Using UNIFAC To Calculate Aqueous Solubilities - American

pug of platinum/mile (1.3 pg of Pt/km) (2), (C) that each vehicle burning leaded gasoline emits 100% of the lead in the fuel it consukes or approximat...
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Envlron. Scl. Technol. 1986,20, 1060-1064

converters. If we assume (A) that all vehicles in the county system average 15 miles/gal of fuel (6.4 km/L), (B)that each vehicle equipped with a catalytic converter emits 2 pug of platinum/mile (1.3 pg of Pt/km) (2),(C) that each vehicle burning leaded gasoline emits 100% of the lead in the fuel it consukes or approximately (0.8 g of Pb/gal)/(l5 miles/gal) = 53 000 pg of Pb/mile (33 000 pg of Pb/km), and (D) that all of the emitted metals end up in road dust, a Pb/Pt ratio of (53000 pg of Pb/mile)/[(Bpg of Pt/mile) X 31 or 9O00 results. This value is roughly the average ratio observed for the seven environmental road dust samples in Table I (8600) and suggests that the complex set of factors perturbing this ratio are interacting to produce a range of at least a factor of 5. In conclusion, dust accumulating along freeways and busy streets can concentrate upwards to 1ppm of platinum and half as much palladium. It is probable that the first rains after long periods of dry weather, which are common in southern California, will concentrate platinum and palladium from rooftops and streets and send relatively large amounts of both soluble (in laboratory conditions approximately 10% of the platinum emissions was water soluble (2))and insoluble forms of these rare metals into storm drains leading to the Pacific coastal waters. Thus, the release of platinum and palladium into the environment from auto emissions may not only impact the environments close to streets and highways but also the local ocean waters where the platinum and palladium concentrations are very low, approximately 150 pg of P t / L and 40 pg of Pb/L (4, 8), as well as other open water systems. There is one report of an increase in palladium concen-

trations in the most recently deposited sediments in the moat that surrounds the Emperor’s Palace in Tokyo (8). This may indeed be due to runoff from adjacent streets traveled by automobiles equipped with catalytic converters.

Acknowledgments We thank Edward D. Goldberg of Scripps Institution of Oceanography and Robert J. Mross and Virginia Bigler-Engler of the San Diego County Air Pollution Control District for the data on gasoline consumption by vehicle types. Registry No. Pt, 7440-06-4; Pd, 7440-05-3; Pb, 7439-92-1;Fe, 7439-89-6.

Literature Cited (1) Young, G. Nl. Geogr. 1983, 164, 686-706. (2) Hill, R. F.; Mayer, W. J. IEEE Trans. Nucl. Sci. 1977 NS-24, 2549-2554. (3) Platinum Group Metals; The National Research Council, National Academy of Sciences: Washington, DC, 1977. (4) Goldberg, E. D.; Hodge, V.; Kay, P.; Stallard,S.; Koide, M. Appl. Geochem. 1986, I, 227-232. (5) Mason, €3. Principles of Geochemistry, 2nd ed.; Wiley: New York, 1958. (6) Hodge, V.; Stallard,M.; Koide, M.; Goldberg, E. D. Earth Planet. Sci. Lett. 1985, 72, 158-162. (7) Mross, R. J., San Diego County Air Pollution Control

District, personal communication, 1985. (8) Lee, D. S. Nature (London) 1983, 305, 47-48. Received for review October 7, 1985. Accepted May 12, 1986.

Using UNIFAC To Calculate Aqueous Solubilities Wllllam Brian Arbuckle Department of Civil Engineering, University of Akron, Akron, Ohio 44325

Several problems have been noted in the literature when UNIFAC has been used to calculate environmental parameters. This article evaluates UNIFAC to aid those interested in applying the technique. The original UNIFAC calculation procedure should be used with the most recent (1982) interaction parameters. When organic solid solubilities are calculated, fugacity corrections should not be made, even though theory requires them, because poorer estimates result. Within a family of compounds systematic errors may result, but they can be corrected. Missing interaction parameters can be estimated if sufficient data are available. UNIFAC’s accuracy for solubility estimates could be improved if a new set of interaction parameters were developed on the basis of infinite-dilution activity coefficients of compounds in aqueous solution.

Introduction UNIFAC-calculated infinite-dilution activity coefficients (7”) can be used to calculate the aqueous solubility (Cs, mol/m3) of immiscible organic compounds using (1, 2) C, = 55556/y” (1) where 7”is greater than 1000 for liquid solutes and greater than 100 for solid solutes (3, 4 ) . This technique underestimates solubility for many compounds ( I ) ,so regression equations have been proposed to improve solubility estimates (5). Others have used UNIFAC to calculate activity coefficients and state “UNIFAC results in very inaccurate 1060

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activity coefficients” (6). To aid those interested in applying UNIFAC, this article evaluates (1) UNIFAC interaction parameter data bases (7, 8) (2) standard and modified calculation procedures (9, IO) (3) solid solubility and indicates UNIFAC accuracy. In addition, systematic errors and missing interaction parameters are discussed.

Data Sets UNIFAC calculates activity coefficients (y)by dividing them into two parts: log y = log yc + log Y R (2) Both are calculated on the basis of the molecule’s functional groups (CH2, C=C, OH, COOH, etc.), and the combinatorial fraction (yC)is based on the functional group surface area and volume; these values are available in a table (7). The residual fraction (yR) is calculated by considering interaction energies between functional groups within the mixture; again the values are in a table (7),but many values are missing, indicating that insufficient data were available for determining the interactions between those functional groups. The original UNIFAC article identified 18 functional groups with their assaociated interaction parameters (9);these parameters worked well for vapor-liquid equilibria (VLE) but did not perform satisfactorily for liquid-liquid equilibria (LLE) calculations (8). This LLE weakness resulted in the development of an additional set of interaction parameters (8). Later, the


0 1986 American Chemical Society

Table 11. Solid Solubility Entropy Correction

Table I. Interaction Parameter Comparisonn average absolute errorbin log C, modified basic UNIFAC UNIFAC

no. of LLE VLE/LLE VLE/LLE comfamily of compounds pounds parameters parameters parameters saturated hydrocarbons unsaturated hydrocarbons halogenated hydrocarbons halogenated aromatics aromatic hydrocarbons polynuclear aromatics polychlorinated biphenyls totals


































“VLE/LLEparameters from ref 7. LLE parameters from ref 8. Basic UNIFAC technique from ref 9. Modified UNIFAC technique from ref 10. *The average of absolute values of the difference between calculated and actual 109 C..

number of functional groups was expanded to 40, and new interaction parameters were developed by using both VLE and LLE data (7); these new parameters should therefore apply to both systems. When aqueous solubility was calculated, these new parameters were claimed to perform better than the LLE parameters ( I ) , but data were not presented. Miller et al. solubilities for 98 compounds (11)are used to evaluate both the VLE/LLE interaction parameters and the LLE parameters. This set of solubility data was selected because it is a cooperative effort between two groups actively involved in solubility determinations and because it (1)summarizes solubilities from several recent efforts (2) includes many compounds from several different families of organic compounds (3) contains consistency of solubilities for the compounds within each family Solubilities for 82 of the compounds were calculated by using UNIFAC; the remaining solubilities could not be calculated because interaction parameters are missing (bromine-containing compounds accounted for nine of these). Solubilities and absolute errors (the absolute value of the difference between the logarithm to the base 10 of the actual and calculated solubilities) are calculated for each compound. The average absolute errors are determined for the compounds grouped into seven families and also for all 82 compounds (Table I). The combined VLE/LLE data set resulted in smaller average absolute errors for four families, with the smallest improvement being 0.779 log unit, or a factor of 6 better. The largest average difference is 3.2 log units (over a thousand times better) and occurred with the polychlorinated biphenyls (the statement quoted above about UNIFAC’s inaccuracy was a result of using LLE parameters for this family (6)). The LLE data set results are better for three families, with the saturated hydrocarbons showing the largest improvement of 0.225 log unit (less than a factor of 2). Campbell and Luthy (4)found the VLE/LLE parameters to perform better when predicting partition coefficients of aromatic organics between several organic solvents and water. Overall, the VLE/LLE parameters perform substantially better than the LLE data except for the saturated hy-

average absolute error in log C, family of compounds

no. of compounds whose predictions

uncorrected corrected improved worsened

halogenated aromatics polynuclear aromatics polychlorinated biphenyls

0.513 0.373 1.240

0.932 1.105 1.998

2 0

6 25 16







drocarbons or the saturated hydrocarbons with substituted halogen groups; for the 82 compounds, the average improvement in the prediction of log C, is 1.6 log unit (a factor of 40). The VLE/LLE parameters presented in ref 7 should be used.

Calculation Technique b Two UNIFAC calculation procedures exist, the original technique (9) and a “modified” one (10) used to correct for problems observed with linear hydrocarbons. Solubilities for the 82 compounds were calculated by using both techniques (Table I). The standard calculation procedure out performs the modified one for four of the seven compound families, with the smallest improvement being nearly 1 log unit (about a factor of 10); a 2.7 log unit difference occurs when all 82 compounds are considered; the basic UNIFAC calculation technique reduces the error by a factor of 500. The modified technique performs better for the three families of linear compounds tested, with about 0.7 log unit improvement in average absolute error, or better by a factor of 5. Since there are fewer linear compounds in the data than aromatics, the results indicate the modified procedure is less satisfactory than the basic procedure. When linear hydrocarbons are involved, the standard calculation method should still be used, but systematic errors should be accounted for (as will be discussed). Solid Solubility When the solubility of a solid is calculated by using infinite-dilution activity coefficients, a fugacity correction is required due to fugacity difference between the solid state (f,) and that in the reference state (fJ; this changes eq 1 to (1,12)

Cs = (55556)(fs/fr)/~”


where the fugacity correction ratio can be calculated from the entropy change between solid and liquid phases (12). Yalkowsky has shown the entropy of fusion to be approximately the same for many compounds (13), so at 298

K (12) In ( f , / f r )= -0.023(Tm - 298)


where T,,, is the normal melting point. By use of eq 3 and 4 with the 51 solid compounds, log C, values were calculated and compared to the values obtained with eq 1 (no fugacity correction). For each family (Table II), the uncorrected log C, values are better than the entropy change corrected values; for 47 of the 51 compounds, better agreement was obtained without the fugacity correction. Others have obtained similar results (14). Even though theory requires a fugacity correction when organic solid solubilities are predicted from UNIFAC-calculated infinite-dilution activity coefficients, better results are obtained without the correction; therefore, it is recommended that solubility predictions should not include the correction for the change in reference fugacity. Environ. Sci. Technol., Vol. 20,No. 10, 1986





-e -

2 .-e/ 0“ h h








‘ 0

, ,’




In mo1/m3











U N I F A C log C,

Figure 1. Polychlorinated biphenyl (PCB) solubllltles.

U N I F A C log C ,

Figure 2. PCB solubilities with new UNIFAC parameters.

Miscellaneous Systematic Errors. Plotting solubility vs. UNIFACcalculated solubility sometimes indicates systematic errors. With polychlorinated biphenyls (PCBs), calculated solubilities are less than the actual values, with the error increasing with increasing chlorine substitution (Figure 1; solid line indicates a perfect prediction). This systematic error could be corrected by an empirical correlation or a change in the responsible interaction parameter. The empirical approach generates a regression line (5)whose resultant equation is used to predict solubilities. For the PCBs, the resultant equation is (log Cs)a&ual = 0.7411(10g Cs)calcd- 0.2309

(5) with a correlation coefficient (r) of 0.975 (dashed line Figure 1). (log CJcalcdis the C, value obtained by using is the actual eq 1 with the UNIFAC ymand (log Cs)actual C,, or when predicting C,, the predicted value. With the correlation line, the average absolute error for PCB solubility is reduced to 0.356 log unit (a factor of 2.25), significantly less than the 1.233 log units obtained without the regression line. Rather than developing a “universal” regression equation that includes all compounds (5),an equation should be developed for each family of compounds when sufficient data are available. Combining all compounds into a single regression equation would result in poorer predictions than could be obtained with separate regression equations; with these data, including aromatic hydrocarbon solubility predictions into an equation accounting for the systematic errors of the other compounds would increase the average errors over their low average value (Table I, average error of 0.223 log unit). The second method of handling systematic errors is to determine more appropriate UNIFAC interaction parameters; with PCBs, the more aromatic chlorines on the biphenyl group, the larger the error. The aromatic chlorine group energy of interaction term with either water or with the biphenyl aromatic carbon group must be in error. The aromatic chlorine/ water interactions were evaluated; the interaction parameters for water/aromatic chlorine and aromatic chlorine/water were varied, and the square of the difference in logarithims of actual and calculated infinite-dilution activity coefficients was minimized (log ymactd - log ymdCd).’ This results in the water/aromatic chlorine value changing from 678.2 to 545 K and the aromatic chlorine/water value changing from 920.4 to 315 K. These values improved UNIFAC’s solubility predictions for the PCBs (Figure 2; fugacity corrections were not performed), with the average absolute error reduced to 0.356 log unit, the same value as obtained by the correlation line. Using 1062

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U N I F A C log C,

Flgure 3. Linear hydrocarbon solubilities.

these interaction parameters with the chlorobenzenes results in a slight increase in average absolute error from 0.476 to 0.596 log unit. What is illustrated is a method to compensate for systematic errors; if new interaction parameters are to be determined, they should be optimized by including all aromatic-chlorine-containing compounds and by including the fugacity correction for solids so the new parameters could be used in a manner consistent with theory. The problems noted earlier with the linear hydrocarbons (discussed in the data-set and calculation-technique sections) indicate that systematic errors may exist, as seen by plotting the alkane, alkene, and chlorinated alkane solubilities vs. the predicted solubilities (Figure 3). Using infinite-dilution activity coefficients calculated by using eq 1 and the actual solubilities for these 10 linear com- log ymcdcd)2, was minimized with the pounds, (log ymactd resultant parameters: CH2/water = 500 K water/CH2 = 575 K These parameters result in an average absolute error of 0.302 log unit, down from 1.105 log unit (Table 111). Even though the data are better represented, a systematic error still exists (Figure 4). Completely new interaction parameters could be determined for the alkanes (when the CH2/water parameters are the only ones in the molecule), but optimizing values are beyond the scope of this article. A new set of interaction parameters could be developed by using only aqueous solution infinite-dilution activity coefficients; prediction accuracy should be improved sub-

Table IV. UNIFAC-Calculated Solubilities for Bromine-Containing Compounds

Table 111. Modified CH2/Water Interaction Parameter Predictions average absolute error in log C, existing new parameters parameters"

no. of compounds

family of compounds

4 2

1.675 0.741 0.695

0.333 0.324 0.195




saturated hydrocarbons unsaturated hydrocarbons halogenated hydrocarbons



OInteraction parameters: CH2/water = 500 K; water/CH, = 575 K.




1-bromobutane 1-bromopentane 1-bromohexane 1-bromoheptane 1-bromooctane bromochloromethane 1-bromo-3-chloropropane

0.802 -0.077 -0.807 -1.431 -2.063 2.111 1.152

0.642 -0.029 -0.695 -1.358 -2.018 2.478 1.467

average absolute error

absolute error a a

a 0:073 0.045 0.367 0.315 0.200

"These compound solubilities were used to obtain the interaction parameters.

of 0.2 log unit. These good predictions result even though the solubility of one of the compounds used to determine the interaction parameters appears to be out-of-line with the other compounds: 1-bromobutane's solubility is underestimated, while the remaining six compound's solubilities are overestimated.

Summary C,











in m01/m3 '






log C,

Flgure 4. Linear hydrocarbon soiubilitles with new UNIFAC parameters.

stantially for environmentally oriented applications. By only changing the interaction parameters for the functional groups and water, the interaction with other solutes and solvents would remain unchanged. Therefore, using UNIFAC with mixed solvents should perform even better than has been shown (15). Considering that UNIFAC parameters were developed from vapor-liquid and liquid-liquid equilibria spanning the entire concentration range, they perform very well. Missing Interaction Parameters. To calculate a compound's infinite-dilution activity coefficient, all functional groups composing the molecule need interaction parameters with other groups within the molecule and with water. Unfortunately, many interaction parameters do not exist. If infinite-dilution activity coefficients exist for two compounds containing the group with the unknown interaction parameters, two equations would exist with the two unknown parameters. Since these equations cannot be solved analytically, a trial-and-error search can be performed to find the parameters that minimize (log ymadual - log ymdd)2.The resultant interaction parameters could be used to predict the solubility of the compound of interest. Using Miller et al. data ( I I ) , nine compounds contain the bromine group whose interaction parameters with water are unavailable (bromine's interaction with the alkene group also does not exist, so only seven compounds will be evaluated). 1-Bromobutane, 1-bromopentane, and 1-bromohexane solubilities were used to determine the unknown interaction parameters by using the CH,/water parameters discussed earlier: water/bromine = 440 K bromine/water = 285 K Solubilities for all seven compounds could then be predicted (Table IV). The constants perform well, with an average absolute error for the four predicted solubilities

When UNIFAC is used to calculate aqueous solubilities, the original calculation procedure (9) should be used with the combined VLE/LLE interaction parameters (7). When organic solid solubilities are calculated, the fugacity correction (based on the entropy change between the solid and liquid phase) should not be used since it gives poorer results, but it should be remembered that the correction is required by theory. Systematic errors result with some compound families; by use of either a correlation line or new UNIFAC interaction parameters, these errors can be eliminated. If solubilities are available for several compounds containing a functional group with missing interaction parameters, the missing interaction parameters can be estimated so reasonable estimates of solubility can be made for other compounds containing that functional group. To improve aqueous solubility predictions, a new set of interaction parameters should be developed on the basis of infinitedilution activity coefficients of compounds in aqueous solution.

Literature Cited Arbuckle, W. B. Environ. Sci. Technol. 1983,17,537-542. Lyman, W. J. Handbook of Chemical Property Estimation Methods; Lyman, W. J.; Reehl, W. F.; Rosenblatt, D. H., Eds.; McGraw-Hill: New York, 1982; Chapter 2. Lyman, W. J. Handbook of Chemical Property Estimation Methods; Lyman, W. J.; Reehl, W. F.; Rosenblatt, D. H., Eds.; McGraw-Hill: New York, 1982; Chapter 3. Campbell, J. R.; Luthy, R. G. Environ. Sci. Technol. 1985, 19,980-985. Banerjee, S. Enuiron. Sci. Technol. 1985, 19, 369-370. Burkhard, L. P.; Armstrong, D. E.; Andren, A. W. Enuiron. Sci. Technol. 1985, 19, 590-596. Gmehling, J.; Rasmussen, P.; Fredenslund, A. Ind. Eng. Chem. Process Des. Deu. 1982,21, 118-127. Magnussen, T.; Rasmussen, P.; Fredenslund, A. Ind. Eng. Chem. Process Des. Deu. 1981, 20, 331-339. Fredenslund, A.; Jones, R. L.; Prausnitz, J. M. AIChE J. 1975,21,1086-1099. Kikic, I.; Alessi, P.; Rasmussen, P.; Fredenslund, A. Can. J. Chem. Eng. 1980,58, 253-258. Miller, M. M., e t al. Enuiron. Sci. Technol. 1985, 19, 522-529. Mackay, D.; Shiu, W. Y. J . Phys. Chern. R e f . Data 1981, 10, 1175-1199. Yalkowsky, S. H. Ind. Eng. Chem. Fundam. 1979,18,108. Environ. Sci. Technol., Voi. 20, No. 10, 1986


Munz, C., EAWAG, Duebendorf, Switzerland, personal communication, Oct 27, 1983. Fu, J. K.; Luthy, R. G. Proceedings Specialty Conference on Environmental Engineering; ASCE: Boston, MA, 1985; pp 903-910.

Received for review December 13, 1985, Accepted June 4, 1986.


Environ. Sci. Technol., Vol. 20,No. 10, 1986

This project was partially supported by University of Akron Grant RG 761 and in part by the U S . Environmental Protection Agency under Assistance Agreement R810730-01-0 to the University of Akron. I t has not been subjected to the AgencyB required peer and administrative review and therefore does not necessarily reflect the uiews of the Agency, and no official endorsement should be inferred.