
764.53 760.07 752.61 744.60 735.97 728.84 720.96 714.33 707.02 700.34 694.39 688.01 684.61
0.0478 0.0841 0.1240 0.1494 0.1658 0.1680 0.1578 0.1434 0.1267 0.1100 0.0774 0.0332 0.0029
0.7052 0.6950 0.6713 0.6498 0.6181 0.5621 0.5440 0.3716 0.2848 0.2060 0.1493 0.0893 0.0306
0.2770 0.2728 0.2654 0.2546 0.2434 0.2485 0.2210 0.1456 0.1244 0.0801 0.0592 0.0350 0.0142
fm = 3 0.0179 0.0322 0.0633 0.0956 0.1385 0.1894 0.2351 0.4828 0.5908 0.7139 0.7916 0.8757 0.9552
765.20 763.66 760.39 757.05 752.67 747.70 743.19 720.50 711.40 701.40 695.27 688.87 682.94
0.0223 0.0298 0.0421 0.0498 0.0639 0.0744 0.0788 0.0867 0.0598 0.0396 0.0337 0.0156 0.0080
{Methylcyclohexane (1) + cyclohexane (2) + n-octane (3)} fm = 0.3 0.0819 762.49 0.1658 753.89 0.3165 740.53 0.4031 733.70 0.4726 728.68 0.5543 723.20 0.6385 717.92 0.7162 713.23 0.7883 709.13 0.8731 704.68 0.9536 700.83
0.1459 0.2370 0.3267 0.3412 0.3270 0.2941 0.2497 0.2261 0.1974 0.1317 0.0331
0.1897 0.1851 0.1409 0.1305 0.1220 0.1020 0.0812 0.0625 0.0554 0.0318 0.0134
0.7285 0.6491 0.5425 0.4665 0.4054 0.3437 0.2803 0.2213 0.1563 0.0951 0.0329
0.4238 0.3915 0.3513 0.3125 0.2738 0.2376 0.2042 0.1665 0.1389 0.0944 0.0593 0.0205
0.4939 0.4535 0.4089 0.3681 0.3247 0.2801 0.2409 0.1937 0.1646 0.1094 0.0684 0.0227
fm = 1 0.0822 0.1549 0.2398 0.3194 0.4015 0.4822 0.5549 0.6398 0.6964 0.7962 0.8723 0.9568
760.87 754.02 746.55 740.12 733.89 728.20 723.36 718.01 714.66 709.03 705.00 700.65
0.6704 0.6049 0.5488
0.2562 0.2450 0.2155
fm = 3 0.0734 0.1501 0.2357
760.18 753.50 746.43
0.1142 0.1699 0.2241 0.2453 0.2567 0.2470 0.2321 0.2084 0.1796 0.1274 0.0778 0.0401
0.0738 0.1160 0.1423 (continued on next page)
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TABLE 3 (continued) X2
X1 0.5002 0.4365 0.3815 0.3221 0.2633 0.2057 0.1492 0.0901 0.0310
X3
0.1912 0.1697 0.1472 0.1260 0.1031 0.0811 0.0595 0.0351 0.0128
0.3085 0.3938 0.4712 0.5519 0.6335 0.7132 0.7913 0.8748 0.9562
q
VE
kg Æ m3
cm Æ mol1
740.79 734.53 729.15 723.86 718.76 714.01 709.61 705.10 700.81
0.1519 0.1608 0.1594 0.1454 0.1271 0.1059 0.0711 0.0340 0.0140
TABLE 4 Values of parameters, Ak, of equation (3) and standard deviations, r, for binary Systems at T = 298K System
A0
A1
A2
{X Methylcyclohexane + (1 X) n-hexane} {X Methylcyclohexane + (1 X) n-heptane} {X Methylcyclohexane + (1 X) n-octane} {X Cyclohexane + (1 X) n-hexane} {X Cyclohexane + (1 X) n-heptane} {X Cyclohexane + (1 X) n-octane} {X Methylcyclohexane + (1 X) cyclohexane}
0.7084 0.1000 0.1975 0.5203 1.2061 1.5667 0.0365
0.0082 0.0041 0.0240 0.1447 0.5697 0.7205 0.1124
0.0276 0.0420 0.0719 0.2298 0.1955 0.0539 0.0471
A3 0.1285 0.6638
r/(cm3 Æ mol1) 0.0011 0.0025 0.0014 0.0001 0.0003 0.0050 0.0003
TABLE 5 Values of parameters, Ak, of equation (4) and standard deviations, r, for the ternary system at T = 298.15 K A
B
C
D
fm = 0.3 fm = 1 fm = 3
0.2930 0.1986 0.0473
{Methylcyclohexane (1) + cyclohexane (2) + n-hexane (3)} 19.7330 58.260 3.9245 43.633 2.5385 52.774
fm = 0.3 fm = 1 fm = 3
13.097 15.426 24.576
{Methylcyclohexane (1) + cyclohexane 164.750 76.906 87.990
fm = 0.3 fm = 1 fm = 3
1.2848 1.0489 1.0638
{Methylcyclohexane (1) + cyclohexane (2) + n-octane (3)} 20.076 492.72 0.5732 10.305 2.556 3.228
multicomponent system. In this work, we applied the following models [11–18]. 4.1. Tsao–Smith [11] model V E123 ¼ X 2 V E12 =ð1 X 1 Þ þ X 3 V E13 =ð1 X 1 Þ þ ð1 X 1 ÞV E23 : ð5Þ X 0i
Binary contributions were evaluated at ¼ X1 and X 0j ¼ 1 X 0i for 1-2 and 1-3 binaries, and X 02 ¼ X 2 =ðX 2 þ X 3 Þ and X 03 ¼ X 3 =ðX 2 þ X 3 Þ for 2-3 binary (option a in table 6). As this model is asymmetric, we evaluated binary contributions alternatively at
300.260 66.869
(2) + n-heptane (3)} 892.32 279.20 289.80
r/(cm3 Æ mol1) 0.0004 0.0079 0.0064 0.0320 0.0700 0.0050
3223.2 179.65 21.852
0.0065 0.0064 0.0062
X 0i ¼ X 2 and X 0j ¼ 1 X 0i for 2-1 and 2-3 binaries and X 03 ¼ X 3 =ðX 1 þ X 3 Þ and X 01 ¼ X 1 =ðX 1 þ X 3 Þ for the 3-1 binary (option b in table 6). The third alternative (option c in table 6), was using X 0i ¼ X 3 and X 0j ¼ 1 X 0i for 3-1 and 3-2 binaries and X 02 ¼ X 2 =ðX 2 þ X 1 Þ and X 01 ¼ X 1 =ðX 2 þ X 1 Þ for the 1-3 binary. 4.2. Jacob–Fitzner [12] model V E123 ¼ X 1 X 2 V E12 =½ðX 1 þ X 3 =2ÞðX 2 þ X 3 Þ=2þ X 1 X 3 V E13 =½ðX 1 þ X 2 =2ÞðX 3 þ X 2 Þ=2þ X 1 X 3 V E23 =½ðX 2 þ X 1 =2ÞðX 3 þ X 1 Þ=2:
ð6Þ
H. Iloukhani, M. Rezaei-Sameti / J. Chem. Thermodynamics 37 (2005) 1151–1161 TABLE 6 Standard deviations, r, in the predictions, VE with different models for the ternary system at T = 298.15K fm = 0.3
fm = 1
fm = 3
r/(cm3 Æ mol1)
r/(cm3 Æ mol1)
r/(cm3 Æ mol1)
{Methylcyclohexane (1) + cyclohexane (2) + n-hexane (3)} Radojkovic 0.0149 0.0112 0.0050 Rastogi 0.0507 0.0281 0.0458 Kohler 0.0220 0.0320 0.0723 Jacob and Fitzner 0.0613 0.0270 0.0585 Tsao and Smitha 0.0186 0.0267 0.0244 Tsao and Smithb 0.0296 0.0170 0.0159 0.0843 0.0124 0.0898 Tsao and Smithc Colinet 0.0171 0.0206 0.0499 Toopa 0.0080 0.0071 0.0273 Toopb 0.0230 0.0273 0.0200 0.0719 0.0151 0.0981 Toopc Scatcharda 0.0334 0.0581 0.0650 Scatchardb 0.0451 0.0171 0.0148 Scatchardc 0.0990 0.0326 0.0806
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Binary contributions were evaluated at mole fraction calculated by X 0i ¼ ð1 X 0j Þ ¼ X i =ðX i þ X j Þ. 4.4. Rastogi [14] model V E123 ¼ ½ðX 1 þ X 2 ÞV E12 þ ðX 1 þ X 3 ÞV E13 þ ðX 2 þ X 3 ÞV E23 =2:
ð8Þ
Binary contributions were evaluated at mole fraction calculated by X 0i ¼ ð1 X 0j Þ ¼ X i =ðX i þ X j Þ. 4.5. Radojkovic [15] model V E123 ¼ V E12 þ V E13 þ V E23 :
ð9Þ E ij
Binary contributions V were evaluated using the ternary mole fraction directly.
{Methylcyclohexane (1) + cyclohexane (2) + n-heptane (3)} Radojkovic 0.0167 0.0183 0.0132 Rastogi 0.0881 0.0458 0.0145 Kohler 0.0575 0.0445 0.0101 Jacob and Fitzner 0.1342 0.0437 0.0672 Tsao and Smitha 0.0201 0.0303 0.0353 0.0831 0.0186 0.0276 Tsao and Smithb Tsao and Smithc 0.2555 0.1284 0.0425 Colinet 0.0478 0.0282 0.0159 Toopa 0.0133 0.0178 0.0192 0.0499 0.0446 0.0391 Toopb Toopc 0.2295 0.1076 0.0404 Scatcharda 0.0501 0.0956 0.1544 Scatchardb 0.1256 0.0353 0.0082 0.2870 0.1644 0.0568 Scatchardc
4.6. Colinet [16] model V E123 ¼ 0:5 X 2 V E12 ðX 1 ; 1 X 1 Þ=ð1 X 1 Þþ X 1 V E12 ð1 X 2 ; X 2 Þ=ð1 X 2 Þþ X 3 V E13 ðX 1 ; 1 X 1 Þ=ð1 X 1 Þ þ 0:5 X 1 V E12 ð1 X 3 ; X 3 Þ=ð1 X 3 Þþ X 3 V E23 ðX 2 ; 1 X 2 Þ=ð1 X 2 Þþ X 2 V E23 ð1 X 3 ; X 3 Þ=ð1 X 3 Þ :
{Methylcyclohexane (1) + cyclohexane (2) + n-octane (3)} Radojkovic 0.0256 0.0268 0.0204 Rastogi 0.1039 0.0640 0.0208 Kohler 0.0663 0.0515 0.0340 Jacob and Fitzner 0.1625 0.0509 0.1095 Tsao and Smitha 0.2280 0.0306 0.0358 Tsao and Smithb 0.0988 0.0026 0.0450 Tsao and Smithc 0.4760 0.0246 0.1411 Colinet 0.0623 0.0501 0.0247 Toopa 0.0272 0.0338 0.0246 Toopb 0.0633 0.0609 0.0621 Toopc 0.4470 0.2200 0.1288 0.0495 0.1112 0.1628 Scatcharda Scatchardb 0.1448 0.0375 0.0123 Scatchardc 0.5116 0.2887 0.1644
ð10Þ
4.7. Toop [17] model The same argument is applied as Section 4.1 V E123 ¼ X 2 V E12 ðX 01 ; X 02 Þ=ð1 X 1 Þþ X 3 V E12 ðX 01 ; X 03 Þ=ð1 X 1 Þþ 2
ð1 X 1 Þ V E23 ðX 02 ; X 03 Þ:
ð11Þ
4.8. Scatchard [18] model Binary contributions were evaluated as Section 4.1 V E123 ¼ X 2 V E12 ðX 01 ; X 02 Þ=ð1 X 1 Þþ X 3 V E12 ðX 01 ; X 03 Þ=ð1 X 1 Þ þ V E23 ðX 02 ; X 03 Þ:
ð12Þ
Binary contributions were evaluated at mole fraction calculated by X 0i ¼ ð1 X 0j Þ ¼ ð1 þ X i X j Þ=2.
Standard deviations r, presented in table 6, were determined for all models as
4.3. Kohler [13] model
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi , u n 2 uX E E t V ðexp Þi V ðcalcÞi r¼ ðn pÞ;
ð13Þ
i¼1
V E123 ¼ ðX 1 þ X 2 Þ2 V E12 þ ðX 1 þ X 3 Þ2 V E13 þ 2
ðX 2 þ X 3 Þ V E23 :
ð7Þ
where p is the number of parameters and n is the number of experimental data.
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Experimental data and fits equation (3) for VE for the nine binary systems are depicted in figures 1 to 3. Comparison of VE for different systems reveals several interesting features. Excess molar volumes for the binary systems formed by cyclohexane with (n-hexane, n-heptane, n-octane) and methylcyclohexane with noctane are positive. This would indicate that molecular interactions between different molecules are weaker than interactions between molecules in the same pure liquid and that repulsive forces dominate the behaviour of the solutions. The negative values of excess molar volumes for the binary systems of methylcyclo-
hexane with n-hexane and n-heptane suggested the specific intermolecular interactions, between different molecules. The negative values of excess molar volumes also means that the mixtures is less compressible than the corresponding ideal mixture. Therefore, in the systems, a compression in free volume is considered to occur, making the mixtures less compressible than the ideal mixture, which ultimately culminates into the negative value of VE. For the binary systems with methylcyclohexane with cyclohexane, an inversion of the sign of VE is observed over some concentration of methylcyclohexane.
0.20 0.15
VE/(cm3· mol-1)
0.10 0.05 0.00 -0.05 -0.10 -0.15 -0.20 0.0
0.2
0.4
0.6
0.8
1.0
X
FIGURE 1. Excess molar volumes of the binary mixtures against mole fraction x at T = 298.15 K. Experimental results: (d) x methylcyclohexane + (1 x) cyclohexane, (,) x methylcyclohexane + (1 x) n-hexane, (n) x cyclohexane + (1 x) n-hexane, (——) calculated with equation (3) using parameters from table 4.
0.35 0.30
VE/(cm3· mol-1)
0.25 0.20 0.15 0.10 0.05 0.00 -0.05 0.0
0.2
0.4
0.6
0.8
1.0
X
FIGURE 2. Excess molar volumes of the binary mixtures against mole fraction x at T = 298.15 K. Experimental results: (d) x methylcyclohexane + (1 x) cyclohexane, (,) x methylcyclohexane + (1 x) n-heptane, (n) x cyclohexane + (1 x) n-heptane, (——) calculated with equation (3) using parameters from table 4.
H. Iloukhani, M. Rezaei-Sameti / J. Chem. Thermodynamics 37 (2005) 1151–1161
1159
0.5
VE/(cm3· mol-1)
0.4
0.3
0.2
0.1
0.0
-0.1 0.0
0.2
0.4
0.6
0.8
1.0
X
FIGURE 3. Excess molar volumes of the binary mixtures against mole fraction x at T = 298.15 K. Experimental results: (d) x methylcyclohexane + (1 x) cyclohexane, (,) x methylcyclohexane + (1 x) n-octane, (n) x cyclohexane + (1 x) n-octane, (——) calculated with equation (3) using parameters from table 4.
0.10 0.08 0.06
E 3 -1 V /(cm . mol )
0.04 0.02 0.00 -0.02 -0.04 -0.06 -0.08 -0.10 -0.12 0.0
0.2
0.4
0.6
0.8
1.0
X3 FIGURE 4. Excess molar volumes of the ternary mixtures formed by addition of n-hexane (3) to the binary mixtures of {methylcyclohexane (1) + cyclohexane (2)} for (d) fm = 0.3, (s) fm = 1 and (.) fm = 3 at T = 298.15 K.
Experimental data for VE of the ternary system at three fixed compositions, fm are shown in figures 4 to 6. Excess molar volumes for the ternary systems of {methylcyclohexane (1) + cyclohexane (2) + n-hexane (3)} is positive at fixed fm = 0.3, whereas at fm = 3 is negative over the whole range of composition of n-hexane. An inversion of the sign of VE is observed at fm = 1 for the above ternary systems (figure 4). For longer nalkanes, i.e., n-heptane and n-octane the VE values are positive over the whole composition range of n-alkanes
at three different fixed fm (figures 5 and 6). As can be seen in table 6, the standard deviations presented by Radojkovic et al. [15], Rastogi et al. [14], Kohler [13], Jacob and Fitzner [12], Taso and Smith [11], Colinet [16], Toop [17], Scatchard et al. [18], fitting equations for VE are similar and, although small, are beyond experimental errors. Thus, it is up to the design engineer to consider, the advantages of relying on these relations for the description of these properties as continuous models for the whole range of ternary compositions.
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H. Iloukhani, M. Rezaei-Sameti / J. Chem. Thermodynamics 37 (2005) 1151–1161 0.30
0.25
E 3 -1 V /(cm · mol )
0.20
0.15
0.10
0.05
0.00 0.0
0.2
0.4
0.6
0.8
1.0
X3
FIGURE 5. Excess molar volumes of the ternary mixtures formed by addition of n-heptane (3) to the binary mixtures of {methylcyclohexane (1) + cyclohexane (2)} for (d) fm = 0.3, (s) fm = 1 and (.) fm = 3 at T = 298.15 K. 0.4
E 3 -1 V / (cm . mol )
0.3
0.2
0.1
0.0 0.0
0.2
0.4
0.6
0.8
1.0
X3 FIGURE 6. Excess molar volumes of the ternary mixtures formed by addition of n-octane (3) to the binary mixtures of {methylcyclohexane (1) + cyclohexane (2)} for (d) fm = 0.3, (s) fm = 1 and (.) fm = 3 at T = 298.15 K.
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[15] N. Radojkoric, A. Tasic, D. Grozdanic, B. Djordjevic, M. Malic, J. Chem.Thermodyn. 9 (1977) 349–352. [16] C. Colinet, Ph.D. Thesis, University of Grenoble, France, 1967. [17] G.W. Toop, Trans. TMS-AIME 223 (1965) 850–855. [18] G. Scatchard, L.B. Ticknor, J.R. Goates, E.R. McCartney, J. Am. Chem. Soc. 74 (1952) 3721–3724.
JCT 04-226