Linear Solvation Energy Relationship of the Limiting Partition

Environ. Sci. Technol. 1996, 30, 143-152

Linear Solvation Energy Relationship of the Limiting Partition Coefficient of Organic Solutes between Water and Activated Carbon D E A N C . L U E H R S , * ,† JAMES P. HICKEY,‡ PETER E. NILSEN,§ K. A. GODBOLE,| AND TONY N. ROGERS§ Department of Chemistry, Department of Chemical Engineering, and Department of Mathematical Sciences. Michigan Technological University, Houghton, Michigan 49931, and Great Lakes Center-National Biological Survey, 1451 Green Road, Ann Arbor, Michigan 48105

A linear solvation energy relationship has been found for 353 values of the limiting adsorption coefficients of diverse chemicals: log K ) -0.37 + 0.0341Vi 1.07β + D + 0.65P with R ) 0.951, s ) 0.51, n ) 353, and F ) 818.0, where Vi is the intrinsic molar volume; β is a measure of the hydrogen bond acceptor strength of the solute; D is an index parameter for the research group which includes the effects of the different types of carbon used, the temperature, and the length of time allowed for the adsorption equilibrium to be established; and P is an index parameter for the flatness of the molecule. P is defined to be unity if there is an aromatic system in the molecule or if there is a double bond or series of conjugated double bonds with no more that one non-hydrogen atom beyond the double bond and zero otherwise. A slightly better fit is obtained if the two-thirds power of Vi is used as a measure of the surface area in place of the volume term: log K ) -1.75 + 0.227V2/3 - 1.10β + D + 0.60P with R ) 0.954, s ) 0.49, n ) 353, and F ) 895.39. This is the first quantitative measure of the effect of the shape of the molecule on its tendency to be adsorbed on activated carbon.

Introduction In addition to treatment of municipal wastewater, treatment of water before use as well as after use is a major process * Corresponding author telephone: (906) 487-2702; fax: (906) 4872061; e-mail address: [email protected]. † Department of Chemistry, Michigan Technological University. ‡ Great Lakes Center-National Biological Survey. § Department of Chemical Engineering, Michigan Technological University. | Department of Mathematical Sciences, Michigan Technological University.

0013-936X/96/0930-0143$12.00/0

 1995 American Chemical Society

in the pulp and paper, petroleum, and chemical industries (1). The use of activated carbon in wastewater treatment is growing rapidly to meet the increasingly rigorous Environmental Protection Agency regulations on wastewater quality (2). Because activated carbon is a selective adsorbent, a knowledge of the tendency of different chemicals to adsorb on activated carbon is necessary for design and operation of water purification systems (3). However, it is estimated that over 70 000 different synthetic chemicals are in use. Adsorption coefficients have been measured for only a small fraction of these (4). In order to extract the maximum amount of information from the data available, it is desirable to develop quantitative structure-activity relationships (QSARs) to estimate values that are not known and to identify measurements that need to be reevaluated (5). Most previous QSAR studies of adsorption on activated carbon have involved only a limited number of compounds with a limited variety of structural types (2, 6-15). Recently, 363 limiting adsorption coefficients at low concentrations of diverse chemicals were used in a QSAR with the connectivity indices (16). Blum et al. found it necessary to use an index parameter to identify the research group that did the particular measurement. This included the effect of the different types of activated carbon used by the various groups as well as differences in technique such as the time allowed for equilibrium to be established and the temperature at which the measurement is done. Although some groups have allowed as little as 2 h for equilibrium to be established, careful studies have shown that to be sure equilibrium is established at least 3 weeks time should be allowed for equilibrium to be established between aqueous solution and activated carbon (3, 17). A dependence on three connectivity indices and the index parameter for research group gave a correlation coefficient of 0.92 and a standard deviation of 0.66 for 363 values of log K where K is the limiting adsorption coefficient. The ratio is calculated at the lowest concentration of solute measured with the expectation that the isotherms are linear at the lowest concentrations of solute (3, 8, 9, 15, 18-20). Although this limiting linear isotherm behavior is rarely observed, even at the lowest solute concentrations measured, there is still enough information about relative adsorption tendencies at solute concentrations of environmental importance to make estimation of this value of practical importance. The linear solvation energy relationship (LSER) system of the Kamlet and Taft group has the following advantages: it is relatively easy to use, it can be applied to a wide range of problems from electronic spectra to toxicity to fish, the results can be interpreted to give chemical information, and the parameters are not highly correlated (21-23). In particular, the LSER approach has had considerable success in application to adsorption equilibria (8, 24, 25). Kamlet et al. (8) showed how well the LSER approach could be applied to adsorption on activated carbon. However, this study was based on only 38 solutes, all monofunctional aliphatic oxygenated compounds with a limited range of molar volumes and β (measure of the ability to be a hydrogen bond acceptor) values. They reported difficulties with aromatic solutes. At the time this study was done, a weakness of the LSER approach was that

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the parameters were available for only a relatively limited set of chemicals. Now that a convenient, reliable scheme is available to give consistent estimates of LSER parameters for a much wider range of chemicals (26), the large data set of diverse chemicals, including many of environmental concern, collected by Blum et al. (16) can be correlated with the LSER parameters to obtain a correlation with possibly a better fit but certainly with more physical significance and statistical reliability. Greater robustness for diverse chemical structures not included in the data set is also expected using the LSER approach.

Experimental Section and Results For the case of adsorption on activated carbon, the LSER equation is expected to take the form

log K ) log Ko + s(π* - dδ) + aR + bβ + mVi (1) where π* is the polarity/polarizability parameter, δ is a polarizability correction factor (1.0 for aromatic solutes, 0.5 for polychlorinated aliphatic solutes, and 0.0 for other aliphatic solutes), R is a measure of the ability of the solute to be a hydrogen bond donor, β is a measure of the ability of the solute to be a hydrogen bond acceptor, Vi is the molar volume of the solute in solution, and log Ko is a fitting constant. Usually in a particular case, not all of the terms are statistically significant, and the equation takes a simpler form (21-23). Values of Vi, π*, R, and β were calculated by the procedure of Hickey and Passino-Reader (26) for the chemicals in the data set of 363 values of log K used by Blum et al. (16). The two entries for PCBs were omitted because they are mixtures, not pure chemicals. Dalapon was omitted from the correlation because it is a salt, and the system for estimating LSER parameters is not designed for salts. This left 360 values of log K (see Table 1). Multiple linear regression of log K against the LSER parameters and index parameters for the six research groups indicated that log Ko and the parameters π* and R were not significant at the 95% level of confidence

log K ) -(0.05 ( 0.15) + (0.0329 ( 0.0014)Vi + (0.26 ( 0.15)π* + (0.15 ( 0.14)R + (1.31 ( 0.12)β + D R ) 0.921, s ) 0.65, n ) 360

(2)

where D is the consolidated index parameter for the research group as used by Blum et al. (16). It was found that the Dobbs and Cohen (14) and Belfort et al. (6) groups could not be distinguished from each other at the 90% level of confidence, in agreement with Blum et al. The values of the other index parameters for the different research groups were similar to those obtained by Blum et al. (16) within the limits of uncertainty at the 95% level of confidence. Omitting the log Ko and the variables π* and R, which are not statistically significant, the regression is

assigned D ) 0. It can be seen that omitting log Ko and the variables π* and R did not lower the correlation coefficient or increase the standard deviation. Recalculation of the data set of Blum et al. (16) using the connectivity indices and index parameters given duplicated the results given in the paper except that the value of R2 was 0.84 and not the value of 0.92 given in the paper. An R2 of 0.84 means an R of 0.92, so perhaps that is the source of the confusion. Thus, the correlation with the two LSER parameters gave as good a correlation as measured by the standard deviation and R value as the three connectivity indices which accounts for the F statistic being somewhat higher for the correlation with the LSER parameters. Further regressions attempting to combine the LSER and connectivity indices did not yield any improvement over the correlation with either set alone. Examination of the correlation of Vi, β, 3χp, 6χvp, and 2χv showed that for this data set β is not highly correlated with any of the other parameters, but the other four are highly correlated (see Table 2). Thus, a correlation involving the three connectivity indices has a serious flaw (29, 30). However, a correlation with Vi and β does not have this autocorrelation flaw. The orthogonal descriptors technique of Randic´ recognizes the autocorrelation problem and shows how to avoid it when using connectivity indices (30). A number of studies have shown that when doing correlations of solubility or partitioning equilibria involving compounds that are solids at room temperature, a correction for the entropy of fusion needs to be made (29, 31, 32). This is often approximated by 0.010(Tm - 25) where Tm is the melting point of the solid (in °C. An attempt to improve the correlation by adding a term in (Tm - 25) was unsuccessful even though the data set contains 85 values for solids with melting points extending to over 300 °C. Because there is some uncertainty about whether the sum of the individual β’s of the various functional groups should be added to obtain the overall β of a polyfunctional compound (26, 33), all the compounds with an estimated β value greater than 1.00 were checked to see if there were any systematic errors. This check found only a random relationship of size of residuals with β. This is reasonable if the main effect of a nonzero β value is to increase the solubility of the compound in the aqueous phase (33), which would tend to decrease adsorption on the carbon. When the compound is in the aqueous phase, all the functional groups should be able to interact with the water. Since one theory of solutions predicts that interactions between the solute and solvent water should depend more on the surface area of the solute exposed to the water than on the solute volume (6, 34-37), regression of log K against V2/3, β, and the index parameters was carried out with V2/3 as a measure of the surface area. This yielded

log K ) -(1.37 ( 0.14) + (0.225 ( 0.008)V2/3 (1.16 ( 0.09)β + D (4)

log K ) (0.0335 ( 0.0014)Vi - (1.14 ( 0.09)β + D (3)

R ) 0.928, s ) 0.61, n ) 360, F ) 740.55

R ) 0.920, s ) 0.65, n ) 360, F ) 652.97

with D ) 1.04 ( 0.10 for the Speth and Miltner group, -1.22 ( 0.14 for the Abe group, -1.14 ( 0.09 for the Guisti group, and -1.47 ( 0.14 for the Arbuckle group, again with no statistical difference between the Dobbs and Cohen group and the Belfort group. This is slightly better than the correlation with the volume as shown by the values of the correlation coefficient, standard deviation, and F statistic.

where D ) 1.01 ( 0.10 for the Speth and Miltner group (17), 1.29 ( 0.15 for the Abe et al. group (9), 1.20 ( 0.10 for the Guisti et al. group (27), and 1.53 ( 0.15 for the Arbuckle data (28) with no statistical difference between the Belfort group (6) and the Dobbs and Cohen group (14) that was

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TABLE 1

Chemicals, LSER Variables, Experimental Log K, and Calculated Log K (eq 7) Valuesa Blum No. (16)

name

log K (exp)

log K (calc)

Vi/100

π*

β

r

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74

acetaldehyde acetone butyl acetate butyraldehyde butyric acid diethyl ether dipropyl ether ethyl acetate hexanoic acid methyl acetate pentanoic acid propionaldehyde propionic acid propyl acetate valeraldehyde 1-butanol 1-hexanol 1-pentanol 1-propanol 2-butanone 2-hexanone 2-pentanone 1-butanol 1-heptanol 1-hexanol 1-pentanol 2-butanone 2-ethyl-1-butanol 2-heptanone 2-hexanone 2-methyl-1-butanol 2-methyl-3-pentanol 2-methyl-3-pentanone 2-nonanone 2-octanone 2-pentanone 2-propanone 2,3-dimethyl-2-butanol 2,4-dimethyl-3-pentanol 2,4-dimethyl-3-pentanone 2,6-dimethyl-4-heptanone 3-ethyl-3-pentanol 3-heptanone 3-methyl-2-butanone 3-methyl-2-heptanone 3-pentanone 3,3-dimethyl-1-butanol 3,3-dimethyl-2-butanone 4-heptanone 4-methyl-1-pentanol 4-methyl-2-hexanone 4-methyl-2-pentanone 5-methyl-2-hexanone 5-methyl-3-heptanone 5-nonanone phenol 2-butylphenol 2-hexylphenol 2-methylphenol 2-pentylphenol 2,3-dimethylphenol 2,3,5-trimethylphenol 2,3,6-trimethylphenol 2,5-dimethylphenol 2,6-dimethylphenol 3,4-dimethylphenol 3,5-dimethylphenol 4-tert-butylphenol 4-tert-pentylphenol 4-butylphenol 4-ethylphenol 4-isopropylphenol 4-pentylphenol 4-propylphenol

-1.25 -0.90 1.20 -0.19 -0.09 -0.26 0.84 -0.04 1.21 -0.56 0.58 -0.82 -0.64 0.63 0.38 -0.17 0.96 0.35 -0.74 -0.44 0.71 0.14 0.56 2.05 1.79 0.93 0.51 1.45 2.09 1.58 1.10 1.37 1.23 2.17 2.16 1.36 -0.36 0.77 1.50 1.69 2.69 1.43 2.25 0.73 2.16 1.16 0.90 1.12 2.39 1.53 1.92 1.42 1.93 2.08 2.19 2.04 3.13 3.08 2.35 3.13 2.69 2.82 2.91 2.65 2.82 2.65 2.65 2.82 2.91 3.14 2.56 2.52 3.21 2.74

-0.79 -0.52 0.66 -0.10 -0.01 -0.08 0.59 -0.01 0.65 -0.31 0.32 -0.44 -0.35 0.34 0.23 -0.08 0.57 0.24 -0.41 -0.19 0.47 0.14 0.85 1.84 1.50 1.17 0.74 1.47 1.73 1.40 1.14 1.41 1.39 2.40 2.07 1.08 0.41 1.37 1.74 1.56 2.36 1.68 1.72 1.05 2.05 1.05 1.37 1.33 1.72 1.47 1.70 1.39 1.70 2.03 2.38 1.76 3.06 3.42 2.09 3.39 2.42 2.77 2.73 2.41 2.39 2.40 2.41 3.00 3.34 3.04 2.41 2.75 3.34 2.75

0.283 0.380 0.716 0.480 0.519 0.505 0.699 0.521 0.715 0.424 0.617 0.381 0.421 0.622 0.577 0.499 0.690 0.593 0.402 0.477 0.670 0.574 0.499 0.789 0.690 0.593 0.477 0.680 0.767 0.670 0.583 0.680 0.672 0.963 0.865 0.574 0.380 0.670 0.778 0.720 0.957 0.778 0.767 0.565 0.859 0.574 0.670 0.650 0.767 0.680 0.757 0.672 0.757 0.855 0.963 0.536 0.918 1.024 0.634 1.016 0.730 0.830 0.830 0.732 0.726 0.732 0.732 0.908 1.006 0.918 0.732 0.830 1.006 0.830

0.67 0.71 0.55 0.65 0.60 0.27 0.27 0.55 0.52 0.60 0.54 0.65 0.58 0.55 0.65 0.40 0.40 0.40 0.40 0.67 0.63 0.65 0.40 0.40 0.40 0.40 0.67 0.40 0.61 0.63 0.40 0.40 0.66 0.65 0.59 0.65 0.71 0.40 0.40 0.67 0.67 0.40 0.61 0.65 0.65 0.65 0.40 0.65 0.61 0.40 0.66 0.66 0.65 0.66 0.57 0.72 0.63 0.63 0.70 0.63 0.65 0.63 0.63 0.65 0.65 0.64 0.65 0.62 0.60 0.62 0.66 0.63 0.60 0.64

0.42 0.48 0.45 0.41 0.45 0.47 0.46 0.45 0.45 0.42 0.45 0.41 0.45 0.45 0.41 0.45 0.45 0.45 0.45 0.48 0.48 0.48 0.45 0.45 0.45 0.45 0.48 0.45 0.48 0.48 0.45 0.51 0.50 0.48 0.48 0.48 0.48 0.51 0.51 0.49 0.50 0.57 0.49 0.48 0.48 0.50 0.51 0.48 0.49 0.45 0.48 0.50 0.48 0.48 0.50 0.33 0.33 0.33 0.33 0.33 0.33 0.32 0.36 0.34 0.34 0.35 0.34 0.35 0.35 0.35 0.34 0.34 0.35 0.34

0.00 0.06 0.00 0.00 0.54 0.00 0.00 0.00 0.55 0.00 0.56 0.00 0.67 0.00 0.00 0.33 0.33 0.33 0.33 0.05 0.03 0.03 0.33 0.33 0.33 0.33 0.05 0.33 0.05 0.03 0.33 0.31 0.03 0.00 0.03 0.03 0.06 0.31 0.32 0.03 0.03 0.29 0.05 0.05 0.05 0.04 0.31 0.05 0.05 0.33 0.00 0.03 0.00 0.00 0.00 0.60 0.56 0.56 0.57 0.56 0.57 0.56 0.53 0.57 0.55 0.55 0.57 0.57 0.57 0.35 0.58 0.56 0.57 0.58


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Table 1 (Continued) Blum No. (16)

name

log K (exp)

log K (calc)

Vi/100

π*

β

r

75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 139 140 141 142 143 146 147 148 149 150 151 152 153 155

acrolein acrylonitrile adipic acid aldrin R-BHC R-endosulfan β-BHC β-endosulfan bis(2-chloroethoxy)methane bis(2-chloroethyl) ether bis(2-chloroisopropyl) ether bromoform carbon tetrachloride chlordane chloroethane chloroform cyclohexanone dibromochloromethane dichlorobromomethane dieldrin EDTA endrin heptachlor heptachlor epoxide hexachlorobutadiene hexachlorocyclopentadiene hexachloroethane isophorone lindane methylene chloride N-nitrosodimethylamine N-nitrosodipropylamine tetrachloroethene trichloroethene trichlorofluoromethane 1,1-dichloroethane 1,1-dichloroethene 1,1,1-trichloroethane 1,1,2-trichloroethane 1,1,2,2-tetrachloroethane 1,2-dibromo-3-chloropropane 1,2-dichloroethane 1,2-dichloropropane 1,2-dichloropropene 1,2-trans-dichloroethene 2-chloroethyl vinyl ether acenaphthene acenaphthylene acetophenone adenine R-naphthol R-naphthylamine anethole anthracene benzene benzo[a]pyrene benzo[ghi]perylene benzo[k]fluoranthene benzoic acid benzothiazole β-naphthol β-napthylamine chlorobenzene cytosine DDE DDT dibenzo[a,h]anthracene dimethylphenylcarbinol diphenylamine ethylbenzene fluoranthene fluorene guanine hexachlorobenzene hydroquinone N-nitrosodiphenylamine

-0.17 -0.11 0.76 3.08 4.37 4.87 4.02 3.31 0.88 0.09 0.87 2.11 1.33 4.34 -0.20 0.85 0.84 2.76 1.67 4.23 0.54 3.26 3.35 3.98 3.94 4.57 3.70 2.04 3.53 -0.13 0.14 1.54 2.69 2.22 1.66 0.96 1.60 2.02 1.63 2.49 2.85 0.93 1.40 1.85 1.65 0.43 2.95 3.45 2.13 2.15 2.16 3.10 3.23 3.76 0.32 4.04 4.02 4.27 1.72 3.11 2.39 2.88 1.94 0.49 6.01 5.19 2.85 3.53 3.10 1.72 3.96 4.38 2.41 4.33 2.20 3.32

0.46 0.51 0.95 4.86 3.15 3.81 3.15 3.92 1.63 1.14 0.48 1.55 1.28 4.66 0.73 1.09 1.18 1.30 1.13 4.89 2.56 3.70 4.41 4.61 2.94 3.49 2.22 2.17 3.28 0.67 0.33 1.63 2.20 1.91 1.08 1.09 1.61 1.29 1.40 1.63 1.95 1.03 1.37 1.88 1.61 1.01 3.22 3.03 2.11 2.08 2.65 2.56 3.07 3.53 1.85 4.80 5.18 4.71 2.07 1.57 2.65 2.56 2.19 1.41 5.03 5.59 5.21 2.39 3.02 2.50 3.87 3.34 1.82 3.80 1.62 3.49

0.357 0.344 0.670 1.674 1.031 1.656 1.031 1.656 0.828 0.685 0.489 0.561 0.514 1.648 0.352 0.427 0.619 0.520 0.470 1.745 1.648 1.475 1.558 1.638 0.795 0.988 0.790 0.889 1.146 0.336 0.455 0.837 0.578 0.492 0.455 0.442 0.406 0.519 0.519 0.617 0.716 0.442 0.540 0.530 0.406 0.570 0.916 0.890 0.690 0.812 0.798 0.824 0.950 1.015 0.491 1.418 1.547 1.392 0.650 0.584 0.798 0.824 0.581 0.741 1.516 1.632 1.539 0.810 0.991 0.687 1.130 0.960 0.838 1.031 0.581 1.172

0.75 0.80 0.95 1.04 0.70 1.64 0.70 1.54 1.24 0.97 0.97 0.49 0.28 1.07 0.47 0.58 0.76 0.65 0.73 1.26 2.16 1.44 1.02 1.59 0.30 0.95 0.50 0.80 0.68 0.82 0.66 0.66 0.28 0.53 0.22 0.48 0.72 0.49 0.85 0.95 0.70 0.81 0.81 0.87 0.44 0.80 0.26 0.36 0.90 1.23 0.92 0.83 0.83 0.40 0.59 0.60 0.70 0.50 0.74 0.87 0.92 0.83 0.71 1.08 1.90 1.90 0.60 0.99 0.83 0.53 0.40 0.26 1.79 0.70 0.72 1.72

0.36 0.28 0.90 0.45 0.00 1.37 0.00 1.27 0.77 0.77 0.77 0.00 0.10 0.55 0.10 0.00 0.53 0.10 0.10 0.65 2.52 0.90 0.50 0.57 0.05 0.15 0.10 0.46 0.24 0.10 0.80 0.80 0.05 0.05 0.10 0.05 0.05 0.10 0.00 0.10 0.12 0.10 0.10 0.20 0.05 0.53 0.17 0.27 0.49 0.91 0.33 0.50 0.42 0.20 0.10 0.30 0.35 0.30 0.40 0.66 0.33 0.50 0.07 1.31 0.39 0.24 0.30 0.61 0.60 0.12 0.25 0.20 1.23 0.00 0.60 0.74

0.00 0.00 1.10 0.43 0.00 0.38 0.00 0.38 0.12 0.12 0.12 0.05 0.00 0.52 0.00 0.20 0.00 0.06 0.35 0.41 1.76 0.25 0.51 0.51 0.00 0.16 0.00 0.04 0.29 0.13 0.00 0.00 0.00 0.12 0.00 0.10 0.00 0.00 0.13 0.25 0.06 0.10 0.10 0.00 0.00 0.06 0.00 0.05 0.06 0.26 0.61 0.35 0.05 0.00 0.00 0.00 0.00 0.00 0.74 0.18 0.61 0.16 0.00 1.03 0.05 0.00 0.00 0.29 0.34 0.00 0.00 0.00 0.21 0.00 1.11 0.00

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9



name

log K (exp)

log K (calc)

Vi/100

π*

β

r

156 157 158 159 160 161 162 163 164 165 166 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233

naphthalene nitrobenzene o-anisidine o-chlorophenol o-dichlorobenzene o-nitrophenol p-dichlorobenzene p-nitroaniline p-nonylphenol p-xylene p-chloro-m-cresol pentachlorophenol phenanthrene phenol styrene thymine toluene uracil 1-chloro-2-nitrobenzene 1,1-diphenylhydrazine 1,2-diphenylhydrazine 1,2,3,4-tetrahydronaphthalene 1,2,4-trichlorobenzene 1,3-dichlorobenzene 2-acetylaminofluorene 2-chloronaphthalene 2,4-dichlorophenol 2,4-dimethylphenol 2,4-dinitrophenol 2,4-dinitrotoluene 2,4,6-trichlorophenol 2,6-dinitrotoluene 3,3′-dichlorobenzidine 3,4-benzofluoranthene 4-aminobiphenyl 4-bromophenyl phenyl ether 4-chlorophenyl phenyl ether 4-dimethylaminoazobenzene 4-nitrobiphenyl 4-4′-methylene-bis(2-chloroaniline) 4,6-dinitro-o-cresol 5-bromouracil 5-chlorouracil 5-fluorouracil acetaldehyde acetic acid acetone acrylaldehyde acrylic acid allylamine benzaldehyde butyl acetate butyl acrylate butylamine butyraldehyde butyric acid crotonaldehyde cyclohexanone dibutylamine diethylene glycol diethylenetriamine diisopropyl ether dipropylamine dipropylene glycol ethanol ethyl acetate ethyl acrylate ethylene glycol ethylenediamine formaldehyde formic acid hexanoic acid isobutyl acetate isopropyl acetate methanol methyl acetate

2.52 3.57 1.84 1.65 2.21 2.48 2.39 3.69 3.49 1.74 2.60 2.60 3.82 1.25 2.30 1.38 1.29 0.81 2.61 2.34 2.95 1.98 2.28 2.00 3.80 3.19 3.91 2.19 3.09 2.72 3.04 2.70 4.30 4.56 3.69 2.44 2.48 4.20 3.69 2.36 3.28 1.80 1.29 0.83 -1.24 -0.80 -0.86 -0.63 0.12 -0.60 1.25 0.70 1.43 -0.15 -0.14 0.00 -0.29 0.17 0.80 -0.74 -0.66 0.54 0.54 -1.04 -1.35 -0.18 0.46 -1.57 -1.31 -1.40 -0.82 1.63 0.60 0.20 -1.68 -0.74

2.69 2.06 1.93 2.51 2.54 2.04 2.53 2.16 4.75 2.44 2.49 3.48 3.53 1.76 2.39 1.67 2.18 1.34 2.46 2.84 2.84 3.16 2.88 2.53 3.96 3.04 2.46 2.40 2.30 2.65 2.80 2.65 3.51 4.71 2.98 3.75 3.56 4.22 3.32 4.26 2.58 1.64 1.49 1.24 -0.82 -0.71 -0.55 -0.50 -0.48 -0.74 0.52 0.63 0.93 -0.25 -0.13 -0.04 -0.17 0.21 1.10 -0.78 -0.93 0.57 0.44 -0.11 -0.77 -0.04 0.27 -1.09 -1.50 -1.32 -0.98 0.62 0.59 0.27 -1.08 -0.34

0.753 0.631 0.705 0.726 0.671 0.673 0.670 0.702 1.418 0.671 0.724 0.986 1.015 0.536 0.660 0.785 0.592 0.687 0.721 1.120 1.120 0.883 0.761 0.670 1.341 0.843 0.716 0.732 0.810 0.866 0.806 0.866 1.242 1.392 0.991 1.101 1.060 1.327 1.060 1.402 0.908 0.828 0.777 0.717 0.283 0.323 0.380 0.357 0.390 0.408 0.480 0.716 0.786 0.535 0.480 0.519 0.455 0.619 0.933 0.586 0.632 0.699 0.734 0.782 0.305 0.521 0.590 0.354 0.390 0.140 0.224 0.715 0.706 0.612 0.205 0.424

0.30 1.01 0.82 0.75 0.80 1.11 0.70 1.25 0.67 0.51 0.73 1.02 0.40 0.72 0.58 1.53 0.55 1.52 1.11 1.73 1.73 0.50 0.75 0.75 1.41 0.42 0.82 0.64 1.16 1.02 0.95 1.02 1.56 0.50 0.52 0.85 0.77 1.25 0.60 0.16 1.16 1.95 1.87 1.60 0.67 0.60 0.71 0.75 0.60 0.35 0.65 0.55 0.63 0.32 0.65 0.60 0.75 0.76 0.25 1.07 0.86 0.27 0.25 1.05 0.40 0.55 0.63 0.80 0.65 0.69 0.65 0.52 0.55 0.55 0.40 0.60

0.15 0.35 0.71 0.23 0.03 0.50 0.03 0.48 0.34 0.12 0.24 0.15 0.20 0.33 0.13 1.20 0.11 1.20 0.26 1.18 1.18 0.12 0.00 0.03 0.84 0.11 0.25 0.35 0.70 0.55 0.22 0.55 0.94 0.30 0.64 0.27 0.31 0.55 0.54 0.75 0.75 1.37 1.35 1.39 0.42 0.45 0.48 0.36 0.45 0.75 0.41 0.45 0.39 0.69 0.41 0.45 0.36 0.53 0.70 1.35 1.64 0.45 0.68 1.35 0.45 0.45 0.38 0.90 1.40 0.43 0.38 0.45 0.45 0.45 0.42 0.42

0.00 0.00 0.23 0.63 0.00 0.12 0.00 0.42 0.57 0.00 0.67 0.66 0.00 0.60 0.00 0.85 0.00 0.85 0.00 0.45 0.45 0.00 0.00 0.00 0.25 0.00 0.60 0.55 0.12 0.00 0.62 0.00 0.33 0.00 0.16 0.00 0.00 0.05 0.16 0.45 0.12 0.90 0.91 0.91 0.00 0.55 0.06 0.00 0.54 0.00 0.00 0.00 0.00 0.05 0.00 0.54 0.00 0.00 0.00 0.66 0.00 0.00 0.00 0.66 0.33 0.00 0.00 0.66 0.00 0.00 0.78 0.55 0.00 0.00 0.35 0.00


9

147


name

log K (exp)

log K (calc)

Vi/100

π*

β

r

234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309

paraldehyde pentanoic acid pentyl acetate propionaldehyde propionic acid propyl acetate propylene oxide tetraethylene glycol triethylene glycol vinyl acetate 1-butanol 1-hexanol 1-pentanol 1-propanol 1,1′-dimethyl-2,2′-iminodiethanol 1,2-dichloroethane 1,2-dichloropropane 1,2-propanediol 2-(2-butoxyethoxy)ethanol 2-(2-ethoxyethoxy)ethanol 2-amino-1-methylethanol 2-aminoethanol 2-butanone 2-butoxyethanol 2-ethoxyethanol 2-ethoxyethyl acetate 2-ethyl-1-butanol 2-ethyl-1-hexanol 2-hexanone 2-hexyloxyethanol 2-methoxyethanol 2-methyl-1-propanol 2-methyl-2-propanol 2-methyl-2,4-pentanediol 2-pentanone 2-propene-1-ol 2,2′,2′′-nitrilotriethanol 2,2′-iminoethanol tetraethylene glycol 4-methyl-2-pentanone 5-methyl-2-hexanone acetophenone aniline benzene benzoic acid ethylbenzene hydroquinone isophorone N-ethylmorpholine N-methylmorpholine nitrobenzene phenol pyridine styrene styrene oxide toluene 2-methyl-5-ethylpyridine acetaldehyde acetone butyl acetate butyraldehyde diisopropyl ether ethanol ethyl acetate isopropyl acetate propionaldehyde propyl acetate 1-butanol 1-hexanol 1-pentanol 1-propanol 2-butanone 2-ethyl-1-butanol 2-ethylhexanol 2-methyl-1-propanol 2-propanol

0.35 0.52 0.84 -0.70 -0.58 0.39 -0.74 -0.02 -0.15 0.11 -0.12 1.40 0.47 -0.96 -0.28 0.57 1.16 -1.26 0.62 -0.33 -0.92 -1.54 -0.26 -0.07 -0.61 0.15 0.73 2.03 0.55 0.80 -1.17 -0.37 -0.63 0.05 0.24 -0.89 -0.57 -0.70 0.24 0.71 0.72 1.66 0.38 1.34 1.03 0.69 0.65 1.56 -0.13 -0.35 1.43 0.55 -0.25 0.96 1.39 0.51 0.92 -1.89 -0.96 0.29 -0.23 0.48 -1.70 0.02 0.20 -0.78 0.11 -0.01 0.68 0.33 -0.85 -0.41 0.55 1.15 -0.35 -1.07

-0.45 0.29 0.95 -0.47 -0.38 0.31 -0.68 -0.32 -0.63 -0.14 -0.11 0.54 0.21 -0.44 -0.25 0.07 0.40 -1.03 0.42 -0.09 -0.99 -1.26 -0.22 0.19 -0.43 0.37 0.50 1.15 0.44 0.90 -0.77 -0.20 -0.24 0.12 0.11 -0.51 -0.61 -0.91 -0.32 0.42 0.73 1.15 0.70 0.88 1.11 1.53 0.66 1.21 0.01 -0.33 1.09 0.79 0.47 1.43 1.63 1.22 1.39 -1.02 -0.76 0.42 -0.34 0.36 -0.98 -0.24 0.07 -0.68 0.10 -0.32 0.33 0.00 -0.65 -0.43 0.30 0.95 -0.41 -0.75

0.733 0.617 0.810 0.381 0.421 0.622 0.347 1.002 0.770 0.496 0.499 0.690 0.593 0.402 0.821 0.442 0.540 0.384 0.938 0.787 0.477 0.380 0.477 0.697 0.546 0.767 0.680 0.870 0.670 0.938 0.448 0.489 0.498 0.725 0.574 0.377 0.840 0.625 1.002 0.672 0.757 0.690 0.562 0.491 0.650 0.687 0.581 0.889 0.738 0.640 0.631 0.536 0.472 0.660 0.740 0.592 0.766 0.283 0.380 0.716 0.480 0.699 0.305 0.521 0.612 0.381 0.622 0.499 0.690 0.593 0.402 0.477 0.680 0.870 0.489 0.392

1.62 0.54 0.55 0.65 0.58 0.55 0.56 1.54 1.34 0.60 0.40 0.40 0.40 0.40 1.00 0.81 0.81 0.80 0.94 0.94 0.72 0.70 0.67 0.60 0.67 0.75 0.40 0.40 0.63 0.67 0.67 0.40 0.40 0.90 0.65 0.45 1.35 1.00 1.54 0.66 0.65 0.90 0.73 0.59 0.74 0.53 0.72 0.80 0.50 0.50 1.01 0.72 0.87 0.58 1.15 0.55 0.82 0.67 0.71 0.55 0.65 0.27 0.40 0.55 0.55 0.65 0.55 0.40 0.40 0.40 0.40 0.67 0.40 0.40 0.40 0.40

1.51 0.45 0.45 0.41 0.45 0.45 0.50 2.25 1.80 0.47 0.45 0.45 0.45 0.45 1.60 0.10 0.10 0.94 1.35 1.35 1.20 1.14 0.48 0.80 0.90 0.85 0.45 0.45 0.48 0.90 0.90 0.50 0.57 0.95 0.48 0.43 2.00 1.60 2.25 0.50 0.48 0.49 0.50 0.10 0.40 0.12 0.60 0.46 1.10 1.10 0.35 0.33 0.43 0.13 0.20 0.11 0.50 0.42 0.48 0.45 0.41 0.45 0.45 0.45 0.45 0.41 0.45 0.45 0.45 0.45 0.45 0.48 0.45 0.45 0.50 0.51

0.00 0.56 0.00 0.00 0.67 0.00 0.00 0.66 0.66 0.00 0.33 0.33 0.33 0.33 0.60 0.10 0.10 0.66 0.33 0.33 0.32 0.33 0.05 0.33 0.00 0.00 0.33 0.33 0.03 0.33 0.33 0.32 0.32 0.66 0.03 0.33 0.85 0.60 0.66 0.03 0.00 0.06 0.26 0.00 0.74 0.00 1.11 0.04 0.00 0.00 0.00 0.60 0.00 0.00 0.00 0.00 0.00 0.00 0.06 0.00 0.00 0.00 0.33 0.00 0.00 0.00 0.00 0.33 0.33 0.33 0.33 0.05 0.33 0.33 0.32 0.32

148

9



name

log K (exp)

log K (calc)

Vi/100

π*

β

r

310 311 312 313 314 315 316 317 318 319 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368

3-heptanone 3-pentanone 4-methyl-2-pentanone aldicarb bromodichloromethane bromoform carbofuran carbon tetrachloride chloroform cis-1,2-dichloroethene dibromochloromethane dibromochloropropane dibromomethane glyphosate hexachlorocyclopentadiene isophorone lindane methylene chloride oxamyl tert-butyl methyl ether tetrachloroethene trans-1,2-dichloroethene trichloroethene 1,1-dichloroethane 1,1-dichloroethene 1,1-dichloropropene 1,1,1-trichloroethane 1,1,1,2-tetrachloroethane 1,1,2-trichloroethane 1,2-dibromoethane 1,2-dichloroethane 1,2-dichloropropane 1,2,3-trichloropropane 1,3-dichloropropane 2,4,5-trichlorophenoxyacetic acid alachlor atrazine benzene bromobenzene chlorobenzene cyanazine dicamba dinoseb ethyl benzene metolachlor metribuzin o-chlorotoluene o-dichlorobenzene p-chlorotoluene p-dichlorobenzene p-xylene pentachlorophenol pichloroam simazine styrene toluene 1,3,5-trichlorobenzene 2,4-dinitrotoluene

0.62 0.05 0.20 3.85 2.01 2.87 3.94 2.20 1.60 2.01 2.51 4.19 1.45 3.69 4.14 3.42 3.99 0.55 3.16 1.29 3.34 2.17 2.84 1.48 2.27 2.42 1.98 3.00 2.13 3.32 1.35 2.25 2.83 2.65 3.59 5.08 4.15 2.86 3.37 3.19 3.37 3.39 4.45 3.03 3.89 3.39 3.88 3.57 4.10 3.46 3.98 4.89 4.94 5.81 3.53 3.49 4.24 4.19

0.55 -0.12 0.22 3.08 2.08 2.50 4.45 2.23 2.04 2.56 2.25 2.90 2.00 1.01 4.44 3.12 4.88 1.62 3.63 2.15 3.15 2.56 2.86 2.04 1.91 2.90 2.25 2.58 2.35 2.33 1.98 2.32 2.63 2.32 4.13 4.90 4.11 2.80 3.30 3.14 4.05 4.06 4.56 3.45 6.22 3.69 3.46 3.49 3.47 3.49 3.39 4.43 3.46 3.81 3.34 3.13 3.82 3.60

0.767 0.574 0.672 1.202 0.470 0.561 1.303 0.514 0.427 0.406 0.520 0.716 0.430 0.570 0.988 0.889 1.146 0.336 1.472 0.602 0.578 0.406 0.492 0.442 0.406 0.504 0.519 0.617 0.519 0.528 0.442 0.540 0.617 0.540 1.036 1.470 1.307 0.491 0.624 0.581 1.406 0.965 1.192 0.687 1.791 1.368 0.679 0.671 0.681 0.670 0.671 0.986 0.971 1.219 0.660 0.592 0.760 0.866

0.61 0.65 0.66 1.14 0.73 0.49 1.45 0.28 0.58 0.95 0.65 0.70 0.65 1.63 0.95 0.80 0.68 0.82 1.49 0.27 0.28 0.44 0.53 0.48 0.72 0.72 0.49 0.95 0.85 0.75 0.81 0.81 0.90 0.81 1.36 1.10 0.89 0.59 0.79 0.71 1.09 0.89 1.18 0.53 1.72 1.23 0.67 0.80 0.66 0.70 0.51 1.02 1.25 0.89 0.58 0.55 0.70 1.02

0.49 0.50 0.50 1.50 0.10 0.00 1.15 0.10 0.00 0.05 0.10 0.12 0.05 1.42 0.15 0.46 0.24 0.10 1.84 0.45 0.05 0.05 0.05 0.05 0.05 0.05 0.10 0.10 0.00 0.05 0.10 0.10 0.05 0.10 0.59 1.26 1.48 0.10 0.06 0.07 1.85 0.43 0.69 0.12 1.05 1.46 0.08 0.03 0.08 0.03 0.12 0.15 1.01 1.48 0.13 0.11 0.00 0.55

0.05 0.04 0.03 0.30 0.35 0.05 0.30 0.00 0.20 0.00 0.06 0.06 0.00 1.45 0.16 0.04 0.29 0.13 0.30 0.00 0.00 0.00 0.12 0.10 0.00 0.00 0.00 0.25 0.13 0.00 0.10 0.10 0.10 0.00 0.61 0.00 0.34 0.00 0.00 0.00 0.54 0.74 0.12 0.00 0.00 0.36 0.00 0.00 0.00 0.00 0.00 0.66 0.65 0.34 0.00 0.00 0.00 0.00

a The following chemicals were eliminated: (Blum numbers) 137, bis(2-ethylhexyl) phthalate; 138, butyl benzyl phthalate; 144, diethyl phthalate; 145, dimethyl phthalate; and 154, butyl phthalate; 167, PCB-1221; 168, PCB-1232; 320, dalapon. Research groups: 1-22, Abe; 23-74, Belfort; 75-201, Dobbs and Cohen; 202-290, Guisti; 291-312, Arbuckle; 313-368, Speth and Miltner.

A more detailed investigation of this approach using areas calculated by the UNIFAC approach (38, 39) will be the subject of future work. Although the π* parameter was found not to be statistically significant, the coefficient of the δ term was statistically different from zero at the 99.9% level of confidence. The δ parameter is not intended to be used as a stand-alone parameter but only as a correction to the π* parameter (21, 22, 40). Cases where it appears to be significant by itself are usually better interpreted in another manner. In this

TABLE 2

Correlation of LSER and Connectivity Parameters for Data Set Vi β 3χ p 2χv 6χv p

Vi

β

3χ

2χv

6χv

1.000

0.323 1.000

0.901 0.176 1.000

0.816 0.033 0.794 1.000

0.701 0.097 0.808 0.804 1.000

p

p


9

149

case, it appears that the δ parameter is acting as an index parameter for planarity of the molecule. It has been suggested before that adsorption on carbon is favored by planarity of the solute and that globular molecules are not adsorbed as well (27, 41, 42), but this study is the first time the effect has been evaluated quantitatively. When this was tested by defining an index parameter P to be 1 for any aromatic molecule or an olefin with no more than one nonhydrogen atom beyond the double bond or series of conjugated double bonds and zero otherwise, multiple linear regression yielded

log K ) -(0.17 ( 0.09) + (0.0304 ( 0.0013)Vi (0.97 ( 0.09)β + D + (0.67 ( 0.07)P (5) R ) 0.936, s ) 0.58, n ) 360, F ) 624.32 Use of V2/3 in place of Vi yielded

FIGURE 1. Correlation of the limiting partition coefficient of organic solutes between water and activated carbon with LSER parameters: log K ) -0.37 + 0.0341Vi - 1.07β + D + 0.65P; R ) 0.951, s ) 0.51, n ) 353, F ) 818.0.

log K ) -(1.44 ( 0.12) + (0.206 ( 0.078)V2/3 (0.996 ( 0.082)β + D + (0.62 ( 0.07)P (6) R ) 0.941, s ) 0.55, n ) 360, F ) 693.06 where D ) 1.01 for the Speth and Miltner group, -0.99 for the Abe group, -1.02 for the Guisti group, and -1.23 for the Arbuckle group. A preliminary study to evaluate the effects of an aromatic ring and planar olefin separately showed that the effects were not statistically different from each other at the 90% level of confidence. At this point, there were seven chemicals that were more than 3 SD from either one of the regressions: EDTA, dibenz[a,h]anthracene, glyphosate, metolachlor, simazine, aldrin, and 4,4′-methylene-bis(2-chloroaniline). Even for a data set of this size, 3 SD is excessive. EDTA would not be expected to be modeled well by the LSER because it is a zwitterion, which would be more strongly hydrated than an uncharged species. Removal of these outliers from the regression gave

log K ) -(0.368 ( 0.080) + (0.0341 ( 0.0011)Vi (1.07 ( 0.08)β + D + (0.65 ( 0.06)P (7)

FIGURE 2. Correlation of the limiting partition coefficient of organic solutes between water and activated carbon with the surface area of the solute: log K ) -1.75 + 0.227V2/3 - 1.10β + D + 0.60P; R ) 0.954, s ) 0.49, n ) 353, F ) 895.39. TABLE 3

Summary of Factors Influencing Measurement of Log K on Activated Carbona

R ) 0.951, s ) 0.51, n ) 353, F ) 818.0 where D ) 0.951 for the Speth and Miltner group, -0.935 for the Abe group, -0.965 for the Guisti group, -1.17 for the Arbuckle group, and 0.00 for the Dobbs and Cohen and the Belfort groups. Use of V2/3 in place of Vi yielded

log K ) -(1.75 ( 0.13) + (0.227 ( 0.008)V2/3 (1.10 ( 0.08)β + D + (0.60 ( 0.06)P (8) R ) 0.954, s ) 0.49, n ) 353, F ) 895.39 where D ) 0.972 for the Speth and Miltner group, -0.915 for the Abe group, -0.938 for the Guisti group, -1.15 for the Arbuckle group, and 0.00 for the Dobbs and Cohen and the Belfort groups (see Figures 1 and 2). Table 3 summarizes experimental conditions used by different research groups, which leads to the various values of D.

Discussion A strength of the LSER approach is that the terms of the equation can be given a physical interpretation. The strong positive dependence of K on the molecular volume has been observed many times before, generally with data sets limited to hydrophobic compounds (10-12, 27, 43). The

150

9


research group

regression coefficient (D)

carbon

time of equilibrium

Dobbs and Cohen Belfort Speth and Miltner Abe Arbuckle Guisti

0.00 0.00 0.95 -0.94 -1.17 -0.97

F-300 F-400 F-400 CAL F-400 WV-G

2h 24 h 3 weeks 14 h 2h 2h

a In all groups, the carbon was ground and usually sieved to between 100 and 400 mesh, dried at 110 °C, and kept in a desiccator until use. Because of the longer time involved, the Speth and Miltner group took precaution against consumption of solute by microorganisms. The limiting partition coefficient was calculated by Blum et al. (16) by using the measurement at the lowest concentration of solute from the literature data and assuming that from zero concentration to the lowest concentration used that the amount of solute adsorbed on the carbon is directly proportional to the concentration of solute in the water.

earlier work of Kamlet et al. (8) on a much smaller data set with a much less extensive range of compounds found

log K ) -1.93 + 0.0306V + 0.56π* - 3.20β

(9)

R ) 0.974, s ) 0.19, n ) 37 The relative magnitudes of the coefficients are not exactly comparable to ours because of a somewhat different

definition of the molar volumes. Our study with the much larger data set did not confirm the small dependence on π* that Kamlet et al. (8) found. Actually, the difference is not as great as it appears because we also found a positive coefficient of π*, but it was not significant at the 90% level of confidence. They found the term in π* to be significant at the 90% level of confidence, but the margin was moderate. The large negative coefficient of β found in both studies and lack of dependence on R is consistent with the LSER of aqueous solubility of aliphatic solutes found by Kamlet et al. (33):

log S ) 0.05 - 0.0585Vi + 1.09π* + 5.23β

(10)

R ) 0.994, s ) 0.15, n ) 115 for aliphatic solutes where S is the molar solubility at 25 °C. Hydrogen bond acceptor ability of the solute favors hydration by the strongly hydrogen bond donating water, which favors solubility in water (which decreases tendency to adsorb on carbon). Apparently, the hydrogen bond acceptor ability of the water is too weak for solubility of to be noticeably enhanced by hydrogen bond donating strength of the solute. In support of this argument, the R value of pure water is 1.17, and the β parameter of pure water is only 0.18 (21, 22). Increasing molar volume decreases solubility in water because the strong hydrogen bonding of the water must be disrupted to create a cavity for the solute molecule. This would tend to increase the tendency of the solute molecule to adsorb onto the activated carbon (10, 44). The effect of planarity of the molecule favoring adsorption was noticed by Manes et al. (41, 42) and Guisti et al. (27), but this is the first time that there has been a quantitative estimation of the effect. Since the dispersion force of attraction is very sensitive to the distance of separation between the surface of the activated carbon and the center of the solute molecule, it is reasonable that a planar molecule would be adsorbed more strongly than an otherwise similar globular molecule. This would contribute to the tendency of hydrophobic but globular molecules such as carbon tetrachloride or chloroform to be adsorbed so weakly on activated carbon. Although steric effects have long been known to be important in organic chemistry (45), the recent use of the techniques of molecular modeling and computer graphics has reemphasized steric effects in biochemistry and drug design as well as organic chemistry (46, 47). Inspection of Figures 1 and 2 indicates that the variance appears to increase as K increases. It is likely that this is related to the fact that the assumption that the adsorption isotherms are linear at low concentrations may be an increasingly poor assumption as K increases. If the widely used Freundlich equation (3) is used to describe the isotherms:

Q ) KfC1/n

(11)

where Q is mg of solute/g of carbon, C is mg of solute/L of solution, and Kf is the Freundlich adsorption coefficient, then the assumption of linear isotherms is that 1/n approaches 1 as C becomes small. However, it is known that there is a negative correlation between 1/n and Kf (48). That is, the larger Kf is, the poorer the assumption that the value of 1/n is approaching 1. This can then lead to even the relative order of adsorption of various solutes being in error with the possibility of either positive or negative errors

in using a limiting adsorption coefficient calculated from the lowest concentration of solute measured in the original experimental work. It is the assumption of both the work by Blum et al. (16) and other previous works using this limiting adsorption coefficient (8, 10) and this study that even taking this problem into account there is still a lot of information in these limiting adsorption coefficients making it worthwhile to attempt a modeling to use for prediction of adsorption of compounds that have not been measured. It should be noted that Yalkowsky et al. (49) found that the absolute magnitude of residuals in estimating activity coefficients of organic solutes in aqueous solution increased as the value of the activity coefficient increased. They attributed this to increased experimental error for the larger values, which is also a possibility here.

Acknowledgments Professors John C. Crittenden, David W. Hand, and James R. Baker gave many helpful suggestions although the authors are responsible for any shortcomings of this paper. Support by the National Center for Clean Industrial and Treatment Technologies (CenCITTsa research consortium including Michigan Technological University, the University of Minnesota, and the University of WisconsinsMadison) funded by the EPA is gratefully acknowledged. This is contribution no. 909 from the Great Lakes Center-National Biological Survey.

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Received for review March 23, 1995. Revised manuscript received July 19, 1995. Accepted August 7, 1995.X ES950200O X

Abstract published in Advance ACS Abstracts, November 1, 1995.

Linear Solvation Energy Relationship of the Limiting Partition

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