Environ. Sci. Technol. 1995, 29, 2273-2279

Group Contribution Method for Predicting Equilibria of Nonionic

S6l Organic Matter and Water T Y L E R T . A M E S Department of Chemical Engineering, Michigan State University, East Lansing, Michigan 48823

E R I C A . G R U L K E * Department of Chemical and Materials Engineering, University of Kentucky, Lexington, Kentucky 40506

~ ~ ~ ~~~~~~

Soil organic matter (SOM) is known to be responsible for nonionic organic compound sorption in water-saturated soil, but the equilibria and kinetics of this process are not fully understood. Since the kinetics depend on the equilibrium driving force, understanding the equilibrium solubility of organic compounds in SOM is particularly important. This work describes a method of predicting SOM-water parti- tion coefficients for nonionic organic compounds based on the UNIFAC-type models. Partition coefficients are calculated from the predicted activity coefficients of organic compounds in water and in SOM phases. A model humic acid molecule is used to represent SOM as a polymeric phase, and the ELBRO-FV model is applied to predict SOM-solute activity coefficients. This method resulted in partition coefficients that were within 1 order of magnitude of experimental values for most compounds studied. Chlorinated compounds do not seem to be modeled well by this method, and predictions may be in error by an order of magnitude. Using data rather than UNIFAC predictionsforthe water phase activity coefficients improved the predictions to within a factor of 3 of the experimental values for all compounds where activity data was available.

Introduction The equilibrium distribution of nonionic organic com- pounds between soil organic matter and water has been the subject of several studies (1-10) and has been used as a kinetic model parameter in many others (11-19). The rate of solute removal from the soil depends on the equilibrium driving force, so partition coefficients are required for modeling soil remediation regardless of the specific process used. This work describes a method for predicting partition coefficients for these compounds using their chemical structure and a representative structure of soil organic matter.

* Fax: (606)-323- 1929; e-mail address: egrulke@uklans.uky.edu.

0013-936W95/0929-2273$09.00/0 @ 1995 American Chemical Society

This work addresses sorption equilibrium of nonionic organic compounds between soil organic matter and water only and does not deal with sorption on mineral matter (9, 20). SOM-water partition coefficients have been correlated with octanol-water partition coefficients (2, 4) . Flory- Huggins theory (4) and modified Flory-Huggins theory (21) have been applied to model partition equilibria as well. The correlations require octanol-water partition data for the solute, and the Flory-Huggins theory may not correct properly for molar volume differences of the solute and polymer.

Phase equilibria for gases and liquids have been predicted with great success using UNIFAC (221, a group contribution method for determining activity coefficients. UNIFAC represents structural formulas using a relatively small number of functional groups. Activity coefficients of mixture components are calculatedwith molar areas, molar volumes, and interaction parameters for the groups, which have been fitted with existing equilibrium data. The UNIFAC model and parameter sets have been modified with new data (23-26), applied to liquid-liquid system (27-291, modified for specific classes of systems (30-321, and modified for polymer-solvent equilibria systems (33- 38). As soil organic matter is a polymeric substance (16), it is reasonable to apply a UNIFAC-type group contribution model to organic solute-water-soil organic matter equi- librium.

The equilibrium for a solute that is completely dissolved between two partially miscible phases is described by eq 1.

where 4 is the mole fraction of solute i in phase z, yf is the activity coefficient of solute i in phase z, Tis temperature, and P is pressure. Equation 1 can be rearranged to define the mole fraction partition coefficient, Kx:

The distribution or partition coefficient for the solute mole fractions is equal to the reciprocal of the ratio of the solute activity coefficients in the two phases. In this method, the two activity coefficients of the solute are predicted by UNIFAC and then used to calculate the partition coefficient.

Materials and Methods Literature Data. Literature data of nonionic organic compounds included infinite dilution activity coefficients in water (32, 391, octanol-water partition coefficients (3, 41, and soil organic matter-water partition coefficients (20). These data were compared to predicted partition coef- ficients obtained from the ratio of predicted solute activity coefficients in each phase. A preferred comparison would be that of each activity coefficient with data since two given models may yield similar partition coefficients but very different activity coefficients. Aqueous-phase infinite dilu- tion activity coefficient data were collected in order to make this comparison.

VOL. 29, NO. 9, 1995 /ENVIRONMENTAL SCIENCE &TECHNOLOGY B 2273

COOH I I H C - u COO11 COOH ,,/ "\ 0 0

R - 6 ~ L=O

(Peptide) 1 NH

FIGURE 1. Humic acid structure of Stevenson (41).

Octanol-Water Partition Coefficients. Octanol-water partition coefficients were calculated using the UNIFAC method and compared to literature data. The accuracy of octanol-water predictions represents an upper bound for expectations of SOM-water predictions. Octanol is a pure component organic compound with a known molar volume and common structural groups, so group contribution method predictions of its partition equilibria are expected to be accurate. SOM-water predictions should be less accurate since the precise structure and molar volume of SOM is not known. Comparison of octanol-water and SOM-water predictions may indicate source of error, such as chosen SOM structure versus inability to handle com- plicated solutes.

Model Soil Organic Molecules. UNIFAC models require only the structural formula in order to simulate a compound. The ELBRO-FVmodel (and other polymer-solvent models) also requires the pure component molar volume for each component. This information is readily available for water, octanol, and many solutes. Soil organic matter, however, is far from a pure component, and assumptions must be made in order to provide a structural formula and molar volume.

A density of 1.1 g/mL was chosen for SOM. This is comparable to avalue assumed in the literature of 1.2 g/mL ( 4 ) . The molar volume is given by the molecular weight (from the structural model below) divided by the density. The molar volume can also be determined experimentally by measuring the specific gravity of a soil organic matter sample. The SOM molar volume is also used to convert the mole fraction basis partition coefficients of eq 2 to the concentration units typically found in the literature.

Two structural models for SOM were evaluated. The first is a tetramer structure proposed for humic acid by Steelink (40). The second model is a hypothetical humic acid structure of Stevenson (41), which is shown in Figure 1. Exact representations of the molecules were not possible with UNIFAC subgroup sets as some of the required subgroups were not available. The quinone group, com- mon to both SOM models, was represented by an aromatic carbon and a hydroxyl. Representations can vary slightly depending on the set of groups and subgroups used. A UNIFAC representation of the Stevenson model is shown in Table 1.

The two SOM models were evaluated by comparing UNIFAC-predicted partition coefficients to literature values for benzene, toluene, ethylbenzene, and propylbenzene.

~ ~

TABLE 1

UHIFAC Sllbgroup Representation for Stevenson Model (Gmekiiwg Molar Volume Case)

molar vol surlace area subgroup frequency parameter ( R ) parameter (0)

CHz CH ACH AC OH (sec) ACOH CH2CO CHO HCOO CHO CHzNH ACNH2 CHNH

1 3 15 22 4 13 2 1 5 6 1 1 1

0.6325 0.6325 0.3763 0.3763 1.0630 1 .oaoo I .704a 0.7 173 1 .goo0 1.1434 1 .36ao 1.1849 1.3680

0.7081 0.3554 0.4321 0.2113

0.9750 1.5542 0.77 10 1.8000

0.8663

0.8968 1 .oao5 0.8067 0.7278

Parameter sets from Sander (42) and Magnussen (27) were used to calculate activity coefficients. The Stevenson model gave significantly better values in both cases than the Steelink model (results not shown). The Stevenson model was therefore chosen for the remainder of the studies. While only one model is presented here, the method offers a unique tool for exploring the relationship between chemical structure of SOM samples and partition equilibrium.

Modified ELBRO-FV Model. The choices available for calculating phase equilibria with UNIFAC for polymer- solvent systems differ primarily in their treatment of free volume contributions. The ELBRO-FV model of Konto- georgis et al. (33) was selected as it has a simplified derivation of a single free volume and combinatorial contribution term as well as proven predictive capabilities. ELBRO-FV was evaluated with polymer solution data from athermal to strongly polar systems. Predicted infinite dilution activity coefficients were in very good agreement with experimental data, and they compared favorably with

In the ELBRO-FVmodel, the activity coefficient yi is the sum of the free volume term and the residual term as given by eq 3 for a given component i:

UNIFAC-FV (33).

(3)

The free volume term $is given by eq 4. The free volume fraction 4: is given by eq 5 .

2274 ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 29, NO. 9, 1995

(4)

(5)

where x i is the mole fraqion of component i, v,i is the component molar free volume, and the summation in eq 5 includes all components. The molar free volume can be defined as the difference between the pure component molar volume and the van der Waals volume as calculated by the method of Bondi (44). However, Gmehling et al. (23) published a set of fitted molar volumes in place of the traditional van der Waals molar volumes. Therefore, the free volume term could be calculated with group molar volumes taken from either (i) van der Waals molar volume parameters based on the method of Bondi (45) or (ii) fitted/ optimized molar volumes of Gmehling et al. (23). Both sets of values were used in partition calculations in order to determine whether one set was successful in predictions than the other. For either case, the molar free volume of component i is given by eqs 6 and 7:

(7)

where R is the Bondi or Gmehling subgroup molar volume parameter and Y is the frequency of that subgroup in component i.

The residual coefficients of the ELBRO-FV model (33) were those of Fredenslund et al. (22). However, preliminary results indicated that interaction parameter coefficient sets (used in residual term calculations) improve the size and breadth of the database on which they are based. For this reason, the most recent interaction parameter set of Gmehling et al. (33) was used. The residual term (yj"") for component i is calculated by eqs 8-14 (46):

'i = c v i $ k k

ski = x G m i T m k m

where Q and R are the subgroup molar surface area and

TABLE 2

Summary of Method for Predicting Activity Coefficients

phase method

solute in soil modified ELBRO-FV organic matter [Kontogeorgis et al. (33)l

molar group volumes by (a) method of Bondo ( 4 4 ) (b) fitted Gmehling e t al. (23)

interaction parameters of Gmehling et al. (23)

modified UNIFAC [Gmehling et al. (23)l modified UNIFAC [Gmehling et al. (2311

solute in water solute in octanol

molar volume parameters from ref 1, and Y is the frequency of the subgroups in component i. Finally, the interaction parameter between the two subgroups is given by eq 15 (23):

where a, b, and c comprise the interaction parameter coefficient set.

Application of Modified ELEiRO-FV Model. In many environmental pollutant releases, solute concentrations are very low. As solute concentrations approach zero, activity coefficients are essentially constant with respect to con- centration and equal to infinite dilution activity coefficients (46). For the sparsely soluble compounds studied in this work, the activity coefficients were assumed independent of concentration as verified in preliminary calculations. This conveniently allows the use of a single partition coefficient that does not depend on solute concentration. While infinite dilution systems are evaluated in this work, the theory is applicable to nondilute systems as well.

It was assumed that all phases (SOM, water, or octanol) contained only the solute and the primary phase compo- nent; any limited mutual solubilities were ignored. In reality, the water phase would have a small amount of octanol while the octanol phase would have a small amount of water. The effects of this assumption were tested for octanol-water partitioning. Predicted partition coefficients decreased by less than 3% when octanol-water solubility was accounted for. Solvent-phase mixing was considered negligible for SOM-water as soil organic matter is a cross- linked, polymeric substance.

The ELBRO-FV model did not describe activity coef- ficients well for the aqueous phase. Activity coefficients calculated for benzene, toluene, and ethylbenzene in water were 2 or 3 orders of magnitude too low. The ELBRO-FV free volume contribution was apparently not appropriate for the aqueous phase since residual term contributions alone were close to experimental values, but free volume term contributions were negative. It should be noted that predictions with an aqueous phase were not evaluated in the development of ELBRO-FV (33). Therefore, the modi- fied ELBRO-FV model was used only for SOM phase predictions while the modified UNIFAC model of Gmehling etal. (23) was used for water and octanol phase predictions. Table 2 summarizes the final modified ELBRO-FV model used for calculating partition coefficients.

Results and Discussion Comparison of Predictions by UNIFAC and Modified ELBRO-FW Models. Despite a high variation in relative

VOL. 29. NO. 9.1995 /ENVIRONMENTAL SCIENCE &TECHNOLOGY 2275

TABLE 3

UNIFAC vs Modified ELBRO-FV Partition Coefficient Predictions (&OM) for Stevenson SOM Model

solute

predicted ratio

UNIFAC ELBRO exptl' UNIFAC ELBRO

benzene 45.1 23.0 18.2 2.48 1.26 ethylbenzene 144 70.4 95.5 1.50 0.738 propylbenzene 242 124 218 1.11 0.569 hexachlorobenzene 20 000 000 2990 17 800 1130 0.169

Experimental partition coefficients from refs 3 and 4.

TABLE 4

Predicted and Experimental Octanol- Water Partition Coefficients (Kow)

solute

MTBE benzene ethyl benzene propyl benzene naphthalene 1,2,4-trichlorobenzene hexachlorobenzene 2-chlorobiphenyl phenol chlorobenzene nitrobenzene 4-bromonitrobenzene aniline rn-toluidine ca rba ry I captan ethyl-N-phenylcarbamate n-propyl-N-phenyl-

carbamate

predicted

136 1420 4 490 5 310

625 2 960

1 750 000

226

105

12.9

8.2

6.7

5.2 18.2

3.5 2 640

260 834

exptl'

N/Ab 135

1410 4 790 2 290

10 500 275 000

34 700

692

398

28.8

70.8

7.9 26.3

209 347 182 63 1

ratio

N/A 1.01 1.01 0.937 2.32 0.0597 0.0107

0.286 0.326 0.0955 0.263 0.667 0.691

0.0102 1.43 1.32

50.5

12.6

a Experimental partition coefficients from refs 3 and 4. NIA, not applicable.

error, the modified ELBRO-FV predictions are an improve- ment over the UNIFAC predictions. The original UNIFAC model generally leads to an underestimation of solvent activities as free volume differences are neglected (33). This would result in aoverestimation of the SOM-water partition coefficient. Table 3 provides a comparison of UNIFAC (42) predictions to the modified ELBRO-FV predictions using the Bondi molar group volumes. Table 3 includes all of the solutes for which predictions have been made by both methods (excepting MTBE as no experimental data was available). The modified ELBRO-FV predictions compare favorably except for propylbenzene. Additionally, the error in the modified ELBRO-FV predictions is fairly uniform, while the UNIFAC error is unpredictable as exemplified by hexachlorobenzene.

Comparison of Predictions by Modified ELBRO-FV Model to Data. The modified EURO-FV method developed in this work was used to predict partition coefficients for the solute list in both octanol-water and SOM-water systems. Table 4 shows the predicted and experimental partition coefficients for octanol-water along with the ratio of the predicted to the experimental value. Accuracy of the prediction varied as much as &2 orders of magnitude from the data.

Some trends are apparent in the results of Table 4. The predictions for the alkylbenzenes are very good. This is expected for these simple, nonpolar compounds. The error for naphthalene (a factor of 2.3) however indicates that

some effect of two aromatic rings is not accounted for. Halogenated solutes, in particular chlorinated compounds, are poorly described. Chlorobenzene, 1,2,4-trichloroben- zene, and hexachlorobenzene show a trend of increasing error with an increasing number of chlorine atoms. Polarity itself does not seem to be a problem as predictions are good for aniline and m-toluidine. Good results are also achieved for the phenylcarbamate pesticides, which are large molecules.

The trends seen with octanol-water predictions are similar to those for the SOM-water system. Table 5 compares the experimental data and the predictions. The simple allcylbenzenes are again the most accurate predic- tions. Halogenated compounds are a problem, but relative errors are lower than the octanol-water case for 1,2,4- trichlorobenzene, hexachlorobenzene, and nitrobenzene (Bondi values). The carbaryl and captan predictions are better, but the phenylcarbamate predictions are worse. Of particular interest is the comparison predictions made with the Bondi versus Gmehling group molar volume param- eters. Neither approach has a clear advantage over the other. The Bondi values are generally better for the alkylbenzenes and chlorinated compounds as well as aniline and toluidine. The Gmehling values are somewhat better for the four pesticides. Molar group volume parameters may be best selected based on the solute(s) of interest.

Octanol-water partition predictions were included in the work to give an upper bound to the error, which could be expected for SOM-water predictions. Comparison of the results shows that neither molar volume set gives predictions superior to the other. Contrary to expectations however, the average error for the octanol-water predic- tions is actually higher (1735%) than the SOM-water predictions (655% and 652% for Bondi and Gmehlingmolar group volumes, respectively). This comparison indicates that application of a group contribution method to soil organic matter is reasonable as poor results stem from difficulties with complex solutes as opposed to a gross inadequacy of the Stevenson model molecule. Good results with simple alkylbenzene solutes reinforce this conclusion.

Partition Coefficients Using Literature Activity Coef- ficients. The accuracy of predictions of SOM-water partition coefficients varies with the solutes examined. As defined in eq 2, the partition coefficient is a function of two variables, the solute activity coefficients in each phase. Large errors in a partition coefficient could be due to the poor prediction of either activity coefficient or of both. Com- parison of predicted to experimental activity coefficients allows the source of error in predicted partition coefficients to be determined. Water phase activity coefficients from the literature were found for some of the solutes examined and are shown in Table 6 along with predicted values. It can be seen by comparing Table 6 with Tables 4 and 5 that

2276 rn ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 29. NO. 9, 1995

TABLE 5

Predicted and Experimental SOM- Water Partition Coefficients (&OM)

predicted ratio

solute Bondi Gmehling

MTBE 1.9 1.4 benzene 23.0 14.2 ethylbenzene 70.4 44.2 propylbenzene 124 80.1 naphthalene 67 5 104 1,2,4-trichIorobenzene 159 79.5 hexachlorobenzene 2 990 1500 2-chlorobiphenyl 109 000 74 800 phenol 4.0 2.6 chlorobenzene 4.1 2.8 nitrobenzene 10.1 5.2 4-bromonitrobenzene 517 261 aniline 9.4 6.0 m-toluidine 18.0 11.4 carbaryl 266 179 captan 60.9 59.2 ethyl-N-phenylcarbamate 207 145 n-propyl-N-phenylcarbamate 353 2 48

a Experimental partition coefficients from refs 3 and 4. N/A, not applicable.

exptP

N/Ab 18.2 95.5

218 240 50 1

17 800 1700

30.2 47.9 50.1

14.8 25.7 60.2

38.0 66.0

151

115

Bondi

N IA 1.26 0.737 0.570 2.82 0.318 0.168

0.132 0.0855 0.202 3.42 0.637 0.702 4.41 0.530 5.56 5.35

64.3

Gmehling

NIA 0.778 0.463 0.367 0.435 0.159 0.0842

0.0863 0.0586 0.104 1.72 0.408 0.443 2.97 0.516 3.80 3.76

44.0

TABLE 6

Predicted and Literature Infinite Dilution Activity Coefficients in Water

solute predicted literaturea ratio

MTBE benzene ethylbenzene naphthalene 2-chlorobiphenyl chlorobenzene nitrobenzene aniline

167 82.1 2 320 2 430

28 700 36 900 172 000 63 000

88600000 1550000 3 320 13 900

46 1 3 540 137 118

a Literature activity coefficients from ref 38.

2.03 0.955 0.778

173 57.2 0.239 0.130 1.16

large errors in the activity coefficient predictions parallel large errors in the partition coefficient predictions. This suggests that error in partition coefficient predictions is primarily due to to error in water phase activity coefficient predictions. If the water phase predictions are erroneous, then experimental activity coefficient values should be used when available for the best partition coefficient predictions.

The use of experimental water phase activity data for predicting octanol-water partition coefficients results in improved predictions as shown in Table 7. The results indicate that the SOM-water partition coefficients should also be improved by using experimental water phase activity

coefficients. While this approach is no longer purely predictive as it requires experimental data, it is still ofutility since activity coefficient data for water may be available and are easy to measure. The UY of experimental water phase activity data for predicting SOM-water partition coefficients results in predictions that are within a factor of 3 (Bondi molar volumes) or 7 (Gmehling molar volumes) for all data. Averaged predictions are within a factor of 1.6 and 2.7 for Bondi and Gmehling molar volumes, respec- tively. The results are shown for Bondi molar group volume predictions in Table 8 and for Gmehling molar group volumes in Table 9. Results are shown for all solutes where activity coefficients in waterwere available. Clearly, solutes that have the poorest partition predictions gain the most from use of activity coefficient data. The results for naphthalene and 2-chlorobiphenyl in particular demon- strate that large errors in partition coefficients are due to errors in the water phase predictions. All three halogenated solutes show significant improvement in both the Bondi and Gmehling cases. Notable is an error decrease of 90 to 20% for nitrobenzene with Gmehling parameters. The difficulty with predictions of halogenated compounds in the SOM-water system apparently lies in the water phase not in the organic phase.

Octanol-water predictions are better on average (31% error) than SOM-water predictions (53% and 67% error

TABLE 7

Changes in Predicted Octanol- Water Partition Coefficients (Kow) Using Water Phase Activity Data activity data

solute predicted exptP

MTBE benzene ethylbenzene naphthalene 2-chlorobiphenyl chlorobenzene nitrobenzene aniline

12.9 136

1420 5310

1 750 000 226

6.7 5.2

NIAb 135

1410 2290

34 700 692 70.8 7.9

ratio

N/A 1.01 1.01 2.32

0.326 0.0955 0.667

50.5

predicted

6.3 142

1830 1950

30 600 945

51.4 4.5

ratio

N/A 1.05 1.29 0.849 0.883 1.37 0.727 0.565

a Experimental partition coefficients from refs 3 and 4. N/A, not applicable.

VOL. 29. NO. 9, 1995 / ENVIRONMENTAL SCIENCE & TECHNOLOGY 2277

TABLE 8

Changes in Predicted SOM- Water Paitition Coefficients (&OM) Using Water Phase Activity Data (Bondi Molar Group Volumes)

activity data

solute predicted exptla ratio predicted ratio

benzene 23.0 18.2 1.26 24.0 1.32 ethyl benzene 70.4 95.5 0.737 90.5 0.948 naphthalene 675 240 2.82 247 1.03 2-chlorobiphenyl 109 000 1700 64.3 1910 1.12 chlorobenzene 4.1 47.9 0.0855 17.1 0.358 nitrobenzene 10.1 50.1 0.202 77.7 1.55 aniline 9.4 14.8 0.637 8.1 0.547

a Experimental partition coefficients from refs 3 and 4.

TABLE 9

Changes in Predicted SOM- Water Partition Coefficients (&OM) Using Water Phase Activity Data (Gmehling Molar Group Volumes)

activity data

solute predicted exptl' ratio predicted ratio

benzene 14.2 18.2 0.778 14.8 0.814 ethylbenzene 44.2 95.5 0.463 56.8 0.595 naphthalene 104 240 0.435 38.2 0.159 2-chlorobiphenyl 74 800 1700 44.0 1310 0.770 chlorobenzene 2.8 47.9 0.0586 11.7 0.245 nitrobenzene 5.2 50.1 0.104 40.0 0.799 aniline 6.0 14.8 0.408 5.2 0.350

a Experimental partition coefficients from refs 3 and 4.

for Bondi and Gmehling molar volumes, respectively). This is an expected result as the exact structure of octanol is known, in contrast to SOM. The Bondi results in particular show the feasibility of the group contribution method. The results suggest the exclusive use of Bondi molar volumes when water phase activity coefficient data are being used.

Unfortunately, the accuracy of predictions for some compounds can actually be reduced by using experimental activity coefficients. In these cases, errors in water phase activity coefficient predictions were off-set by errors in the SOM phase activity coefficient predictions. The result is better partition coefficients before any adjustment (see benzene and ethylbenzene). The benefit of using experi- mental activity coefficients is more uniform with predictable error, making the results useful as an engineering estimate when data are not available.

This group contribution method offers a number of advantages over previous techniques that correlate the partition coefficients of nonionic organic compounds in soil organic matter. Free volume effects for the SOM phase solubility, a factor causing major prediction errors for other polymer systems, are accounted for explictly rather than through a Flory-Huggins coefficient or an analogy to octanol-water results. Predictions are based on the chemical structure of the solute, so that it is possible to estimate how new compounds will sorb onto SOM. The method can be used with fluids other than water and can be scaled with temperature. The chemical structure of the soil organic matter affects the partition equilibrium, and the method premits predictions for SOMs with varied chemistries, whether from natural variation or chemical modification.

Acknowledgments The authors wish to thank Professor Stephen Boyd of the Corp and Soil Science Department of Michigan State University for his many comments on partition coefficients of organic compounds in soil systems.

Glossary a, b, c i

j Kow

KsoM

K X

k m P Q R T vi V,",, vvdw

X

z

Greeks

Y Y f v YreS V

z

Qf"

subgroup interaction parameter coefficients component or species, as in solute or solvent

dummy component index solute partition coefficient for octanol, molar

concentration basis solute partition coefficient for soil organic matter,

concentration basis [ (mg of solute/g of organic matter)/(mg of solute/mL of water)]

partition coefficient, mole fraction basis subgroup dummy subgroup index pressure subgroup molar surface area parameter subgroup molar volume parameter temperature pure component molar free volume pure component molar volume van der Waals molar free volume mole fraction partition phase

phase

solute activity coefficient free volume contribution to activity coefficient residual contribution to activity coefficient frequency of subgroup in component interaction parameter between two subgroups free volume fraction

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Received for review December 9, 1994. Revised manuscript received May 24, 1995. Accepted June 1 , 1995.@

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@Abstract published in Advance ACS Abstracts, July 15, 1995.

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