J. Phys. Chem. 1991,95, 5299-5308 lecular motions. The formation of associated ion pairs in solution is one such additional mechanism.
Conclusion This paper reports the experimental finding that oxazine 725 reorients according to the identity of its counterion in methanol and acetonitrile. This behavior is not observed in 1-propanol, I-hexanol, DMF,DMSO,or water. The observation of counterion-dependent reorientation depends both on the degree of association between oxazine 725 and each counterion and the relationship between the reorientation times of the ionic (free) and associated species. With the data taken to date it is not possible to determine the values of the formation constants for
5299
these two salts in methanol and acetonitrile. The observation of counterion-dependent reorientation dynamics demonstrates the existence of substantial complexation in these systems. Thus, the assumption of near-complete dissociation, even in dilute polar systems, is not necessarily valid. The data presented here also test the limitations of the dielectric friction model of van der Zwan and Hynes in aprotic solvents. While dielectric friction is indeed one of several phenomena that determine rotational diffusion dynamics for polar systems, it cannot account completely for the state dependence in the data presented here. There is no mechanism in this model (or any other model of dielectric friction) to account for molecular-level association phenomena, such as those reported in this work.
Thermodynamic Interactions in Mixtures of Bromoform with Hydrocarbonst Mrityunjaya I. Aralaguppi, Tejraj M. Aminabhavi,* Ramachandra H. Balundgi, and Sbrikant S. JOSE* Department of Chemistry, Karnatak University, Dhanvad 580 003, India (Received: October 25, 1990)
Thermodynamic interactions in binary mixtures of bromoform with hydrocarbons have been studied in terms of a number of excess functions from the measured mixture properties such as density, viscosity, sound velocity, refractive index, and dielectric constant. Results of excess molar volume, apparent excess molar viscosity, and excess molar Gibbs free energy of activation of flow have been discussed in terms of destruction or creation of order and/or induced conformational changes in liquid n-alkanes in the presence of a nearly spherical bromoform molecule. These facts have been confirmed from a further discussion of thermodynamic interactions from the calculated excess isothermal and isobaric compressibilities. Among the refractive index mixture rules, the Eykman relation appears to give satisfactory results. The dielectric and internal pressure properties of the mixtures seem to provide additional information toward the understanding of thermodynamic interactions in these mixtures. The calculation of polarizability of the mixtures further support 1:l weak molecular complexes formed in these mixtures.
Introduction Excess thermodynamic properties of hydrocarbon-containing mixtures are currently attracting a considerable interest from the viewpoint of providing information on the variation of such properties with increasing number of carbon atoms in long-chain hydrocarbons.’ The interest in such studies stems from their different mixing behavior in the presence of a rigid pseudospherical, platelike, or flexible molecules. Such mixtures are known to exhibit interesting thermodynamic properties which are commonly discussed in terms of the destruction or creation of order and/or induced conformational changes in hydrocarbon^.^.^ In the literature, a large body of thermodynamic data on n-alkane-containing mixtures has been analyzed by using the equation of state approaches.c8 A comparative study of the thermodynamic properties and molecular interactions based on group contribution methods in n-alkane mixtures has been the active area of research by Kehiaian and co-worker~.~J~ These studies suggested a decrease of the molecular order in pure n-alkanes when mixed with other solvents. Most of the research concerning order effects in n-alkanecontaining mixtures is based on the use of a globular molecule which acts as an order breaker.” The most frequently used order breakers have been cyclohexane and 2,2,4-trimethylpentane.3Jz13 The bulk of the literature about mixtures containing n-alkanes has clearly demonstrated that correlation of molecular order plays a fundamental role in explaining the excess thermodynamic properties.IcI6 Author for correspondence. Also, adjunct research professor in Chemistr , Lamar University, Beaumont, TX 77710. {Based on the Ph.D. Thesis of Mr. Aralaguppi. to be submitted to Karnatak University. iPresent address: S.D.M. College of Engineering and Technology, Dharwad. Karnataka, India.
Continued interest in this area makes it desirable to study systematically the influence of the chain length of the n-alkane and of the chemical structure of the other component on excess thermodynamic quantities. This prompted us to undertake a comprehensivestudy on mixtures of bromoform (a nearly spherical molecule) with n-alkanes (C,to Clb). Bromoform having three bromine atoms acts as a u-acceptor when mixed with nonpolar alkane molecules such as n-hexane, n-heptane, n-octane, n-nonane, n-decane, n-dodecane, n-tetradecane, and n-hexadecane. Additionally, bromoform presents a high degree of orientational order and its excess properties with hydrocarbons should be mainly (1) Bhattacharya, S.N.; Costas, M.; Patterson, D.; Tra, H. V. Fluid Phase Equilib. 1985, 20, 21. (2) Svejda, P.; Kohlar, F. Ber. Bunsen-Ges. Phvs. Chem. 1983.87. 672. (3) Lam, V. T.; Picker, P.; Patterson, D.; Tancrede, P. J . Chem. Soc., Faraday Trans. I 1974, 70, 1465. (4) Bhattacharya, S.N.;Patterson, D. J . Chem. Soc., Faraday Trans. I 1985, 81,375. ( 5 ) Rodriguez, A. T.; Patterson, D. J . Chem. Sa.,Faraday Trans. 1982, 78, 917. (6) Cabrerim, U.;Rubio, R. G.; Menduina, C. Fluid Phase Equilib. 1985, 23. 41. (7) Diaz Pena, M.;Tardajos, G.; de Arenosa, R. L.; Menduina, C. J . Chem. Thermodyn. 1979,11,951. (8) Grolier, J. P. E.; Faradjzeideh, A,; Kehiaian, H. V. Thermochim. Acra 1982. 53. 1S7. - . _ _ , _ _ I
(9) Kehiaian. H. V.; Marongiu, B. Fhid Phase Equilib. 1988, 40, 23. (IO) Kehiaian, H.V. Pure Appl. Chem. 1985, 78, IS. (I 1) Barbe, M.; Patterson, D. J . Phys. Chem. 1987, 81, 40. (12) Gomez-Ibanez, J.; Liu, C. T. J . Phys. Chem. 1961, 65, 2148. (13) Aracil, J.; Rubio, R. G.; Caceres, M.; Pena, M. D.; Renuncio, J. A. R. J . Chem. Soc., Faraday Trans. I 1988,84, 539. (14) Treszculnowich, A. J.; Benson, G. C. Fluid Phase Equilib. 1985.23, 117. (IS) Kimura, F.;Benson, G. C. J . Chem. Eng. Data 1983, 28, 387. (16) Tardajos, G.; Aicart, E.; Costas, M.; Patterson, D. J. Chem. Soc., Faraday Trans. I 1906,82, 2977.
0022-3654/91/2095-5299S02.50/00 1991 American Chemical Societv
5300 The Journal of Physical Chemistry, Vol. 95, No. 13, 1991
TABLE I: Comprriraa of Data at m.15K with Llternhrrs P, d c m 3
RD
1.3728
lit. 1.5956 1.3723
1.3835 1.3966 1.4031
1.3851 1.3951 1.4031
1.4095
1.4097
1.4196 1.4260
1.4195 1 .4196d 1.429f
1.4337 1.3883 1.5370
(20 "C) 1.4349 1.3890 1.5392
liquids bromoform n-hexane
Ob
lit.
Ob
2.8760 0.6551
1 S937
n-heptane n-octane n-nonane
0.6799 0.6988 0.7148
n-decane
0.7267
n-dodecane
0.7460
n-tetradecane
0.7599
n-hexadecane
0.7713 0.6878 0.9653
2.8779 0.6551b 0.6548 0.6795 0.6986 0.71406 0.7138 0.7263b 0.7264 0.7454b* 0.7252 0.7592b 0.7594c 0.759V 0.770068 0.6878 0.9646
TMP tetralin
OReference 59. Reference 60. CReference 61. dReference 62. 'Reference 23. /Reference 63.
dominated by the unfavorable hydrocarbon-bromocarbon interactions. In order to obtain further information on the importance of breaking the orientational order of pure bromoform upon mixing, we have found it interesting to study the system bromoform 2,2,4trimethylpentane;the latter being an almost globular molecule and it presents no order correlation at all. However, to show an example of a hydrocarbon molecule having aromatic ring, we have chosen to study the interactions of bromoform with 1,2,3,4tetrahydronaphthalene(tetralin). Since order correlations show a strong temperature dependence, information about mixing functions at higher temperature should be of value. To the best of our knowledge we are not aware of any exhaustive compilation of thermodynamic data on bromoform + hydrocarbon mixtures. As a contribution toward a better thermodynamic description along these lines herein, we report the experimental and 308.15 K,refractive densities and viscositiesat 298.15,303.15, index, dielectric constant, and ultrasonic velocity at 298.15 K. These basic properties of the components and their mixtures have been further used to calculate various excess thermodynamic functions. The results are explained in terms of the nature of molecular interactions during mixing.
+
Experimental Section Materink. The solvents n-hexane, n-heptane, n-octane, n-nonane, n-decane, n-dodecane, n-tetradecane, n-hexadecane, 2,2,4trimethylpentane (TMP), and 1,2,3,44etrahydronaphthalene (tetralin) were all spectroscopic grade samples with purity exceeding 99.5mol %. Bromoform (Thomas Baker, Bombay) was obtained in its highest purity of 99+ mol 4% as claimed by the manufacturer and, thus, no further purification was done. As given in Table I, the properties of the pure components agreed well with the literature findings. Mixtures were prepared by mass in specially designed glassstoppered bottles. A set of nine compositions were prepared for each system and their physical properties were measured on the same day. The possible error in the mole fractions is estimated to be less than lo-' in all cases. Measurements. Densities, p, were measured with a capillary pycnometer of about 20 cm3 volume. The pycnometers were calibrated'' with doubly distilled water at 298.15, 303.15,and 308.15 K. The temperature of the thermostat (Toshniwal, Model GL-15, and INSREF, Model IRI-016AP) was maintained constant to within M.O1 K at the desired value and checked by means of a calibrated thermometer. The standard deviations of the densities of mixtures used were less than 0.01%. Viscosities were measured by means of Cannon-Fenske viscometers (sizes 75, 100, ASTM D 445 supplied by Industrial (17) Kell, G. S. J . Chem. Eng. Dora IWS, 20, 97.
Aralaguppi et al. Research Glassware, Ltd., NJ 07203). In all determinations, the kinetic energy corrections were made according to the recommended method.'* The other details are given in our earlier papers.l9J0 Standard deviation of viscosity measurements at each composition was 0.2%. Refractive indices for the Na D line were measured with a thermostated Abbe refractometer (Bellingham and Stanley Ltd., London) with an error of less than 0.00005 units and their values in Table 111 are reported up to fourth place. Ultrasonic velocities were measured by using a variable path single-crystal interferometer (Mittal Enterprises, New Delhi, Model M-84). A crystal-controlledhigh-frequency generator was used to excite the transducer at a frequency of 1 MHz/s. The frequency was measured with an accuracy of 1 in lo6 by using a digital frequency meter. The current variations across the transducer were observed on a 0-30 PA range microammeter (Lektrolab Equipment Co., Bombay). The interferometer cell was filled with the test liquid and was connected to the output terminal of the high-frequency generator through a shielded cable. Water was then circulated around the measuring cell from a thermostat maintained at 298.15 f 0.01 K. When the liquid attained the temperature of the bath, the micrometer screw was slowly moved until the anode current meter showed a maximum. For increasing the accuracy of the measurement, several such maxima were counted (n) by changing the distance between the transducer and the reflector. The total distance, d, moved by the reflector was used to calculate the wavelength, A, by using d = nA/2. The frequency, Y , of the crystal being known accurately (1 MHz), the sound velocity, u in m s-l, was calculated as u = vX. The sound velocities thus calculated are accurate to 1 in 1000 m. The isobaric compressibilitieswere calculated as ks = 1 /u2p, where p is the density of the liquid. Dielectric constant measurements at a frequency of 1 kHz were carried out by a microprocessor-based digital LCR-Sortester (APLAB, Bombay, Model 4912). This instrument incorporates the four-terminal measuring technique which reduces the errors due to electromagnetic coupling of leads as well as reducing residual inductance and stray capacitance. A measuring cell designed by us was adequate to cover the dielectric constant range of bromoform + n-alkane mixtures. The overall experimental uncertainty in dielectric constant values was approximately equal to fO.S%. In all the measurements temperature was controlled within fO.O1 K and the experiments were generally performed in three replicates for each composition and the results were averaged.
Results and Discussion Experimental results of densities and viscosities of all the binary mixtures at the three investigated temperatures are given in Table 11. Results of sound velocity, u, isobaric compressibility, ks, refractive index, nD, and dielectric constants, c, at 298.15 K are summarized in Table 111. For all the mixtures, results of densities and viscosities increased monotonically with the mole fraction of bromoform over the investigated range of temperature. Other properties, viz, refractive index and dielectric constants, also showed a similar behavior. However, the results of sound velocity and the isobaric compressibility tend to decrease with an increase in concentration of bromoform in the mixture. We will now discuss the various excess properties of mixtures. Volumetric Bebavior. The excess molar volume of mixing, fl, representing the nonideal behavior is calculated as
P = v, - EViXj i= I
where
(1)
represents the molar volume and xi is the mole fraction
(18) Cannon, M. R.; Monning, R. E.; Bell, J. D.Anal. Chrm. 1960, 32, 355. (19) Joshi, S.S.;Aminabhavi, T. M.; Shukla, S. S.Can. J . Chem. 1990, 68, 251. (20) Joshi, S.S.;Aminabhavi, T. M.; Shukla, S.S.J . Chem. Eng. Dara 1990, 35, 241.
The Journal of Physical Chemistry, Vol. 95, No. 13, 1991 5301
Mixtures of Bromoform with Hydrocarbons
XI
298.15
P, g/cm’ 303.15
308.15
298.15
r), cp 303.15
308.15
K
K
K
K
K
K
XI
r). cp 303.15
308.15
K
K
0.8087 0.9885 1.2030 1.5076 1.9092
0.7673 0.9334 1.1351 1.4187 1.7874
0.7306 0.8866 1.077 1 1.3424 1.6801
1.6967 1.9305 2.1958 2.5056 2.8493
0.8773 1.0370 1.2442 1.5279 1.9092
0.8292 0.9786 1.1720 1.4343 1.7874
0.7865 0.9281 1.1075 1.3540 1.6801
1.6598 1.9034 2.1769 2.4951 2.8630
1.6514 1.8937 2.1661 2.4832 2.8493
0.9714 1.1263 1.3217 1.5734 1.9092
0.9156 1.0607 1.2413 1.4755 1.7874
0.8638 1.0017 1.1702 1.3902 1.6801
1.6244 1.8477 2.1336 2.4680 2.8630
1.6160 1.838I 2.1233 2.4564 2.8493
1.0851 1.2144 1.3941 1.6156 1.9092
1.0162 1.1391 1.3064 1.5137 1.7874
0.9588 1.0721 1.2288 1.4242 1.6801
1.5739 1.7983 2.0895 2.4203 2.8630
1.5658 1.7895 2.0799 2.4091 2.8493
1.2070 1.3214 1.4748 1.6514 1.9092
1.1262 1.2351 1.3785 1.5450 1.7874
1.0560 1.1579 1.2950 1.4501 1.6801
1.5208 1.7180 2.0305 2.3710 2.8630
1.5134 1.7097 2.0208 2.3598 2.8493
1.5244 1S796 1.6729 1.7678 1.9092
1.4171 1.4658 1.5593 1.6%8 1.7874
1.3161 1.3666 1.4556 1.5457 1.6801
1.4694 1.6883 1.9762 2.3321 2.8630
1.4623 1.6807 1.9668 2.321 1 2.8493
1.8912 1 .E906 1.9061 1.9113 1.9092
1.7324 1.7397 1.7623 1.7761 1.7874
1.5982 1.6113 1.6343 1.6613 1.6801
298.15
P, dcm’ 303.15
308.15
K
K
K
298.1 5 K
1.7700 2.0151 2.2669 2.5577 2.8630
1.7604 2.0052 2.2565 2.5458 2.8493
1.7057 1.9406 2.2062 2.5174 2.8630
+ n-Hexane (2)
+ n-Heptane (2)
0.1038 0.2033 0.3026 0.4026 0.5043
0.6551 0.8151 0.9803 1.1571 1.3489 1.5591
0.6505 0.8097 0.9742 1.1501 1.3408 1.5501
0.6458 0.8043 0.9679 1.1429 1.3328 1.5417
0.3006 0.3488 0.4058 0.4760 0.5627 0.6757
I. Bromoform (1) 0.2867 0.2745 0.3329 0.3185 0.3877 0.3712 0.4542 0.4351 0.5366 0.5145 0.6422 0.6256
O.oo00 0.1093 0.2079 0.301 1 0.3958 0.4956
0.6799 0.8293 0.9764 1.1280 1.2961 1.4918
0.6755 0.8241 0.9704 1.1215 1.2886 1.4835
‘0.6714 0.8199 0.9646 1.2811 1.4751
0.3907 0.4471 0.4967 0.5607 0.6393 0.7425
11. Bromoform (1) 0.3704 0.3528 0.4180 0.3980 0.4712 0.4486 0.5327 0.5089 0.6065 0.5772 0.7031 0.6682
O.oo00 0.1034 0.2068 0.3010 0.4506 0.5028
0.6988 0.8254 0.9650 1.1060 1.3624 1.4631
0.6948 0.8206 0.9594
0.5074 0.5540 0.6095 0.6707 0.7968 0.8517
111. Bromoform (1) 0.4780 0.4520 0.5219 0.4944 0.5753 0.5442 0.6325 0.5983 0.7510 0.71 1 1 0.8031 0.7592
+ n-Octane (2)
1.3550 1.4552
0.6909 0.8 159 0.9540 1.0940 1.3476 1.4473
O.oo00 0.1003 0.1964 0.3076 0.4008 0.5069
0.7148 0.8258 0.9441 1.0982 1.2445 1.4339
0.7109 0.821 3 0.9389 1.0922 1.2379 1.4265
0.7069 0.8166 0.9339 1.0864 1.2314 1.4193
0.6579 0.6979 0.7446 0.8103 0.8800 0.9761
IV. Bromoform (1) 0.6155 0.5781 0.6538 0.61 39 0.6978 0.6567 0.7602 0.7154 0.8255 0.7768 0.9148 0.8619
+ n-Nonane (2)
O.oo00 0.1090 0.1968 0.2954 0.4005 0.4990
0.7267 0.8372 0.9372 1.0637 1.2177 1.3842
0.7228 0.8330 0.9325 1.0581 1.2115 1.3772
0.7 186 0.8284 0.9276 1.0529 1.2055 1.3701
0.8521 0.8797 0.9166 0.9803 1.0503 1.1094
V. Bromoform (1) 0.7842 0.7301 0.8184 0.7650 0.8518 0.7972 0.9018 0.8442 0.9784 0.9167 1.0337 0.9683
+ n-Decane (2)
O.oo00 0.1030 0.2050 0.3040 0.4052 0.4895
0.7460 0.8351 0.9360 1.0488 1.1834 1.3139
0.7425 0.8312 0.9314 1.0439 1.1776 1.3074
0.7387 0.8269 0.9268 1.0385 1.1719 1.3013
1.3460 1.3518 1.3685 1.3882 1.4211 1.4524
VI. Bromoform (1) 1.2328 1.1339 1.2412 1.1447 1.2587 1.1635 1.2804 1.1851 1.3109 1.2171 1.3335 1.2495
+ n-Dodecane (2)
O.oo00 0.1088 0.2100 0.3039 0.4079 0.499 1
0.7599 0.8423 0.9310 1.0270 1.1524 1.2841
0.7565 0.8384 0.9268 1.0221 1.1475 1.2782
0.7531 0.8344 0.9225 1.0175 1.1416 1.2719
2.0353 I .9888 1.9556 1.9249 1.9048 1.8922
VII. Bromoform (1) 1.8292 1.6546 1.7937 1.6280 1.7703 1.6124 1.7481 1.5982 1.7352 1.5932 1.7299 1.5878
+ n-Tetradecane (2)
O.oo00 0.1085 0.2077 0.3019 0.3984 0.4946
0.7713 0.8439 0.9217 1.008S 1.1140 1.2407
0.7677 0.8403 0.9173 1.0041 1.1088 1.2353
0.7643 0.8363 0.9134 0.9992 1.1038 1.2297
3.0041 2.8701 2.7714 2.6422 2.5593 2.4629
VIII. Bromoform (1) 2.6634 2.3822 2.5561 2.2965 2.4722 2.2305 2.3751 2.1474 2.3098 2.0957 2.2321 2.0332
+ n-Hexadecane (2)
1.4051 1.6087 1.8961 2.2686 2.8630
1.3988 1.6013 1.8871 2.2583 2.8493
2.3701 2.2772 2.1748 2.0589 1.9092
2.1562 2.0787 2.0049 1.9089 1.7874
1.9733 1.9088 1.8512 1.7822 1.6801
O.oo00 0.1054 0.2036 0.3022 0.4043
0.6837 0.8117 0.9436 1.0906 1.2608 1.4482
0.6797 0.8070 0.9379 1.0846 1.2538
0.5045
0.6878 0.8166 0.9490 1.0968 1.2680 I .4560
1.6532 1.8856 2.1731 2.4730 2.8493
1.4403
IX. Bromoform (1) + 2,2,4-Trimethylpcntane (2) 0.4740 0.4474 0.4243 0.6048 1.6711 1.6621 0.5254 0.4966 0.4706 0.7018 1.9051 1.8956 0.5830 0.5510 0.5219 0.8049 2.1943 2.1834 0.6555 0.6193 0.5871 0.8990 2.4962 2.4848 0.7429 0.7005 0.6641 1.oooO 2.8760 2.8630 0.8495 0.8015 0.7583
0.9860 1.1388 I .3420 1.5731 1.9092
0.9284 1.0707 1.2597 I .4775 1.7874
0.8774 1.0113 1.1889 1.3939 1.6801
O.oo00 0.1005 0.2004 0.296 I 0.4001 0.4943
0.9653 1.0929 1.2292 1.3695 I S362 1.6974
0.961 2 1.0878 1.2243 1.3633 1.5299 1.6937
0.9574 1.0835 1.2188 1.3577 1.5232 1.6831
2.0032 2.0914 2.1883 2.231 5 2.2518 2.2649
1.8762 2.0776 2.3045 2.5574 2.8493
2.2483 2.1896 2.1133 2.0186 1.9092
2.0509 2.0 108 1.9484 1.8735 1.7874
1.8845 1.8535 1.8092 1.7510 1.6801
O.oo00
1.1OOo
1.1151
0.6024 0.7039 0.7997 0.9018 1.oooO
0.5993 0.6968 0.7960 0.8990 1.oooO
0.6003 0.7020 0.8015 0.9015
1.oooO
0.6034 0.6978 0.8011 0.9019 1.oooO
0.5983 0.6953 0.7998 0.8971 1.oooO
0.6051 0.6926 0.8037 0.8974 1.oooO
0.6077 0.7066 0.8068 0.9002 1.oooO
X. Bromoform (1) 1.8143 1.6555 1.8919 1.7246 1.9777 1.7948 2.0257 1 A368 2.0537 1.8762 2.0634 1.8836
0.5987 0.6959 0.7996 0.8968
1.oooO
1.7795 2.0254 2.2782 2.5697 2.8760
1.7150 1.9508 2.2174 2.5291 2.8760
1.6685 1.9128 2.1876 2.5072 2.8760
I .6326 1.8565 2.1443 2.4800 2.8760
1.5815 1.8069 2.0998 2.4319 2.8760
1.5282 1.7265 2.0402 2.3823 2.8760
1.4761 1.6964 1.9854 2.3429 2.8760
1.4116 1.6156 1.9051 2.2793 2.8760
+ Tetralin (2) 0.5966 0.6945 0.7953 0.8958 1.oooO
1.8926 2.0964 2.3251 2.5805 2.8760
1 .8846 2.0873 2.3148 2.5694 2.8630
5302 The Journal of Physical Chemistry, Vol. 95, No. 13, 1991
Aralaguppi et al.
TABLE III: sound Velocity, Isobaric Compressibility, Refractive Index, and Dielectric Constants of Mixhues at 298.15 K XI u, m/s lo'Ok., Pa-l nn c x1 u. m/s 10I0k., Pa-' I. Bromoform (1) + n-Hexane (2) 1.3728 1.887 0.6024 899.3 O.oo00 1083.8 12.995 6.949 1.3872 2.014 0.7039 893.9 1013.8 6.178 0.1038 1 1.937 1.4039 2.213 0.7997 897.9 974.2 5.444 0.2033 10.748 1.4211 2.289 0.9018 909.2 4.708 9.781 940.0 0.3026 1.4396 2.504 914.4 4.048 0.4026 8.867 1.0000 926.8 901.3 0.5043 7.896 1.4618 2.707
11.140 10.341 9.575 8.660 7.994
1060.0 1020.3 967.6 956.4
10.453 9.791 9.223 8.823 7.840 7.472
1.3966 1.4051 1.4170 1.4295 1.4521 1.4608
1211.8 1 152.4 1100.0 1052.2 1019.0 981.6
9.527 9.119 8.754 8.225 7.739 7.238
1.4331 1.4117 1.4209 1.4339 1.4460 1.4626
1221.7 1 157.2 1 I 13.0 1067.8 1031.8 991.4
9.2I9 8.920 8.613 8.245 7.714 7.351
1.4095 1.4168 1.4246 1.4338 1.4475 1.4598
1287.8 1227.1 1 184.4 1 132.7 1087.2 1049.9
8.083 7.953 7.616 7.432 7.149 6.905
1.4196 1.4263 1.4323 1.4418 1.4517 1.4622
1301.6 1253.4 1189.1 1151.8 1098.8 1066.4
7.767 7.559 7.597 7.340 7.188 6.848
1.4260 1.4320 1.4385 1.4449 1.4541 1.4637
0.1085 0.2077 0.3019 0.3984 0.4946
1321.5 1280.6 1220.5 1 178.7 1 132.4 1090.8
7.424 7.226 7.283 7.138 7.001 6.774
1.4337 1.4365 1.4431 1.4481 1.4553 1.4617
O.oo00 0.1054 0.2036 0.3022 0.4043 0.5045
1077.20 1022.20 989.80 959.46 925.26 920.94
12.520 11.721 10.756 9.904 9.212 8.098
1.3883 1.4003 1.4124 1.4264 1.4419 1.4588
O.oo00 0.1005
1457.20 1368.40 1299.20 1225.60 1166.67 1 I 13.40
4.879 4.887 4.820 4.861 4.783 4.752
1.5370 1.5413 1.5432 1.5487 1.5511 1.5579
1133.2 1040.4 995.2 962.2 943.9 918.6
O.oo00
1 170.0 1 120.4
1 1.453
1.903 2.052 2.185 2.309 2.482 2.677
0.5993 0.6968 0.7960 0.8990 1 .oooo
1.4824 1.4994 1.5342 1 S631 1.5937
2.957 3.197 3.518 3.873 4.353
904.2 896.7 894.4 893.4 926.8
7.132 6.376 5.638 4.954 4.048
1.4805 1 SO30 1 S290 1.5599 1.5937
2.933 3.162 3.471 3.868 4.353
938.4 923.0 913.9 912.9 926.8
6.806 6.137 5.474 4.786 4.048
1.4797 1SO23 1.5278 1.5579 1.5937
2.870 3.086 3.464 3.842 4.353
957.4 936.6 922.4 921.0 926.8
6.683 6.141 5.481 4.754 4.048
1.4798 1.4996 1 S254 1.5566 1 s937
2.776 3.014 3.386 3.787 4.353
961.6 938.1 924.4 905.8 926.8
6.838 6.289 5.573 5.012 4.048
1.4776 1.4958 1.5231 1.5514 1.5937
2.785 3.015 3.385 3.821 4.353
6.448 6.068 5.461 4.854 4.048
1.4785 I .4954 1.5217 1s937
2.660 2.901 3.201 3.671 4.353
6.545 6.077 5.628 4.975 4.048
1.4778 1.4952 1.5183 1.5474 1.5937
2.664 2.870 3.221 3.620 4.353
6.540 6.215 5.695 5.079 4.048
1.4760 1.4889 1.5144 1.5438 1 s937
2.649 2.83 1 3.156 3.607 4.353
912.20 899.00 898.60 904.54 926.80
7.368 6.495 5.644 4.896 4.048
1.4791
2.814 3.146 3.765 3.826 4.353
1066.00 1022.66 974.40 939.40 926.80
4.650 4.579 4.530 4.391 4.048
1 S620 1 S684
+ n-Octane (2)
111. Bromoform ( I )
0.1034 0.2068 0.3010 0.4506 0.5028
t
+ n-Heptane (2)
11. Bromoform (1)
1.3835 1.3987 1.4117 1.4256 1.4404 1.4605
O.oo00 0.I093 0.2079 0.30I 1 0.3958 0.4956
nD
1.930 2.073 2.142 2.254 2.536 2.640
0.6003 0.7020 0.8015 0.9015 1 .0000
IV. Bromoform (1)+ n-Nonane (2)
O.oo00 0.1003 0.I964 0.3076 0.4008 0.5069
1.951 2.047 2.164 2.252 2.394 2.566
0.6034 0.6978 0.8011 0.9019 1.OoOo
+ n-Decane (2)
V. Bromoform ( I )
O.oo00 0.1090 0.1968 0.2954 0.4005 0.4990
2.000 2.088 2.297 2.279 2.427 2.607
VI. Bromoform (1)
O.oo00 0.IO30 0.2050 0.3040 0.4052 0.4895
0.1088 0.2100 0.3039 0.4079 0.4991
+ n-Dodecane (2) 0.6051 0.6926 0.8037 0.8974 1.oooo
1007.4 977.0 947.4 929.9 926.8
1.5500
+ n-Tetradecane (2)
2.037 2.103 2.199 2.289 2.357 2.500
VIII. Bromoform ( I )
O.oo00
1 .oooo
2.021 2.070 2.156 2.239 2.383 2.507
VII. Bromoform (1)
O.oo00
0.5983 0.6953 0.7998 0.8971
0.6077 0.7066 0.8068 0.9002 1.oooo
1017.4 984.9 946.0 926.3 926.8
+ n-Hexadecane (2)
2.090 2.149 2.224 2.291 2.358 2.471
0.5987 0.6959 0.7996 0.8968 1 .oooo
1040.8 998.0 960.1 929.4 926.8
IX. Bromoform (1)+ 2,2,4-Trimethylpentane
0.2004 0.296I 0.4001 0.4943
1.928 2.074 2.121 2.333 2.435 2.664
0.6048 0.7018 0.8049 0.8990
X. Bromoform ( I )
+ Tetralin (2)
2.853 2.927 3.103 3.224 3.338 3.441
1 .oom
0.5966 0.6945 0.7953 0.8958 1.oooo
1 SO1 1
1.5291 1.5578 1.5937
1S767 1S845 1s937
3.627 3.735 3.882 4.134 4.353
The Journal of Physical Chemistry, Vol. 95, No. 13, 1991 5303
Mixtures of Bromoform with Hydrocarbons
Ido Pd’
A‘
1.0
EXCESS ISOBIRIC COMPRESPBILITY,~ -1.2 -0d -04
-1b 1.2
I
I
0 I
I
I
0.8
-a
;0.6
x
-5
8 E
i2
0-
3
0.4
9
v)
iL!
1: 0.2
I
-120
I
I
-eo
-40 0 ( B P OF BROM)FORM-BP OFn-ALKANE)
I
LO
eo
Figure 2. Excess volume of mixture3 of bromoform with n-alkanes as a function of difference in boiling points of bromoform and n-alkanes (A), and as a function of I / ( n + 2), the line joining the filled circles is fitted to eq 2 and excess isobaric compressibility (0)at 298.15 K.
0
-0.2
-0.4
0
0.2
0.4
0.6
0.8
1
MOLE FRACTION,XI
Figure 1. Excess volume of hydrocarbons and bromoform mixtures as a function of mole fraction of bromoform at 298.15 K: n-hexane (O), n-heptane (A),n-octane ( O ) , n-nonane (V),n-decane (O), n-dodecane (A), n-tetradecane (m), n-hexadecane (V),TMP (X), and tetralin (a).
of the ith component. The quantity, V,, refers to molar volume of the mixture which can be calculated from the mixture density, pmand the component molecular weights M I and M2 as V, = (MIX, + M2X2)IP * The values of fi at 298.15 K are displayed graphically as a function of mole fraction, xl of bromoform in Figure 1 . It is observed that mixtures of bromoform with n-hexane or T M P exhibit negative Ve values over the entire scale of the mixture composition. This suggests the presence of specific interactions in these mixtures and more so with bromoform n-hexane system. An interesting behavior is shown by bromoform + n-heptane system wherein we observe both positive and negative values of Ve;the sign inversion occurs somewhere close to the middle of the mixture composition. In the region of low concentration of bromoform, Ve is positive, suggesting the dispersion forces to be operative. As the bromoform content of the mixture is increased the specific interactions become increasingly redominant over the dispersion forces, thus exhibiting negative V! Such a behavior was also observed earlier in case of o-xylene n-octane mixture2I and n-octyl acetate n-heptane mixture.22 However, with the mixtures containing higher hydrocarbons, we find P to be steadily increasing with the number of carbon atoms; the maxima of such curves tend to shift continuously toward the bromoform-rich region of the mixture, the exception being the bromoform + tetralin system, for which P is positive with no sharp maximum. The increase in P with the chain length of n-alkanes may be the result of pronounced molecular size difference between the nearly spherical bromoform and the rodlike n-alkane components. However, the temperature dependence of Ve does not show any significant effect. This may be due to the extremely sluggish movement of the long-chain molecules over the 10 K interval used in this study. With a rise in temperature, the free volume of a liquid is expected to increase and thus a decrease in VE values
+
+
+
(21) Alonso, M. C.; Delgado, J. N. J. Chem. Eng. Datu 1982, 27, 331. (22) Awwad, A. M.; Jbara, K.A., AI-Dujaili, A. H.Fluid Phase Equilib. 1988, 41, 211.
should be expected with an increase in the temperature. This is indeed the case with bromoform + n-hexane whereas with bromoform + n-tetradecane the positive values of P appear to increase with temperature. However, there are some minor inconsistencies with the other systems. This apparent inconsistency is in agreement with the published data.23,24 A large body of experimental data on excess thermodynamic functions and depolarized Rayleigh scattering studies on binary mixtures of n-alkanes ~uggests~J~*~’ that the long-chain n-alkanes have short-range orientational order and this is attributed to a partial alignment of the neighboring segments or possibly of whole molecules. When mixed with another liquid whose molecules are more globular in shape (e.g., bromoform) the order between the long chain alkanes is destroyed or replaced by the weaker corr e l a t i o n ~ .However, ~ ~ ~ ~ ~ this may not be true with n-hexane or n-heptane whose chains are somewhat shorter than the higher homologues (C8 to Clb). It may, however, be noted that the short-range order which exists in liquid n-alkanes is destroyed when they are mixed with bromoform. We prefer to interpret this effect in terms of the packing effect of the n-alkane segments and the short-range order is gradually destroyed or practically vanished with n-hexadecane, a more flexible long-chain molecule. It has been pointed out earlierM that the difference in boiling points (Abp) of the components can be regarded as a measure of the strength of interaction between the mixing components. Further, realizing the linear relationship between number of carbon atoms of the chain molecule and at equimolar c ~ m p o s i t i o n , ~ ~ 2), where n is the we have plotted P (x, N 0.5) vs l/(n n-alkane carbon number (see Figure 2). From this plot, a generalized empirical equation was obtained by fitting P ( x , N 0.5) vs l/(n + 2) data as shown in Figure 2.
+
P(XlNO.5) = 3.82 - 79.24(n + 2)-’
+ 723.11(n + 2)-’ - 2876.82(n + 2)-3 (2)
(23) Asfour, A. A.; Siddique, M. H.; Vavananellos, T. D. J. Chem. Eng. Data 1990, 35, 192. (241 Garcia, M.; Villar, V. P.; Rodriguez, J. R. J. Chem. Eng. Dura 1986, 31, 481. (25) Costas, M.; Bhattacharya, S.N.; Patterson, D. J. Chem. Soc. Furaday Trans. 1 1985, 81, 387. (26) Ewing, M. B.; Marsh, K. N. J. Chem. Thermodyn. 1977, 9, 357. (27) Ramon. G.; Menduina, G. R.; Pena. M. D. J. Chem. Soc.. Faraday Truns. 1 1985.80, 1425. (28) Bhattacharya, S.N.; Patterson, D. J. Solution Chem. 1980, 9, 247. (29) Awwad, A. M.; North, A. M.; Pethrick, R. A. J. Chem. Soc.,Faraday Trans. 1 1983, 79, 2333. (30) Fort, R. J.; Moore, W. R. Trans. Furaday Soc. 1966, 62, 1 112. (31) Letcher. T. M.; Lucas, A. J. Solution Chem. 1981, 10, 863.
5304 The Journal of Physical Chemistry, Vol. 95, No. 13, 1991
Aralaguppi et al.
0.3 500
-
c
0.2
FE t
3
t
0.1
8
z 300
P
I-
2
;
o
I-
0 VI
200
E
t
w K
v1
u
100
-0.1
W
I00
m
W
E u vl
-0.2
M
2 0 W
- 0.3 -100
-04
-200 0
0.2
0.L 0.6 MOLE FRACTION. X I
0.8
I 0.2
0
Figure 3. Excess viscosity of bromoform and hydrocarbon mixtures as a function of mole fraction of bromoform at 298.15 K (with the same symbols as in Figure 1).
+
with u = 0.0221, This equation refers to bromoform n-alkane equimolar mixtures at 298.15 K. The dependence of other physical properties such as difference in boiling point, Abp, or excess molar compressibility, @,of the equimolar mixture appears to show a systematic variation. This further strengthens the facts32about order correlation effects and systematic conformational changes occurring in mixtures of bromoform with n-alkanes. ViscorseMe Bebrvior. Viscosities of liquid mixtures are required in many practical applications concerning heat, mass transfer and fluid flow. Traditionally viscosity data have also been discussed in terms of an excess quantity given as
0.4 0.6 MOLE FRACTION, X ,
0.8
Figure 4. Excess Gibbs energy of activation of flow for mixtures of bromoform and hydrocarbons as a function of mole fraction of bromoform at 298.15 K (with the same symbols as in Figure 1).
mixtures. The apparent excess molar viscosity (see Figure 3) which refers to the deviations from a rectilinear dependencemof viscosity of the mixture can be explained in terms of intermolecular interactions.” With mixtures having dispersion and dipolar forces, the values of $ should be negative, whereas the existence of charge transfer and other specific interactions tends to make qE values positive. It can be observed from Figure 3 that each set of results for a given mixture falls on a smooth curve and that only bromoform + tetralin shows positive values of qE over the whole composition range. The values of qE are smallest for n-hexane and tend to increase systematically upto n-tetradecane. However, the bromoform n-hexadecane system shows a sign inversion at xl = 0.5; qE becomes more positive as the concentration of bromoform in the mixture increased beyond x1 = 0.5. Even the curve for n-tetradecane shows a slight sigmoidal shape, yet its qE values are all negative. There is again a systematic shift of the minima of the qE vs x1 curves as we go from n-hexadecane down to nhexane toward the bromoform-rich region. For mixtures of bromoform with n-alkanes at any fixed mole fraction, the qE values follow the sequence: n-hexane < n-heptane < n-octane < TMP < n-nonane < n-decane < n-dodecane < n-tetradecane < n-hexadecane < tetralin. This trend in the values of qE gives an evidence in favor of decreasing extent of specific interactions of bromoform with n-alkanes having an increased number of CH2 substituents. The specific interactions between bromoform and aromatic tetralin molecules have been indicated to be of donoracceptor type; the aromatic tetralin molecule acting as the *-type sacrificial electron donor toward bromoform. The excess molar Gibbs free energy of activation of flow as calculated from eq 6 is displayed graphically in Figure 4. It is found that mixtures of bromoform with n-alkanes show a systematic increase from n-hexane, n-octane, n-nonane, TMP, ndecane, n-dodecane, n-tetradecane, tetralin, to n-hexadecane. However, mixtures of bromoform with n-heptane show slightly lower values than bromoform + n-hexane. Such effects have also
+
where q, and qm refer respectively to viscosities of pure components and of the mixture. Quite often another quantity that has been calculated from mixture viscosity is that of an excess molar Gibbs free energy of activation of flow, AGSE,which is defined by the viscosity equation proposed by Eyring and co-workers3’ q m = ( h N / M ) exp(AGZE/RT)
(4)
By definition, AG*E = AG*, - AGSkl, where AG*, and AG*hl refer to the molar Gibbs free energy of activation of a binary mixture and the ideal Gibbs free energy, respectively; for an ideal binary mixture, we have AG*idaI xlAG*l + x ~ A G * ~ (5) Thus, for a binary m i x t ~ r e ’ ~ * * ~ AG*e = RT[ln qmV, - x I In q , V,- x2 In q2V2]
(6) where ql and q, represent pure component and mixture viscosities; R T is the usual energy term. We shall now discuss the experimental viscosity data from the view point of interactions between the components of various (32) Kimura, F.; Benmn, G. C. J. Chem. Eng. Duru 1983, 28, 157. (33) Glasstone, S.;Laidler, K. J.; Eyring, H. The Theory o/Rure Processes; McGraw-Hill: New York, 1953.
I
(34) Nath. J.; Dubey,
S.N. J . Phys. Chem. 1981, 85, 886.
The Journal of Physical Chemistry, Vol. 95, NO. 13, 1991 5305
Mixtures of Bromoform with Hydrocarbons
1
02
0.2
0.6 VOLUME FRACTION, 0,
0.4
0.8
1 I
Figure 6. Excess isothermal compressibility of bromoform and hydrocarbon mixtures as a function of volume fraction of bromoform at 298.15 K (with the same symbols as in Figure 1).
1
1
0
04 06 08 VOLUME FRACTION. 9,
I
Figure 5. Excess isobaric compressibility of bromoformand hydrocarbon mixturm as a function of volume fraction of bromoform at 298.15 K (with the same symbols as in Figure 1).
mixture. Benson and K i y ~ h a r asuggested ~~ a relation to calculate the ideal term as
been observed earlier in the literature.)' Each set of excess functions p,ver and AG*@are fitted to a quadratic equation (7)
where b, Cpj,and ai are respectively the isobaric compressibility, heat capacity, and thermal expansion coefficient of the individual components. The excess isobaric thermal expansion coefficient as calculated from eqs 8 and 9 are not very different. Therefore, we decided to show a graphical presentation of only k: calculated from eq 9 in Figure 5 . The k! data of bromoform with n-alkanes follow a very systematic trend; i.e., they increase from n-hexane to nhexadecane and for the latter the values are positive, whereas for results n-tetradecane k! values are around zero. Just like n-heptane also shows a sign inversion for the dependence of k! on volume fraction; but this inversion occurs in the low bromoform concentration region of the mixture. For bromoform + TMP, the k! results are negative. However, bromoform + tetralin system gives high positive k! values. The isothermal compressibility, kT, which is often needed for the evaluation of the density scattering in light scattering ~tudies?~ is a quantity which is difficult to measure. Its value is known for only a few pure liquids and a handful of mixtures. The kT is related to ks as
to evaluate the coefficients,A,, where the quantity Q& represents P,qE, and AG*E. The calculations were done on an IBM compatible PC (SHIVA,Madras, India) by employing the Marquardt algorithm. The standard errors between the observed and the calculated values of the various parameters are also estimated. A thirdsrder fit in almost all the cases reproduced insignificant differences between the calculated and observed quantities. The $, and AG*@were used as guidelines back-calculated values of P, to draw the smooth curves; the different symbols in Figures 1, 3, and 4 represent the observed points as calculated from eqs 1, 3, and 6. ultnsonie Behavior. Ultrasonic properties of liquids and liquid mixtures find applications in many areas of science and engineering design operations. Liquids with low ultrasound velocity (below loo0 m s-') are particularly useful in sound lenses, cavity resonators, and ultrasound light modulation ~ y s t e m s . Further, ~ sound properties of liquids having a wide range of low ultrasonic velocities are essential in understanding thermodynamic interactions in binary mixtures. k ~ . , ksj + TJ'piz/CP,i (10) In this work we will examine two different approaches which are used in evaluating the excess isobaric c ~ m p r e s s i b i l i t i e s . ~ ~ ~ ~ ~The results of kT were calculated for pure liquids and their mixtures. The excess isothermal compressibility, k!, of mixing The isobaric compressibility, ks, is the property of a liquid which was then calculated as can be obtained from sound velocity measurements. From this the excess isobaric compressibility, k: is calculated as 2 kf = klpiX kT&i (1 1) i= 1
where 4, ( = x , V , / ~ , x l V ,is) the volume fraction of the ith component. The second term on the right-hand side of eq 8 represents the ideal behavior and k!" is the measured property of the (35) Awwad, A. M.; AI-Azzawi, S. F.; Salman, M. A. Fluid Phase Equilib. 1986, 31, 171. (36) Narayana, K. L.; Swamy, K. M. Acoustics Len. 1986, 9, 137. (37) Nath, J.; Tripathi, A. D. J . Chem. Eng. Dora 1983, 28, 263. (38) Benson, 0 . C.; Kiyohara. 0.J . Chem. Thrrmodyn. 1979, 11, 1061.
According to Flory et al.,40,41a theoretical relation based on equation-of-stateapproaches was proposed to calculate k: in terms of reduced volume of the mixture and of pure components as
(39) A W e l - A h , A. A,; Cheng. W.; El-Hibri, M. J.; Munk, P. J . Phys.
Chem. 1988. 92, 2663. (40)A h , A.; Flory, P. J. J. Am. Chem. Soc. 196!3,87. 1838. (41) Flory, P.J.; Onvoll, R. A.; Vrij, A. J . Am. Chem. Soc. 1%4,86,3515.
5306 The Journal of Physical Chemistry, Vol. 95, No. 13, 1991
Aralaguppi et al.
where the reduced volume terms, 8, and a,, of the pure components and of the mixture, respectively, were calculated from the procedures suggested by Flory et al.40*41The parameters needed in these calculations were obtained from various sources. The excess isothermal compressibility kB(F) vs q$ is plotted in Figure 6. For all mixtures it is negative, being largest for bromoform n-hexane and smallest negative for bromoform + n-hexadecane. The intermediate values are seen for mixtures of bromoform with n-heptane to n-tetradecane. However, the kB(F) data for n-dodecane to n-hexadecane are closely spaced. Similarly, for n-nonane and n-decane an identical pattern in the variation of kB(F) is observed; kB(F) values of the bromoform + tetralin mixture are close to zero but pitive. The behavior of bromoform + TMP system falls in between those of n-hexane and n-heptane mixtures with bromoform; this is somewhat identical with k! behavior. It may be further noted that the Flory theory predicts correctly the sign and order of the k: for all the mixtures. The results of k; from e 11 are not displayed graphically as these are identical with kTgF) data. The results of ,k! kT, and kB(F) have been fitted to an identical relation with that given by eq 7
+
2
3
QP#, = 4142LU42 - 41)'
(13)
i-0
where represents k!, k:, or kB(F) as evaluated from eqs 8, 11, and 12. The smooth curves were drawn through the fitted points. Intenmi Pressure Behavior. The internal pressure, P,, of a liquid has been the subject of intensive investigation in the past.42 It is defined as the isothermal internal energy-volume coefficient: Pi = (dE/dV)T (14) Actually, internal pressure is the result of the forces of attraction and repulsion between molecules of liquids. This definition rather resembles the well-known definition of solubility parameter, 6, which is expressed in terms of cohesive energy per unit volume. Internal pressure and solubility parameter are thus related43as 6 = (dE/dV)T1/2= (Pi)'" (15) According to well-established thermodynamic facts,44Pi of a liquid is related to a and kT through the equation-of-state variables, namely, P and T , so that pi = [ ( T f f / k T )- PI (16) Utilizing the definition of kT from eq 10 and of ks = I/&, we may write for PI as a Tu'pC, Pi = -P a2TuZVp C,
+
where P is experimental pressure and all the other symbols have can then be their usual meanings. Excess internal pressure, calculated as
e
In order to calculate the mixture properties of C, and a we have employed additive relations based on mole fractions. on x, is shown in A family of curves for the dependence of Figure 7. For all mixtures the minima of d c u r v e s are shifted toward the bromoform-rich region of the mixture and the values are negative over the entire mixture composition. The skewness of the fl curves is attributed to the wide variation in the basic properties such as density and sound velocity of the mixtures. We observe no systematic trend in the variation of fl with the chain length of the n-alkanes. For mixtures of bromoform with n-octane, n-heptane, TMP, n-nonane, n-decane, and n-dodecane, the Py (42) Barton, A. F. M. Chem. Reus. 1975. 75, 731. (43) Hildebrand, J. H.; Prausnitz, J. M.; Scott, R. L. Regular and Related Solutions; Van Nostrand-Reinhold: Princeton, NJ, 1970. (44) Renuncio, J. A. R.; Breedveld, G. J. F.;Prausnitz, J. M.J. Phys. Chem. 1977,8I,324.
0
0.2
0.L 0.6 MOLE FRACTION, X ,
0.e
I
Figure 7. Excess internal pressure of bromoform and hydrocarbon mixtures as a function of mole fraction of bromoform at 298.15 K (with the same symbols as in Figure 1).
curves are crowded within a narrow range of about (1-1.5) X IO7 Pa. The curves for n-tetradecane and n-hexadecane are about 2 times smaller than that of bromoform n-hexane. This clearly demonstrates the effect of chain length on the calculated excess internal pressure values from the basic properties of the mixtures. For the bromoform + tetralin mixture, the pf! curve shows a peculiar pattern; Le., it decreases steeply upto xI = 0.85 and then suddenly rises toward increased bromoform content of the mixture. The calculated results of fl from eq 18 were also fitted to eq 7 to get the smooth curves drawn in Figure 7. Optical Behavior. Due to the increased interest in the optical a number of studies properties of polymers in mixed solvent~,4~ have been made to investigate the optical properties of binary liquid mixtures. In such studies, molar refraction has been calculated from the refractive index mixjng rules.& A large number of such relations are available in the literature, yet none of them perform perfectl~.~' In this paper, we shall restrict our attention to relationships which are used most often in the modern literature: the Lorentz-hrenz rulea which is based on a model of a molecule within a cavity in a dielectric and the four empirical rules: E ~ k m a n , 4Gladstone-Dale,'O ~ O ~ t e r , and ~ ' Newton.s2 In the theoretical literature, the Lorentz-Lorenz rule is often preferred because it is supported by a plausible theory. However, the other rules are a t least good as the Lorentz-Lorenz one; the Eykman rule is often superior from the experimental view From the molar refraction we have calculated excess molar refraction, RE,of mixtures as
+
Some representative plots of excess molar refraction as calcu(45) (46) (47) (48) (49) (50) (51) (52) (53)
Aminabhavi, T. M.; Munk, P. Macromolecules 1979, 12, 1180. Aminabhavi, T. M. J . Chem. Eng. Dura 1984,29. 54. Parfitt, G. D.;Wood, J. A. Trans. Faraday Soc. 1968. 64. 805. Lorentz, H . A. Theory of Electrons; Teubner: Leipzig, 1909. Eykman, J. F. Red. Trau. Chim. 1895, 14, 185. Gladstone, J. H.; Dale, T. P. Philos. Trans. 1863, 153, 317. Oster, G. Chem. Reu. 1948, 43, 319. Kurtz, S. S., Jr.; Ward, A. L. J . Franklin Inst. 1936, 222, 563. Abdcl-Azim, A. A.; Munk, P. J . Phys. Chem. 1987, 91, 3910.
The Journal of Physical Chemistry, Vol. 95, No. 13, 1991 5307
Mixtures of Bromoform with Hydrocarbons 0
1.59
z
1.56
Y I
--
-10
L
E
a c
-E
Y
1.53
x'
B
8
G -20
f 1.50
d
W
5
W VI
" W
t
W
-30
1.44 0
0.2
0.6 VOLUME FRACTION,
0.E
0.4
1
9,
Figure8. Excess molar refraction based on Eykman relation for mixtures
of bromoform with hydrocarbons as a function of volume fraction of bromoform at 298.15 K (with the same symbols as in Figure 1).
141
1.3 8
0
0.2
0.L 0.6 VOLUME FRACTION, @ I
0.8
v
I
FI 9. Exctss molar refraction of bromoform + n-hexadecane mixture as a function of volume fraction of bromoform at 298.15 K for different mixing rules: Lorentz-Lorenz ( O ) , Gladstone-Dale (V),Eykman (0), Newton (A), and Oster ( 0 ) . lated by eq 19 are shown in Figure 8 for Riyk. It is found that for all mixtures the REvalues are negative over the entire volume fraction scale. Also, there is a very systematic decrease in the values of RE from n-hexane to n-hexadecane. The RE data for the Eykman relation as well as the Lorentz-Lorenz (L-L) relation (not shown graphically) lie nicely on the smooth curves,suggesting their validity over the composition range studied. It may be noted that for mixtures of tetralin and TMP with bromoform we find identical behavior of REvs 4, curves. In any case, the Eykman relation seems to reproduce the experimental data better than the Lorentz-Lorenz and other relations. Some representative plots of RE as calculated from various mixing rules are included in Figure 9 for mixtures of bromoform with n-hexadecane. Here again, the fitted values of RE are used to draw the smooth lines. For these mixtures, large and negative RE values are observed for the Oster relation. For Eykman, Lorentz-Lorenz, and Gladstone-Dale relations the dependence of RE values on & is quite identical; RrL-L exhibits a smaller negative value than the Gladstone-Dale and Eykman relations. The Newton relation exhibits intermediate REvalues between those of Lorentz-Lorenz, Gladstone-Dale, and Eykman and that of Oster relation. A similar situation exists for all the mixtures. Those dependencies are not displayed graphically to avoid overcrowding of the figures. The dependence of refractive index on mole fraction of the mixture as displayed in Figure 10 shows an interesting feature
The use of mole fraction or volume fraction averages as given in eq 20 introduces an error in evaluating the ideal dielectric constant term and hence the corresponding error in cE of the mixture. Therefore, we have used the following equation to calculate tE of the mixture. ...
1- I
where (54) Bottcher, C. J. F. Theory of Elecrric Polarization; Elsevier: Amsterdam, 1952. ( 5 5 ) Oswal, S.L. Indian J . Technol. 1989, 27, 101.
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An alternative possibility to calculate tE would be to evaluate it from the known dielectric constant theories and converting them into mixing rules; but their number is large starting with the original one by Mossotti and Clausius. It was thus decided to use only those models that are based on spherical cavity introducing no correlation factors. This narrowed our choice to only three equations given by Debye,% O n ~ a g e r , ~and ' Kirk~ood.~* Suitable computer programs were written for each equation and least-squares fittings were performed by using eq 13. The estimated standard e m and the smoothing constants of eq 13 have been evaluated for tE by using the dielectric mixing rules and eq 13.
In order to obtain further evidence to support the formation of 1:l complexes in solution as shown by the isorefractive point in Figure 10, the total molar polarization, P,, for mixture has been calculated by using the Kirkwood-Frohlich equations4
P, = ( e ,
- n2)(2r, - ~ I , , , ~ ) V , / ~ C ,
(23)
Thus, if long-chain alkanes have molecular ordering in their pure states, it is possible to use P, values calculated from Kirkwood(56) Debye, P. Polar Molecules; The Chemical Catalog Co., Inc.: New York, 1929. (57) Onsager, L. J . Am. Chem. Soc. 1936, 58, 1486. (58) Kirkwood, J. G.J. Chem. Phys. 1939, 7,911. (59) Riddick, J. A.; Bunger, W.B.; Sahno. T. K. Techniques of Chemistry, Vol II, Organic Solvents; Wiley: New York, 1986. (60) Chevalier, J. L. E.; Petrino, P. J.; Gaston-Bonhomme, Y. H. J. Chem. Eng. Data 1990, 35. 206. (61) Awwad, A. M.;Salman, M. A. Fluid Phase Equilib. 1985,25, 195. (62) Aucejo, A.; Part, E.; Medina, P.; Sancho-Tello, M. J . Chem. Eng. Data 1986,31, 143. (63) CRC Handbook of Chemistry and Physics, 63rd ed.; CRC Press: Boca Raton, FL, 1982-1983.
Frohlich equation as an approximate measure of molecular orientations of n-alkanes in the presence of bromoform. The calculated value of P, from eq 23 a t x l 0.5 is around 17 f l cm3/mol proving the existence of 1:l weak molecular complexes as evidenced by maxima or minima of several excess properties in addition to the isorefractive point shown in Figure 10.
Conclusions In the present paper we have attempted to study a number of excess thermodynamic functions based on the results of densities, viscosities, refractive indices, sound velocities, and dielectric constants of the mixtures of n-alkanes with bromoform. To the best of our knowledge these mixtures have not been studied previously in the literature. It is realized that for a prediction of the thermodynamic behavior of mixtures of n-alkanes with a nearly spherical molecule such as bromoform, it is necessary to have accurate data on thermodynamic excess functions. Further, the results of this study indicate the destruction or creation of order in n-alkanes and that there is a systematic variation of thermodynamic excess properties with the chain length of n-alkane molecules. Acknowledgment. Financial support from the University Grants Commission, New Delhi [No. F 12-55/88(SR-III)] is highly appreciated. These funds were utilized to purchase all the equipment used in this work. We also greatly appreciate the diligent help we received from Mr. S.B. Harogoppad on computational work reported in this paper. Registry No. TMP, 540-84-1; tetralin, 139-64-2; bromoform, 75-25-2; n-hexane, 110-54-3; n-heptane, 142-82-5;n-octane, 1 1 1-65-9;n-nonane, 11 1-84-2; n-decane, 124-18-5; n-dodecane, 112-40-3; n-tetradecane, 629-59-4; n-hexadecane, 544-76-3. Supplementary Material Available: Tables IV-X, listing values of least-squares estimations of the various quantities, viz., P,qE, ACZE,k!, k,! k!(F), Re, and tE (10 pages). Ordering information is given on any current masthead page.
New Developments in the C o n t h " Representation of Solvent Effects D. Mornles-Lagos**tand Juan S. Mmez-Jeria**t Institute of Chemistry, Faculty of Sciences, Austral University of Chile, P.O. Box 567, Valdivia, Chile, and Faculty of Sciences, University of Chile, P.O.Box 653 Santiago, Chile (Received: November 15, 1990; In Final Form: January 2, 1991)
New developments in the continuum representation of solvent effects are presented. General expressions for the Helmholtz free energy of an arbitrary discrete charge distribution placed in spherical and spheroidal (oblate and prolate) cavities and surrounded by multiple dielectric layers are derived. The solutesolvent interaction energy is accounted for by using the multipole expansion. This dielectric partition permits the modeling of nonlinear dielectric effects (NLDE). These results are incorporated into quantum mechanical formalismsat the CND0/2 level, giving origin to prolate spheroidal (PS) generalized Born formula (GBF), PS modified GBF, and PS self-consistent multilayered reaction field with overlap schemes. Some of these schemes incorporate nonsphericity, NLDE, or both. The Miertus and Kysel parametrization of the soluttsolvent interaction is generalized. The electrostatic contributions to some selected thermodynamic properties are presented. The integrative value of this work is shown through the recuperation of the spherical cases and of some expressions presented by Abe and Abrahams.
I. Introduction Continuum models are widely used to deal with solvent eff e c t ~ . ' - ~Their simplicity makes them suitable for a number of applications, especially for large molecules. These models are based on considering the solute molecule inside an empty cavity surrounded by a polarizable continuous dielectric medium. The To whom all the correspondence should be addressed. 'Austral University of Chile. *University of Chile.
0022-3654/91/2095-5308$02.50/0
potential acting on the solute is found by using reaction field theory6 and then incorporated into quantum-mechanical formalisms. Born, M. Z . Phys. 19u1, 1,45. ( 2 ) Onsager, L.J. Am. Chem. Soc. 1936, 58. 1486. (3) Kirkwood, J. G. J . Chem. Phys. 1934. 1 , 351. (4) Constanciel, R.; Contreras, R. Theoret. Chim. Acra 1984, 65, 1. (5) Constanciel, R. Theoret. Chim. Acra 1986, 69, 505. (6) B6ttcher. C. J. F. Theory of Dielectric Polarization; Elsevier: Amsterdam, 1973; Vol. I. (1)
0 1991 American Chemical Society
