Environ. Scl. Technol. lQ85, 19, 980-985
Prediction of Aromatic Solute Partition Coefficients Using the UNIFAC Group Contribution Model James R. Campbell* Environmental Resources Department, Koppers Company,
Inc., Pittsburgh, Pennsylvania
152 19
Rlchard G. Luthy Department of Civil Engineering, Carnegie-Mellon University, Pittsburgh, Pennsylvania 152 13
The UNIFAC group contribution model was evaluated for prediction of partition coefficients (KD)for aromatic solutes and various organic solvent-water systems. Estimates of partition coefficients were shown to be more accurate by use of interaction energy parameters derived from a vapor-liquid equilibria data base rather than a liquid-liquid euqilibria data base. Predictions of KDwere made by using estimates of both solvent- and aqueousphase activity coefficients, and this was compared with predictions where estimates of solvent-phase activity coefficients were used with experimental values of aqueous-phase activity coefficients. It was demonstrated that partition coefficients could, in many cases, be estimated within a factor of 2 by use of experimental aqueous-phase activity coefficients. The technique is also useful for solvent screening purposes as well as for assessing the relative distribution of various compounds between water and a given solvent. Introduction This paper summarizes the results of an investigation that evaluated the UNIFAC group contribution model for prediction of partition coefficients for aromatic solutes. This work compliments results presented in a companion paper ( I ) , where experimental measurement of partition coefficients and other predictive techniques were examined. The previous paper evaluated regular solution theory models ( 2 , 3 )and linear free energy relationships ( 4 ) for estimating aromatic solute partition coefficients. This paper describes the application of the UNIFAC model for estimating partition coefficients and then compares the utility of the UNIFAC, regular solution, and linear free energy approaches. A report encompassing all of the experimental and modeling work performed as part of this investigation is also available (5). The study evaluated eight solvent-water systems which included a wide variety of solute and solvent functionality. The solvents employed in this investigation were chosen to represent various chemical classes: toluene and benzene (aromatics); hexane and heptane (alkanes); octanol (alcohols); n-butyl acetate (esters); diisopropyl ether (ethers); methyl isobutyl ketone (ketones). The aromatic solutes which were considered included nonpolar compounds such as benzene, toluene, and naphthalene, phenolic molecules such as phenol, cresol, and catechol, nitrogenous aromatics such as aniline, pyridine, and aminonaphthalene, and other aromatic solutes such as naphthol, quinolinol, and halogenated compounds. Partition Coefficient Partition coefficients are useful for correlations with various physical and chemical properties of aromatic compounds. Noteworthy among these endeavors are correlations with octanol-water partition Coefficients (KO,) for calculating environmental parameters such as aqueous solubility (6, 7), bioaccumulation (8, 9), and sorption on 980
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soil (10, 1 1 ) . Partition coefficients are also useful in analytical chemistry for evaluating organic chemical extraction efficiency or chromatographic separation. Partition coefficients are also used for design and evaluation of solvent extraction systems for treatment of industrial wastewaters, including use of n-butyl acetate (NBA), diisopropyl ether (DIPE), or methyl isobutyl ketone (MIBK) for treatment of phenolic wastes ( I ) . A partition coefficient describes the equilibrium distribution of a solute between two phases. For the case where the system is comprised of water and an immiscible organic solvent, solute molecules will be distributed in relation to their solubilities in each phase. For low to moderate solute concentrations, the widely accepted definition of the partition coefficient is (12-15) KD = cs/cw (1) where C, and C, refer to the solute concentration in the organic solvent and water phases, respectively. The partition coefficient may also be expressed in terms of solute activity coefficients. At equilibrium the solute chemical potential or fugacity, f, must be equal in each phase. By use of Raoult's law convention (15,161,fugacity may be expressed as f = XYP (2) where x is the mole fraction of the compound in a particular phase, y is the activity coefficient for the compound in that phase, and f is the reference fugacity, i.e., the fugacity of the pure liquid compound (or subcooled liquid) at the system temperature. At equilibrium the solute fugacity is the same in water and solvent phases: (3) f = x w r w f = X,Y$ For dilute solutions the solute mole fraction may be expressed as the product of solute molar concentration and solvent molar volume (5, 6, 17): c, = XJV, c, = x,/v, (4) Combining eq 3 and 4, we get K D = (yw"/ys") ( V W / ~ S ) (5) where ywm= infinite-dilution activity coefficient of solute in aqueous phase, 7,-= infinite-dilutionactivity coefficient of solute in organic solvent phase, V , = molar volume of water (cm3/mol or L/mol), and V , = molar volume of solvent (cm3/mol or L/mol). Note that in eq 5 reference fugacities cancel regardless of whether the solute is a liquid or solid at the system temperature. The UNIFAC model was used to estimate solute activity coefficients for calculating binary system partition coefficients according to eq 5 . UNIFAC UNIFAC is a group contribution model that can be used to predict activity coefficients for nonelectrolytes in liquid mixtures. It is applicable to a wide range of solutions exhibiting either positive or negative deviations from
0013-936X/85/0919-0980$01.50/0
0 1985 American Chemical Society
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Flgure 1. Comparison of VLE-based and LE-based partition coefficient estimates for octanol-water systems.
Raoult’s law (18). The UNIFAC model is attractive because, while there are an ever increasingly large number of organic compounds in existence, the number of functional groups which make up these compounds is much smaller. Hence, it is possible to estimate properties for a very large number of different organic molecules from a small set of functional group properties (18). UNIFAC was developed in 1975 by Fredenslund and co-workers (19) when they combined two methods for predicting phase equilibria: the analytical solution of groups (ASOG) model (20-22) and the universal quasichemical (UNIQUAC)model (23,24). The computational procedures of UNIFAC are based on the structural arrangement provided by the lattice analogy of the UNIQUAC model. UNIFAC divides the molecular activity coefficient into two parts: a combinatorial portion (c), which accounts for differences in the size and shape of molecules, and a residual portion (R),which takes into account the interaction energy arising between functional groups:
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Figure 2. Comparison of VLE-based and LLE-based partition coefficient estimates for MIBK-water and NBA-water systems.
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Figure 3. Comparison of VLE-based and LLE-based partition coefficient estimates for benzene-water and toluene-water systems.
In yi = In y; + In yiR (6) The general form of the expressions for the combinatorial and residual portions of yi,for multicomponent systems, may be found in ref 19. Examples for calculating activity coefficients by the UNIFAC model are presented in ref 5 and 25. The energy interaction parameters from which the UNIFAC model calculates activity coefficients are based on the functional group classifications assigned by Fredenslund and co-workers. At present, UNIFAC energy interaction parameters can be derived from two sources: an extensive vapor-liquid equilibria (VLE) data base and a smaller liquid-liquid equilibria (LLE) data base. The functional group parameters based on VLE data are presented by Gmehling et al. (26,27). These authors have distinguished 76 separate subgroups which are divided among 40 different main-group classifications. The LLE data can be found in Magnussen et al. (28) and are separated into 57 separate subgroups which are divided among 32 main-group sets.
Figure 4. Comparison of VLE-based and LLE-based partition coefficient estimates for heptane-water and hexane-water systems.
Model Evaluation UNIFAC estimates of partition coefficients were evaluated by comparison with experimental values determined as part of this investigation (1, 5 ) or obtained from the Medchem Project (29,301.Comparisons between experimental and UNIFAC estimates of partition coefficients were made for either meta (3-) or para (4-) substitution whenever possible. Comparison with ortho- (2-) substituted compounds was generally avoided because the UNIFAC model does not consider intramolecular interactions which may occur between functional groups of molecules. For example, the interaction energy arising
from intramolecular hydrogen bonding which may occur with ortho-substituted aromatic compounds is not reflected in UNIFAC activity coefficient estimates. Comparison of Interaction Energy Parameters. The initial analysis of the UNIFAC model compared partition coefficients that were calculated from estimates of both aqueous- and solvent-phase activity coefficients by using either VLE-based interaction energy parameters or LLE-based parameters. Estimated partition coefficients were then compared with experimental values for 96 aromatic solute systems. The data for this comparison are shown graphically in Figures 1-4. The solutes employed
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Table I. UNIFAC Partition Coefficient Estimates for Octanol-Water Systems predicted KD exptl est exptl solute
KD
7w-
aniline 4-nitroaniline benzene chlorobenzene l,4-dichlorobenzene ethylbenzene methylbenzene 1,4-dimethylbenzene 1,3,5-trimethylbenzene nitrobenzene naphthalene 2-aminonaphthalene 1-hydroxynaphthalene 2- hydroxyquinoline 8-hydroxyquinoline 4-methyl-8-hydroxyquinoline pyridine phenol 4-hydroxyphenol 4-methylphenol 3,5-dimethylphenol 4-nitrophenol average error factorb
7.9 25 140 450 2500 1400 540 1400 2600 71 2000 180 690 18 100 230 4.5 29 3.9 87 220 81
9.7 3.9 170 1200 8000 1900 750 3300 14000 69 4500 250 330
7w-
14 180 770 2600 1900 590 1800 3900 2200 410 2300
18 18
75 3.5 12 0.9 54 240 5.0
53 35 240 670
Table 111. UNIFAC Partition Coefficient Estimates for Two Aromatic Solvent-Water Systems
error factor" est exptl 7w-
yw-
0.81 6.4 0.82 0.38 0.31 0.74 0.72 0.42 0.19 1.0 0.44 0.72 2.1 1.0 5.6 3.1 1.3 2.4 4.3 1.6 0.92 16 3.0
0.56 0.78 0.58 0.92 0.74 0.92 0.78 0.67 0.91 0.44 0.30
0.55 0.11 0.36 0.33 2.3
OError factor = experimental/predicted. *Average of E.F. and reciprocals of E.F. < 1.
>1
Table 11. UNIFAC Partition Coefficient Estimates for Three Polar Solvent-Water Systems
solute
predicted KD exptl est exptl KD 7w7w-
Methyl Isobutyl Ketone aniline 32 11 naphthalene 5100 15000 1-hydroxynaphthalene 1400 330 8-hydroxyquinoline 130 3.4 2-methyl-8-hydroxyquinoline 320 18 pyridine 2.9 0.84 phenol 8.6 100 4-hydroxyphenol 10 0.19 3-methylphenol 260 45 3,5-dimethylphenol 810 240 naphthalene 1-hydroxynaphthalene phenol 4-hydroxyphenol 4-methylphenol 3,5-dimethylphenol naphthalene average error factorb
n-Butyl Acetate 6500 14000 1400 370 71 9.2 4.5 0.24 200 41 540 180 Diisopropyl Ether 3500 9600
error factor" est exptl 7w-
YWW
16 2.9 6900 0.34 2400 4.2 38 18 3.5 37 12 7.6 53 200 5.8 670 3.4
2.0 0.74 0.57
6700 2600 40 9.4 180 510
0.46 3.8 7.7 19 4.9 3.0
0.97 0.54 1.8 0.48
4500 0.36
0.78 1.6
11
2.7 1.3 1.3 1.2
1.1 1.1
Error factor = experimental/predicted. bAverage of E.F. > 1 and reciprocals of E.F. < 1.
in this evaluation, as well as the VLE-based partition coefficient estimates, are given in Tables I-IV. Tabulations of the LLE-based partition coefficient data are available in ref 5. Our analysis indicates that VLE-based interaction energy parameters provided more accurate estimates of partition coefficients. This was evidenced by VLE-based estimates being within an average factor of 6 of the experimental partition coefficient, while the LLE-based es982
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solute
error predicted KD factora exptl est exptl est exptl KD 7wm 7w7wyw-
Benzene ani1ine 10 4-nitroaniline 8.5 2-aminonaphthalene 280 1-hydroxynaphthalene 78 8-hydroxyquinoline 370 pyridine 2.8 3,5-dimethylpyridine 32 phenol 2.3 4-hydroxyphenol 0.01 5-methyl-3-hydroxyphenol 0.03 2,5-dimethyl-3-hydroxyphenol 0.27 3,5-dimethylphenol 22 2-nitrophenol 210 Toluene aniline 2.0 4-nitroaniline 6.0 2-aminonaphthalene 230 1-hydroxynaphthalene 63 8-hydroxyquinoline 170 2-methyl-8-hydroxyquinoline 560 pyridine 2.5 phenol 2.0 4-hydroxyphenol 0.01 5-methyl-3-hydroxyphenol 0.03 2,5-dimethyl-3-hydroxyphenol 0.21 4-methylphenol 11 20 3,-dimethylphenol 2-nitrophenol 190 average error factorb"
6.0 5.0 360 16 0.18
8.8 590 120
1.2
75 1.2 0.27 1plus reciprocals of error factors < 1,S = standard deviation of sample, n = sample size, and to,,,, = t statistic for the 95% confidence range and specified n. The 95% confidence intervals for the average error factors are shown in Table V. The data in Tables I-V show that partition coefficients derived from UNIFAC VLE-based estimates of both solvent-phase and aqueous-phase activity coefficients are semiqualitative in nature. That is, we should not expect better than an order of magnitude accuracy at the 95% confidence level. Our analysis shows that the approach is useful for relative ranking of KD values for several solutes and a particular solvent. For example, estimated KD values for octanol-water systems decrease in the order naphthalene > methylbenzene > benzene > methylphenol > phenol > aniline > pyridine, etc. The approach also provides a procedure for obtaining a relative ranking of several solvents for extraction of a particular solute. For example, VLE-based estimates show that octanol, MIBK, and NBA are better solvents for extraction of hydroxynaphthalene than benzene, toluene, hexane, or heptane. Likewise, the VLE-based estimates show correct relative ranking of these solvents for phenol, 3,5-dimethylphenol, and 4-methylphenol. It is interesting to note that 8-hydroxyquinoline and 2-nitrophenol are generally responsible for the largest error in estimation of KD for any given solvent system. This is a result of the failure of UNIFAC to adequately account for intramolecular functional group interactions. Both 8-hydroxyquinoline and 2-nitrophenol contain hydrogenbonding functional groups situated close enough to one another to form intramolecular hydrogen bonds ( 1 , 5 ) ,and the UNIFAC group interaction parameters do not account for this behavior. The effect of tautomeric equilibrium and intramolecular hydrogen bonding is shown in Table I, where the estimated KD for 2-hydroxyquinoline (no intramolecular hydrogen bonding) is exact, while that for 8-hydroxyquinoline is low by a factor of about 6. Tables I-IV also show partition coefficients calculated from predicted values of ypmand experimental values of yw". These data show that this procedure results in a significant improvement in estimated KD values. This is evidenced by examination of the error factor confidence intervals in Table V, where use of experimental values of ywmallows for semiquantitative prediction of partition coefficients. At the 95 % confidence level, partition coefficients are predicted within a factor of approximately 2 for all systems, excluding 8-hydroxyquinoline and 2nitrophenol for the reasons sited above. Data in Tables I-IV show that the trend observed previously of overestimating KD for nonpolar solutes and underestimating KD Environ. Sci. Technol., Vol. 19,
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for polar solutes is not apparent when experimental values of ywmare employed. The estimates of KDbased on experimental values of ywm and predicted values of ySm are useful for a relative ranking of several solutes being extracted by a particular solvent. For example, predicted values of KO, decrease correctly in the order 1,3,5-trimethylbenzene > naphthalene > ethylbenzene > 2-aminonaphthalene > benzene > aniline, and predicted values of KD for MIBK decrease correctly in the order naphthalene > 1-hydroxynaphthalene > 33dimethylphenol > 3-methylphenol > phenol > aniline > 4-hydroxyphenol,etc. Correct ranking is also provided for the six solutes and NBA. This trend is generally evident for the other solvent systems. In addition, except for certain relative errors with respect to octanol, partition coefficients estimated by using experimental values of ywm provide correct relative ranking of solvents for extraction of a particular solute. For example, predicted values of KD in Tables I-IV show that for phenol MIBK N NBA > benzene = toluene > hexane = heptane and for aniline MIBK > octanol = benzene = toluene > hexane = heptane, etc. Mukhopadhyay and Dongaonkar (33) suggest that an alternative method of improving the accuracy of UNIFAC phase equilibria predictions is to tailor the functional group interaction parameters to a particular system. This modification will imprave model accuracy at the expense of limiting model applicability. Mukhopadhyay and Dongaonkar used specialized parameters to compute phase equilibria composition diagrams for three ternary systems: cyclohexane-benzene-sulfolane, hexane-benzene-sulfolane, and heptane-toluene-sulfolane. The results compared very favorably with the experimental phase diagrams for these systems. While experimental partition coefficient data were not available for comparison to Mukhopadhyay and Dongaonkar's predictions, their values compared favorably with estimates from the more data intensive UNIQUAC and NRTL models (33). However, Magnussen et al. (28) note that UNIFAC usually works much better for prediction of phase equilibria diagrams than for prediction of partition coefficients, especially at low concentrations. Hence, it is not known if the high accuracy obtained for ternary phase diagrams by modifying UNIFAC parameters will be obtained for prediction of partition coefficients at low solute concentrations. Comparison of UNIFAC, Regular Solution, and Linear Free Energy Models. This investigation also included comparison of the UNIFAC approach for prediction of aromatic solute partition coefficients with a regular solution theory (RST) model and with an approach based on use of linear free energy relationships (LFER). The applicability and utility of the RST and LFER models have been discussed previously ( I , 5 ) . It was concluded that the regular solution theory model may be used to estimate solute activity coefficients only for organic solvent systems that do not include hydrogen bonding. This restricted the utility of the RST model because hydrogen bonding was shown to be the dominant molecular interaction for many of the polar solute-polar solvent systems under consideration. The RST model was found to work fairly well for nonpolar systems, as evidenced by a 95% confidence level error factor range of 5.6-2.3. It appeared that the RST model could be made more accurate by improving the correlations for the empirical correction term, although it is likely that this would require a separate correlation for each solvent system. It should be noted that the RST model cannot be used to estimate aqueous phase activity coefficients. 984
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Figure 5. Comparison of experimental and estimated partition coefficients for various aromatic solute octanol-water systems.
The UNIFAC approach was found to be more accurate than the regular solution theory model for prediction of K Dvalues for the systems under consideration. Figure 5 provides a graphical representation of the improvement in prediction of KD for the various octanol-water systems listed in Table I. In Figure 5, the logarithm of experimental KO, values are plotted vs. the logarithm of KO, values estimated by the RST and UNIFAC models. The scatter of the data about the 45O line provides a measure of the accuracy of estimated KO,values. It is apparent that the most accurate estimates of KO, are obtained when experimental values of ywmare used in conjunction with UNIFAC estimates of solvent-phase activity coefficients. In this comparison the RST estimates of KO,were based with ySmbeing calculated on experimental values of ywm, by using the procedure of Helpinstill and Van Winkle ( I , 3, 5). The LFER approach was shown ( I , 5 ) to provide strong correlations for the solvent-solute systems considered. This is because special attention was given to providing correlations between compatible hydrogen-bonding systems. It appeared, however, that KD values for alkane solvents did not correlate as well as those for polar and aromatic solvents. In addition, LFER correlation equations were found to be specific for each solvent and solute set, thus limiting the approach because estimation of partition coefficients for specific solute-solvent pairs required a correlation based on data for similar solutes and that particular solvent. By comparing experimental KD values with those estimated from the dependent LFER correlations, an error factor interval of 2.6-1.7 was obtained at the 95% confidence level. This is comparable to the error factor range of 2.5-1.5 obtained for partition coefficients calculated from experimental values of ywmand UNIFAC predictions of ysm. Mutual Phase Saturation. The effects of mutual phase saturation, i.e., aqueous phase saturated with solvent and solvent phase saturated with water, were not considered in this investigation. UNIFAC can accouht for this, however, by considering the appropriate mole fraction solubility of water or solvent as another component to the respective phase. Arbuckle ( l a ,Banerjee et al. (34),and Chiou et al. (6)have addressed the effect of mutual phase saturation on solubility and activity coefficients. Review of these studies shows that mutual phase saturation may be an important consideration for single- and double-ring aromatic solutes with a number of hydrophobic substitutions (e.g., hexachlorobenzene) or for condensed polycyclic aromatic hydrocarbons other than naphthalene and its derivatives (e.g., anthracene and pyrene). Results in Table I suggest that mutual phase saturation is not significant for estimation of KD from the predicted value of ySmand measured value of ywmfor aromatic compounds with re-
ported values of KO,less than about 2500. As a matter of expediency, it is important to recognize that experimental values of mutual phase-saturated activity coefficients are not generally available. Conclusion The UNIFAC procedure is the most useful of the techniques examined for prediction of partition coefficients for aromatic solutes, particularly for polar solutepolar solvent systems. The approach is not case specific and can be adapted for prediction of other environmental parameters such as aqueous solubility and Henry’s law constants (17, 19,35). The UNIFAC model was evaluated by using both vapor-liquid equilibria and liquid-liquid equilibria data. Our evaluation has shown that vapor-liquid equilibria data provide more accurate partition coefficient estimates for the systems considered. In addition, it was shown that partition coefficients for most of the solute-solvent systems could be predicted within a factor of approximately 2, when computed by using experimental values of aqueous phase activity coefficients and UNIFAC estimates of solvent phase activity coefficients based on vapor-liquid equilibria data. This is considered acceptable for many screening and assessment purposes in that the partition coefficients for the range of solute-solvent systems considered varied over approximately 6 orders of magnitude. This approach is also useful for solvent screening purposes and for evaluating the relative distribution of several solutes between water and a particular organic solvent. The approach is applicable to many solute-solvent systems provided that group interaction parameters are available for all functional groups and that molecules with strong intramolecular interactions are not included. In those cases, the linear free energy relationship (LFER) procedure is recommended for prediction of KD values. The UNIFAC model, in conjunction with experimental values of aqueous-phase activity coefficients, is considered to be very useful for estimation of partition coefficients for aromatic solutes in recognition of the availability of experimental aqueous-phase activity coefficients. Furhermore, Fredenslund and co-workers are currently working to improve and expand the data base from which the functional group interaction energy parameters are extrapolated. Additional work is in progress to evaluate the applicability of UNIFAC and other procedures for estimating aromatic solute solubility in miscible polar solvent-water systems (36). This information is being used to assess the effect of solubility enhancement on sorption of aromatic solutes onto soil from an aqueous phase containing a polar solvent.
Literature Cited Campbell, J. R.; Luthy, R. G.; Carrondo, M. J. T. Environ. Sei. Technol. 1983, 17, 582-590. Weimer, R. F.; Prausnitz, J. M. Hydrocarbon Process. 1965, 44, 237-242. Helpinstill, J. G.; Van Winkle, M. Znd. Eng. Chem. Process Des. Dev. 1968, 7, 213-220. Leo, A.; Hansch, C. J. Org. Chem. 1971, 36, 1539-1544. Campbell, J. R. Ph.D. Dissertation, Carnegie-Mellon University, Pittsburgh, PA, 1983. Chiou, C. T.; Schmedding, D. W.; Manes, M. Enuiron. Sei. Technol. 1982, 16, 4-10.
(7) Hansch, C.; Quinlan, J. E.; Lawrence, G. L. J. Org. Chem. 1968, 33, 347-350. (8) Chiou, C. T.; Freed, V. H.; Schmedding, D. W.; Kohnert, R. L. Environ. Sei. Technol. 1977, 11, 475-478. (9) Mackay, D. Environ. Sei. Technol. 1982, 16, 274-278. (10) Karickhoff, S. W. J. Hydraul. Diu. A S C E 1984, 110, 707-735. (11) Schwarzenbach, R. P.; Westall, J. Enuiron. Sei. Technol. 1981,15, 1360-1367. (12) Sawyer, C. H.; McCarty, P. L. “Chemistry for Environmental Engineering”, 3rd ed.; McGraw-Hill: New York, 1978. (13) Kiezyk, P. R.; Mackay, D. Can. J. Chem. Eng. 1971,49, 747-752. (14) Leo, A.; Hansch, C.; Elkins, D. Chem. Rev. 1971, 71, 525-616. (15) Mackay, D. Enuiron. Sei. Technol. 1977, 11, 1219. (16) Prausnitz, J. M. “Molecular Thermodynamics of Fluid Phase Equilibria”; Prentice-Hall: Englewood Cliffs, NJ, 1969. (17) Arbuckle, W. B. Enuiron. Sci. Technol. 1983,17,537-542. (18) Fredenslund, A.; Gmehling J.; Rasmussen, P. “Vapor Liquid Equilibria Using UNIFAC”; Elsevier: New York, 1977. (19) Fredenslund, A.; Jones R. L.; Prausnitz, J. M. AZChE J. 1975,6, 1086-1099. (20) Wilson, G. M.; Deal, C. H. Znd. Eng. Chem. Fundam. 1962, 1, 20-23. (21) Derr, E. L.; Deal, C. H. Znst. Chem. Eng. Symp. Ser. 1969, N o . 32, 37. (22) Ronc, M.; Ratcliff, G. A. Can. J . Chem. Eng. 1971, 49, 825-830. (23) Abrams, D. S.; Prausnitz, J. M. AZChE J. 1975,1,116-128. (24) Guggenheim, E. A. “Mixtures”; Clarendon Press: Oxford, 1952. (25) Grain, C. F. In “Handbook of Chemical Property Estimation Methods”; Lyman, W. J.; Reehl, W. F.; Rosenblatt, D. H., Eds.; McGraw-Hill: New York, 1982; Chapter 11. (26) Gmehling, J.; Rasmussen P.; Fredenslund, A. Znd. Eng. Chem. Process Des. Dev. 1982,21, 118-127. (27) Macedo, E. A,; Weidlich, U., Gmehling, J.; Rasmussen, P. Znd. Eng. Chem. Process Des. Dev. 1983, 22, 678-681. (28) Magnussen, T.;Rasmussen, P.; Fredenslund, A. Znd. Eng. Chem. Process Des. Deu. 1981,20, 331-339. (29) Leo, A. Director, Medchem Project, Pomona College, Clarmont, CA 91711, 1983. (30) Hansch, C.; Leo, A. “Substituent Constants for Correlation Analysis in Chemistry and Biology”; Wiley: New York, 1979. (31) Tsonopoulos, C.; Prausnitz, J. M. Incl. Eng. Chem. Fundam. 1971,10, 593-600. (32) Miller, I.; Freund, J. E. “Probability and Statistics for Engineers”, 2nd ed.; Prentice-Hall: Englewood Cliffs, NJ, 1977. (33) Mukhopadhyay, M.; Dongaonkar, K. R. Znd. Eng. Chem. Process Des. Deu. 1983,22, 521-532. (34) Banerjee, S. J.; Yalkowsky, S. H.; Valvani, S. C. Environ. Sei. Technol. 1980,14, 1227-1229. (35) Lyman, W. J.; Reehl, W. F.; Rosenblatt, D. H. eds. “Handbook of Chemical Property Estimation Methods”; McGraw-Hill: New York, 1982. (36) Fu, J. K.; Luthy, R. G., paper presented a t the American Society of Civil Engineers, 1985 Environmental Engineering National Conference, Boston, MA, July 1985.
Received for review November 26,1984. Accepted April 5, 1985. Support for this investigation was provided by the U S . Department of Energy, Grand Forks Project Office,under Contract 8OFC10157-79 t o R.G.L. Leland E . Paulson was the Project Officer.
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