Environ. Sci. Technol. 1003, 27, 266-270
Jensen, J. N.; Johnson, J. D. Environ. Sci. Technol. 1990, 24, 981-985. Jensen, J. N.; Johnson, J. D. Environ. Sei. Technol. 1990, 24, 985-990. Scully, F. E., Jr.; Hartman, A. C.; LeBlanc, N. Natl. Meet.-Am. Chem. SOC.,Diu. Environ. Chem. 1992, 32, Abstr. 62. Nweke, T.; Scully, F. E. Environ. Sci. Technol. 1989,23, 989-994. McCormick, E. F.; Conyers, B.; Scully, F. E., Jr. Environ. Sci. Technol., preceding paper in this issue. Franson, M. A., Ed. Standard Methods For the Examination of Water and Wastewater,14th ed.;American Public Health Assoc., American Water Works Assoc., Water Pollution Control Federation: Washington DC, 1975. Jones, B. N.; Paabo, S.; Stein, S. J . Liquid Chromatogr. 1981, 4, 565-586. Hill, D.; Walters, F.; Wilson, T.; Stuart, J. Anal. Chem. 1979, 51, 1339-1341. Scully, F. E., Jr.; Howell, G. D.; Penn, H. H.; Mazina, K.; Johnson, J. D. Environ. Sci. Technol. 1988,22,1186-1190. Stanbro, W. D.; Lenkevich, M. J. Int. J. Chem. Kinet. 1983, 15, 1321-1328. Morris, J. C. In Principles and Applications of Water Chemistry; Faust, S. D., Hunter, J. V., Eds.; Wiley: New York, 1967; pp 23-53. Isaac, R. A.; Morris, J. C. In Water Chlorination: Environmental Impact and Health Effects;Jolley, R. L., et al.,
Eds.; Ann Arbor Science: Ann Arbor, MI, 1983; Vol. 4, pp 63-75. Friend, A. G. Rates of N-Chlorination of Amino Acids. Ph.D. Dissertation, Harvard University, Cambridge, MA, 1954. Johnson, J. D. In Water Chlorination: Environmental Impact and Health Effects; Jolley, R. L., Ed.; Ann Arbor Science: Ann Arbor, MI, 1978; Vol. 1, pp 37-63. Jolley, R. L.; Carpenter, J. H. In Water Chlorination: Environmental Impact and Health Effects; Jolley, R. L., et al., Eds.; Ann Arbor Science: Ann Arbor, MI, 1983; Vol. 4, pp 3-47. Cooper, W. J.; Mehran, M. F.; Slifker, R. A.; Smith, D. A.; Villate, J. T.; Gibbs, P. H. J.-Am. Water Works Assoc. 1982, 74, 546-552. Scully, F. E., Jr. Technol. Conf. Roc.-Am. Water Works ASSOC. 1986, 14, 611-622.
Received for review May 21, 1992. Revised manuscript received October 1, 1992. Accepted October 5,1992. This research was presented in part at the 202nd National Meeting of the American Chemical Society, Washington, DC, and is based on work supported by the National Science Foundation, Grant BCS-9002442, Dr. Edward Bryan, project manager. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and to not necessarily reflect the views of the National Science Foundation.
Application of the Mobile Order Theory to the Prediction of Aqueous Solubility of Chlorinated Benzenes and Biphenyls Paul Ruelie," Michel Buchmann, H6 Nam-Tran, and Uirich W. Kesselrlng Institut d' Analyse Pharmaceutique, Ecole de Pharmacie, Universit6 de Lausanne, BEP, CH-10 15 Dorigny-Lausanne, Switzerland
Prediction of the aqueous solubility of solid and liquid polychlorinated biphenyls and benzenes is obtained by means of the mobile order theory. The solubility values are mainly determined by the magnitude of the hydrophobic effect. This effect does not result from the breaking of solvent H-bonded chains in order to separate the solvent molecules to provide a suitably sized cavity for the solute, but from a decrease of the mobile order entropy of each water molecule when the hydrogen-bonded molecules are brought in a large volume consecutively to the addition of the solute. The evolution of the solubility with the chlorine substitution is further explained. The predictive ability of the present model compared to other approaches adapted to predict aqueous solubility as well as its applicability to any given solvent makes this model a very attractive one.
Introduction Influence of the Mobile Order on the Entropy and the Hydrophobic Effect. Both the order introduced in the liquid by the formation of the hydrogen bonds and the perpetually moving character of these bonds constitute the basic foundations of the "mobile order" theory initiated by Huyskens and Siege1 (1-3). The mobile order theory starts from the statement that, in a liquid, the neighbors of a given molecular group of a molecule constantly change identity, distance, and direction. Nevertheless, for the groups like hydroxyl protons that form hydrogen bonds, this change of environment occurs only during a limited fraction of the time, y, during which the H bond is temporarily broken and the OH proton is free. During the 286
Environ. Sci. Technol., Voi. 27, No. 2, 1993
complementary fraction (1- y) of the time, the considered proton is involved in H bonding and is confined in a small volume, Vo, of its domain, DomA, in the vicinity of one of the electron lone pairs of the oxygen atom of a neighboring molecule. (The domain, DomA, of an alcohol molecule in solution is the total volume of the solution, V, divided by the number, N,,, of alcohol molecules). If y would be entirely negligible, the effect on the molar entropy of the alcohol, brought about by the mobile order, would be equal to Asmobile order = '%ith mobile order - Swithout mobile order = R In (Vo/DomA) = R In ( V a a l c )- R In V As Vo is much smaller than DomA, the mobile order leads to a decrease of the entropy (ASmobileorderis negative) with respect to the situation where all the OH protons would be free, which is related to the ratio Vo/DomA (4-6). This ratio corresponds to the reduction of freedom of one alcohol molecule in the liquid consecutive to the mobile order. Furthermore, as the addition of an inert substance to an alcohol or to water leaves Va,, unchanged but increases the total volume of the liquid, V, it is clearly seen that the entropy of mobile order still becomes more negative. The chief reason for the hydrophobic effect, which is at the origin of the low solubility of inert substances in alcohols or in water (7), is thus that the dissolution of a foreign substance in perpetually moving molecular systems increases the domain of each alcohol or water molecule and thus extends the territory of the mobile order: the H bonds move in a larger domain, which decreases the entropy. The bigger the size of the solute, the larger the decrease.
0013-936X/93/0927-0266$04.00/0
0 1993 American Chemical Society
Mobile Order and the Solubility Equation. The quantitative development of the mobile order theory led to equations describing the effect of solvent-solvent, solumolvent, and solumolute interactions on the chemical potential of the solute. A universal predictive equation (eq 1)for solubility (in volume fraction) of solid and liquid substances has therefore been derived (8). As far as only proton acceptor solutes are concerned, five terms have to be considered the fluidization of the solute ( A term), the placing (exchange) entropy correction resulting from the difference in the molar volumes of solvent and solute ( B term), the changes in the nonspecific cohesion forces upon mixing (D term), the effect of the hydrogen-bonded chains of the solvent (hydrophobic effect) (F term), and the positive effect of H bond formation between proton acceptor sites on the solute and proton donor solvents (0 term). In @B = A B D + F 0 (1) Representing a physical phenomenon related to the solubilization, each term in the equation has a well-defined expression: A = -A,,@( 1/ T - 1/ T,) / R B = 0.5@S(vB/Vs - 1) + 0.5 In (@B + @svB/Vs)
+ +
+
D = -@s2VB(BB’ - 6s’)2/RT F = -rs@sVB/Vs 0 = In (1.0 + Koas/ Vs) In these expressions, AmeltHand T , represent the molar heat and the temperature of fusion; V,, BB‘, @B, Vs, 64, and as stand for the molar volume, the modified nonspecific cohesion parameter, and the solubility in volume fraction, respectively, of the solute B and of the solvent S; rs represents the “structuration or mobile order factor” of the associated solvent, which is -2 for solvents with double H-bond chains like water and diols; and KOis the stability constant which governs the H-bond formation between a proton acceptor solute and a proton donor solvent. In this study, eq 1 is applied to predict the aqueous solubility of highly hydrophobic chemicals, Le., polychlorinated benzenes and biphenyls, that are of considerable environmental concern. One of the main characteristic properties of these chemicals is their very low aqueous solubility (hydrophobicity) which, with their octanol-water partition coefficient, is partly responsible for their fate. In this connection, the detailed analysis of the relative magnitude of the different terms involved in eq 1and of their evolution through the set of solutes bring information about the importance of the hydrophobic effect as regard to the origin of their low solubility in water. The relationship between the hydrophobic effect and the molecular volume of the solute is illustrated. Finally, the aqueous solubilities predicted by eq 1are compared to the results obtained by other models, especially those dedicated to predicting aqueous solubility, based on either various correlation equations between determined solubilities and other physical constants such as log P values, melting points, molar volumes, and molar surface areas, simple molecular descriptors, or the sum of fragment solubility constants satisfying an addition rule. Results and Discussion To predict solubility of polychlorinated benzenes and biphenyls in water by means of eq 1, one needs to know the following properties of the pure components: (1)the molar volumes of solutes, VB, and water, Vs. The values of the molar volumes of the solid solutes corresponding to their subcooled liquid states are obtained by addition of
Table I. Physical Properties of the Polychlorinated Biphenyls and Benzenes VB
solute biphenyl 2-PCB 3-PCB 4-PCB 2,4-PCB 2,5-PCB 2.6-PCB 2;4,6-PCB 2,4,5-PCB 2,2’,4,4’-PCB 2,3,4,5-PCB 2.2’.4’.5-PCB 3;3‘;4,4’-PCB 2,3,4,5,6-PCB 2,2’,4,5,5’-PCB 2,2’,4,4’,5,5‘-PCB 2,2’,4,4’,6,6’-PCB 2,2’,3,3’,6,6’-PCB 2,2’,3,3’,4,4’-PCB 2,2’,3,3’,4,4’,6-PCB 2,2’,3,3’,5,5’,6,6’-PCB 2,2’,3,3’,4,4’,5,5’,6-PCB 2,2’,3,3’,4,5,5’,6,6’-PCB 2,2‘,3,3‘,4,4‘,5,5’,6,6‘-PCB
benzene chlorobenzene o-dichlorobenzene rn-dichlorobenzene p-dichlorobenzene 1,2,3-trichlorobenzene 1,2,4-trichlorobenzene 1,3,5-trichlorobenzene 1,2,3,4-tetrachlorobenzene 1,2,3,5-tetrachlorobenzene 1,2,4,5-tetrachlorobenzene pentachlorobenzene hexachlorobenzene
(cm3/ 6~ ArneltHn mol) (MPa1/2) (J/mol) 160.0 174.9 174.9 174.9 189.8 189.8 189.8 204.7 204.7 219.6 219.6 219.6 219.6 234.5 234.5 249.4 249.4 249.4 249.4 264.3 279.2 294.1 294.1 309.0 89.4 104.3 119.2 119.2 119.2 134.1 134.1 134.1 149.0 149.0 149.0 163.9 178.8
19.98 20.77 20.77 20.77 21.41 21.41 21.41 21.94 21.94 22.39 22.39 22.39 22.39 22.77 22.77 23.11 23.11 23.11 23.11 23.40 23.66 23.89 23.89 24.09 18.95 20.42 21.49 21.49 21.49 22.28 22.28 22.28 22.90 22.90 22.90 23.39 23.79
18601.0 15300.0
69.0 32.1
13318.0
75.4
12600.0 16500.0 22800.0 19000.0b 25200.0 23400.0 27100.0b 21800.0 18800.0 20900.0b 17500.0 21100.0 29200.0 20300.0 22800.0 28 700.0b 22600.0 39434.0
34.7 61.1 76.3 42.gb 90.7 65.9 179.gb 124.4 76.9 112.gb 113.5 112.0 151.7 122.2 160.6 205.gb 182.6 304.5
17153.0 20498.0
52.7 53.7
18198.0 17000.0 19000.0 24100.0 20600.0 23853.0
63.5 46.8 50.7 148.0 84.5 231.8
”Reference 11,except as noited. bReference 12.
group contributions (8). The molar volume of water is 18.1 cm3/mol (8); (2) the modified nonspecific cohesion parameter of solutes, BB’, and of water, &’. Given the predominantly dispersive nature of the polychlorinated benzenes and biphenyls, their modified cohesion parameter has been considered to be equal to their Hildebrand solubility parameter, BB In the present work, the Hildebrand solubility parameters of the polychlorinated substances have been calculated from Fedors’ molar vaporization energy group contributions (9,101 and Huyskens’ molar volume contributions (8). The modified nonspecific cohesion parameter of water amounts to 20.5 MPa1I2(8);(3) the melting temperature, T,, and the molar heat of fusion, Amel&, of the solid solutes in order to calculate the fluidization constant (term A of eq 1). The values of these parameters for 24 polychlorinated biphenyls and 13 polychlorinated benzenes are gathered in Table I. However, to apply eq 1,one still needs to know the order of magnitude of the stability constant, KO,when hydrogen bonds are formed between proton donor solvents and the solutes. In the particular case of the solubility in water, it has been shown (7) that the greater aqueous solubility of a polycyclic aromatic in comparison to an aliphatic hydrocarbon of similar volume was due to the existence of weak hydrogen bonds between the 7~ electrons of the aromatic rings and the proton donor OH groups of water. These hydrogen bonds are characterized by a stability constant, KO,amounting to -80 cm3/mol, the order of magnitude of which is explained by the possible competition of these heteromolecular bonds with the rather weak self-association bonds in the secondary chains of Environ. Scl. Technol., Vol. 27, No. 2, 1993
267
-
10.
-
WCYCHLCRNATEO BFHENYL PCCYCMCRNATED BENZENE
v
2.2'.3.3'.4,1'.5.5:6-PCB 2.2,3.S.5.S,6,5'-PCB
2.2.3.S.4.4-PCB
10'. 1
I
I
I
I
I
10'.
10'
10'0
10'
106
10'
experimental solubility (X.) Flgun 1. Redlcted (eq 1) versus e x p e h m a l aqueous &bMy of polychlorlnated aromtlc hydrocarbons at 25 'C.
(X$
water. In fact, in liquid water, the two protons of a given water molecule are involved in H bands which do not have the same strength, and two kinds of chains can he roughly distinguished (13): the strong ones and the weak ones. In the latter, the 0-0 interdistances are larger, the bonds show important deviations from linearity, and the bond anglea deviate markedly from the tetrahedral value hecause the weaker bonds have to adapt themselves to the local constraints imposed hy the stronger ones. As the ammatic hydrocarbons do not exhibit very efficientproton acceptor sites, they cannot he inserted in the first stronger chains of water, but can compete with the OH groups involved in the secondary chains of water for making P-OH hydrogen bonds. To make solubility predictions, one should use real values of KOwhich, in fact, depend on the individual solutes in a given solvent. As these values are generally not known,and to keep the predictive character of the model, it is necessary to use standard values. For the polychlorinated biphenyls we used therefore the same value of the stability constant, KO,that we used for the polycyclic aromatic hydrocarbon aqueous Solubility predictions, i.e., 80 cm3/mol (7) and we used 0 cm3/mol for the polychlorinated benzenes. The subdivision of the chemicals into two groups of structurally related compounds gave greatly improved predictive capabilities. The predictions of the aqueous solubilities of the polychlorinated biphenyls and benzenes at 25 OC converted intomolar fractions, X,,as well as the experimental values are reported in columns 2 and 3 of Table 11. The agreement between the observed and predicted solubilities (Figure 1) illustrates the quality of the prediction. The most appropriate expression to measure the differences between the experimental and predicted solubilities is the factor by which the experimental and predicted values differ, i.e., their ratio, rather than the percentage difference. Of the 37 compounds considered, 31 had a factor of leas than 3, with an average factor of 1.56,7 had a factor in the range of 3-10, and 1had a factor greater than 10. As can be seen in Figure 1,the discrepancies increase with decreasing solubility of the PCB. A comparable behavior had already been observed in the case of the polycyclic aromatic hydrocarbons (7). Such a trend reflects the increased difficulty in getting reliable experimentally determined solubility data for very hydrophobic substances. Consequently, considering the variability of the reported data in the literature, the selected experimental values presented here should he used with appropriate caution. To gain deeper understanding of the origin of the solubility, Figures 2 and 3 present the relative Contributions to the Solubility of each term involved in eq 1 for some polychlorinated biphenyls and benzenes, respectively, arranged in increasing order of their molar volume, V,. The 266 Envimn. Scl. Technol.. Vol. 27, NO. 2. 1993
-30
-10
-20
10
0
contribution of the terms of eq.1 !%urn 2. Confibutons ofthe dmerent terms of eq Ito me sciu~ilty of polychlorinated biphenyls In water at 25 OC. hexachiorobenzeene
p-dichlorobenzene
-20
-15
-10
-5
0
5
Contribution of the terms of eq.1
-re a. confibutom of me merent terms 01 eq I to me sdubility of polychbrlnated benzenes In water at 25 O C .
A, 0, and 0 term contributions are very small with respect to those of the B and F terms. The solubility values of both polychlorinated biphenyls and benzenes mainly depend on the hydrophohic term (F),which represents an entropic contribution unfavorable to the solubility, increasing rapidly with the growing size of the solute. As described in the Introduction, addition of an inert substance to water leads, by increasing the total volume of the solution, to the extension of the domain, DomA, of each water molecule and consequently the entropy of mobile becomes more negative. The chief order, ASmobi,. reason for the hydrophobic effect is thus that the dissolution of a foreign substance in perpetually moving asso ciated molecular systems such as water increases the d o main of each water molecule and thus extends the territory of the mobile order. The hydrophohic effect/solute size dependence (Figure 4) largely explains why the aqueous solubility of the polychlorinated hydrocarbons decreases with increasing solute volume and chlorine substitution. As a result, isomers with lower chlorine substitution will be preferentially dissolved in water, as observed experimentally. For isomers of the same degree of chlorination, the solubilities only vary according to their melting properties, Le., their enthalpy and temperature of fusion, involved in fluidization term A (all the remaining terms being equal for a given family of isomers): the higher the energy needed to make the solute fluid (the higher the absolute value of the A term in eq l),the lower the solubility (Table 111). Finally, the preparative power of the
Table 11. Experimental and Predicted Aqueous Solubilities, XB, of the Polychlorinated Biphenyls and Benzenes reference solute biphenyl 2-PCB 3-PCB 4-PCB 2,4-PCB 2,5-PCB 2,6-PCB 2,4,6-PCB 2,4,5-PCB 2,2’,4,4’-PCB 2,3,4,5-PCB 2,2’,4’,5-PCB 3,3’,4,4’-PCB 2,3,4,5,6-PCB 2,2’,4,5,5’-PCB 2,2’,4,4’,5,5’-PCB 2,2’,4,4’,6,6’-PCB 2,2’,3,3’,6,6’-PCB 2,2’,3,3’,4,4’-PCB 2,2’,3,3’,4,4’,6-PCB 2,2’,3,3’,5,5’,6,6’-PCB 2,2’,3,3’,4,4’,5,5’,6-PCB 2,2’,3,3’,4,5,5’,6,6’-PCB 2,2’,3,3’,4,4’,5,5’,6,6’-PCB benzene chlorobenzene o-dichlorobenzene rn-dichlorobenzene p-dichlorobenzene 1,2,3-trichlorobenzene 1,2,4-trichlorobenzene 1,3,5-trichlorobenzene 1,2,3,44etrachlorobenzene 1,2,3,5-tetrachlorobenzene 1,2,4,5-tetrachlorobenzene pentachlorobenzene hexachlorobenzene 10‘
’
.
this work
exp 12, 14, 15
:
0.72 X 0.46 X 0.53 X 0.24 X 0.14 X 0.i4 X 0.12 x 0.17 x 0.92 X 0.56 X 0.14 X 0.27 X 0.20 x 0.23 x 0.66 x 0.69 X 0.94 X 0.69 X 0.14 X 0.14 X 0.14 X 0.07 X 0.23 X 0.44 x 0.15 x 0.45 x 0.12 x 0.12 x 0.64 x 0.13 x 0.28 x 1.21 x 0.41 X 0.35 X 0.38 x 0.37 x
10”
0.82 X 0.53 X 0.24 X 0.11 x 0.10 x 0.16 X 0.11 x 0.14 x 0.98 X 0.56 X 0.12 x 0.99 x 0.06 x 0.26 x 0.55 x 0.51. x 0.35 X 0.40 X 0.30 X 0.92 X 1.27 X 4.34 x 0.69 X 4.34 x 0.41 x 0.81 x 0.11 x 0.15 x 1.12 x 0.31 x 0.34 X 0.66 X 0.36 X 0.29 X 0.50 x 0.40 x 0.31 x
10” 10”
10” 10-6 10” 10”
10-7 10-8 10-9 10-9
10-9 10-9 10-10
lo-” 10‘12
10-14 10-3 10-4 10-4 10-4 10-5
10-5 10-5 10” 10” 10” 10-7 10-7 10-9
0.63
x
10” 10” 10”
10” 10” 10” 10”
10-7 lo-@
10-9 10-9 10-9
:
. I
I 0
0.87 0.55 0.59 0.18 0.16 0.17
X 10“ X 10” X 10” X
1.02 x 10-8 0.37 X lo-@ 0.75 X
1.35 X 0.71 X 0.32 X
3.00 X 1.69 x 10-9 0.44 x 10-9 0.70 X 0.31 X
1.07 x 0.50 X 0.90 x 1.39 X 1.02 x
1.22 x
0.66 X
10-10
10”
X 10” X 10“
10-9 lo4 10-10 10-10
0.15 X lo-” 3.45 x 10-12
0.37 X lo-” 0.50 X
10-14 10-3 10-4 10-4 10-4 10-5 10-5 10-5 10” 10”
18.10 X 0.29 x 10-3 0.60 x 10-4 0.17 x 10-4 0.13 x 10-4 0.66 x 10-5 0.44 x 10-5 0.34 x 10-5 1.17 X lo4 2.23 X 10” 0.93 X 10” 0.81 x 10-7 4.65 x 10-7 32.19 X lo4
2.00 x 0.42 x 0.87 X 0.15 x 0.15 x 0.85 x 0.18 x 0.33 X 1.44 X 0.34 X 0.30 X 0.45 x 0.27 x 0.22 x
10”
10-7 10-7 10-9
solute I
10-14 10-3 lo4 10-4 10-4 10-5
0.22 x 0.07 X 0.07 X 0.06 X 0.02 x 0.02 x 0.02 x 0.06 x 0.57 X 0.17 X 0.17 X 0.17 X 1.69 x 0.50 x 0.50 x 1.47 X 1.47 X 1.47 X 1.47 X 0.43 x 1.25 X 3.69 X 3.69 X 1.09 x
19
10” lo* 10” 10” 10“ 10“ 10” 10-7
1.85 X 1.07 X 1..44 X 0.25 X 0.26 X 0.26 X
10-9 10-9 10-9
0.05 X 0.06 x 0.29 x 0.21 x 0.15 X
10” 10” 10” lo4 10“ 10“
0.83 x . W 0.51 X 0.09 x 10-8
lo4 10-9 10-9 10-10
0.05 X 10-lo lo-” 10-12
10-5
10” 10”
10” 10-7 10-7 10-9
.
.
I
.
.
A
3,3’,4,4’-PCB -3.737 2,3,4,5-PCB -1.836 2,2’,4,5’-PCB -1.139 2,2‘,4,4’-PCB -0.436 1,2,4,5-tetrachlorobenzene -2.839 1,2,3,5-tetrachlorobenzene -0.608 1,2,3,4-tetrachlorobenzene -0.467
POLYCHLORINATED BIPHENYL I
10” 10” 10” lo4 10” 10”
lo-”
v
‘ .
4
1.02 x 0.46 X 0.57 X 0.18 X 0.12 x 0.12 x
18
0.01 x 10-11 0.44 X
0.31 X 0.29 x 0.52 x 0.09 x 0.09 x 0.37 x 0.07 X 0.17 x 0.50 X 0.16 X 0.14 X 0.07 x 0.09 x 0.01 x
10-3 10-4 104 10-4 10-5 10-5 10” 10” 10” 10-7 10-7 10-9
Table 111. Relationship between the Fluidization Term (A ) and the Solubility (X,)
T
10
15, 17
16
POLYCHLORINATED BENZENE I
I
I
I
I
I
I
I
I
I
1
2
3
4
5
6
7
8
9
10
chlorine number Flgure 4. Evolution of the predicted (eq 1) aqueous solubility (X,) of polychlorinated aromatic hydrocarbons versus chlorine substitution.
present theoretical and general solubility model can be compared with other models proposed in the literature especially dedicated to predict aqueous solubility of organic compounds. Among the different models tested, the semitheoretical ones of Suzuki (16) and Yalkowsky (1.517)use the octanol-water partition coefficient,the melting point, and the surface area of the solute as molecular descriptors, while the empirical ones of Nirmarlankhandan (18) and Wakita (19) utilize either a combination of valence molecular connectivity indexes and a modified polarizability parameter or fragment solubility constants satisfying an addition rule. All the solubility values (in molar fraction) calculated for the polychlorinated biphenyls and benzenes by means of these approaches are gathered in columns 4-7 of Table 11. In order to compare the results, Table IV
XBPred
0.20 x 10-9 0.14 x 10-8 0.27 x 10-8 0.56 x 0.38 x 10-7 0.35 X 10” 0.41 X 10”
XBexP 0.60 x 0.12 x 0.99 x 0.56 x 0.50 x 0.29 X 0.36 X
10-9 10-9 10-9 lo-@ 10-7 10” 10”
reports, for each model considered in this work, the factors by which the experimental and predicted solubility values differ as well as the mean of those factors. Except for the model of Wakita, for which large deviations are observed, especially in the case of isomers with higher chlorine substitution, all the models possess great potential in predicting aqueous solubility. On the basis of the mean ratio between experimental and calculated solubility values, the preparative power of the present model derived from the mobile order theory of Huyskens would be intermediate between the models of Yalkowsky and Suzuki (or Nirmalakhandan). However, the range of applicability of these models is different: whereas Suzuki or Yalkowsky’s models permit prediction of the solubility in water only, Huyskens’ equation can be used to predict solubility in any given solvent.
Conclusion The predictive ability of the solubility model derived from mobile order thermodynamics is demonstrated by the Envlron. Sci. Technoi., Vol. 27, No. 2, 1993
260
Table IV. Factors by Which the Experimental and Predicted Solubility Values Differ reference
solute
this work
16
15, 17
18
19
biphenyl 1.14 1.24 1.06 3.73 2.26 2-PCB 1.15 1.15 1.04 7.57 2.02 6.00 2.21 2.38 2.46 3.43 3-PCB 2.27 2.18 1.64 1.64 1.83 4-PCB 1.40 1.20 1.60 5.00 2.60 2,4-PCB 1.14 1.33 1.06 8.00 2,5-PCB 1.63 1.09 5.50 2,6-PCB 1.21 2.33 2,4,6-PCB 1.07 1.04 1.38 1.72 1.18 2,4,5-PCB 1.10 2,2‘,4,4’-PCB 1.00 1.51 1.27 3.29 1.17 6.25 2.67 1.42 1.33 2,3,4,5-PCB 2,2’,4’,5-PCB 2.73 1.72 1.20 3.33 20.00 17.83 28.17 3,3’,4,4’-PCB 4.33 1.13 6.50 1.92 1.92 2,3,4,5,6-PCB 1.90 1.20 1.25 6.11 1.10 2,2’,4,5,5’-PCB 2.43 1.35 1.37 2.73 2.88 2,2’,4,4’,5,5’-PCB 2.69 1.13 2.91 4.20 2.33 2,2’,4,4’,6,6’-PCB 1.72 3.67 2,2’,3,3’,6,6/-PCB 2.14 4.07 2.20 4.90 6.00 2,2/,3,3/,4,4’-PCB 6.57 2.14 2,2’,3,3’,4,4’,6-PCB 9.07 8.47 3.43 1.02 127.00 2,2’,3,3’,5,5’,6,6’-PCB 2,2’,3,3’,4,4’,5,5’,6-PCB 62.00 1.26 8.68 1.18 986.36 2,2‘,3,3’,4,5,5’,6,6’-PCB 3.00 5.35 2,2’,3,3’,4,4’,5,5’,6,6’-PCB 9.86 4.17 2.17 25.12 1400.00 1.41 2.73 1.41 1.02 benzene 1.56 1.80 1.35 1.07 chlorobenzene 1.22 o-dichlorobenzene 1.09 1.55 1.36 1.67 m-dichlorobenzene 1.25 1.15 1.00 3.03 1.75 1.70 1.32 p-dichlorobenzene 4.43 1,2,3-trichlorobenzene 2.38 1.42 1.72 1.21 1.00 1.03 2.00 1,2,4-trichlorobenzene 1.32 1.83 1.77 2.18 1,3,5-trichlorobenzene 6.19 1.06 2.25 1,2,3,4-tetrachlorobenzene 1.14 3.21 1.03 2.07 1,2,3,5-tetrachlorobenzene 1.21 7.14 1.62 1.11 1,2,4,5-tetrachlorobenzene 1.32 1.08 11.63 1.48 4.44 pentachlorobenzene 31.00 2.03 103.87 1.41 hexachlorobenzene 84.37 3.85 6.57 2.55 5.30 mean
prediction of the aqueous solubility of liquid and solid polychlorinated biphenyls and benzenes. Taking into account the different physical contributions to the freeenergy change accompanying the dissolution of the solute, the success of the method mainly originates from the correct description of the entropic and hydrophobic effects ( B and F terms). The quantitative treatment of the last effect shows that, at equilibrium, the aqueous solubility, In aB,is reduced by an amount equal to - 2 @ s V B / v S . A direct consequence of this effect is that any increase in the chlorine substitution decreases the solubility. For H-bond formation between the proton donor OH group of the secondary chains of water and the proton acceptor 7
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electrons of the aromatic rings, the present treatment is based on the concentration of the active sites in solution and on the stability constant, KO. Finally, compared to other models, the present equation yields solubility values as accurate as those obtained by Yalkowsky’s model, one of the best models suited to predict aqueous solubility of organic compounds. However, owing to its large range of applicability, Huyskens’ mobile order theory derived solubility equation appears to have greater practical value.
Acknowledgments The authors are grateful to Professor P. L. Huyskens (University of Leuven, Belgium) for his advice.
Literature Cited Huyskens, P. L. J . Mol. Liq. 1990, 46, 285. Huyskens, P. L.; Siegel, G. G. Bull. SOC.Chim. Belg. 1988, 97, 821. Siegel, G. G.; Huyskens, P. L.; Vanderheyden, L. Ber. Bunsen-Ges. Phys. Chem. 1990, 94, 549. Huyskens, P. L.; Haulait-Pirson, M. C.; Siegel, G. G.; Kapuku, F. J . Phys. Chem. 1988,92,6841. Huyskens, P. L.; Haulait-Pirson, M. C. J . Mol. Liq. 1985, 31, 153. Huyskens, P. L. J . Mol. Struct. 1983, 100, 403. Ruelle, P.; Buchmann, M.; H6 Nam-Tran; Kesselring, U. W. J. Cornput.-Aided Mol. Des., in press. Ruelle, P.; Rey-Mermet, C.; Buchmann, M.; H6 Nam-Tran; Kesselring, U. W.; Huyskens, P. L. Pharm. Res. 1991,8, 840. Fedors, R. F. Polym. Eng. Sei. 1974, 14, 147. Fedors, R. F. Polym. Eng. Sei. 1974, 14, 472. Acree, W. E., Jr. In Handbook of Chemistry and Physics, 72nd ed.; Lide, D. R., Ed.; CRC Press: Boca Raton, FL, 1991; Section 5, p p 83-90. Opperhuizen, A.; Benecke, J. I.; Parsons, J. R. Environ. Sci. Technol. 1987,21, 925. Huyskens, P. L. In Interactions of Water in Ionic and Nonionic Hydrates; Kleeberg, H., Ed.; Springer: Berlin, 1987; p 113.~ Shiu, W. Y.; Mackay, D. J . Phys. Chem. Ref. Data 1986, 15, 911. Yalkowsky, S. H.; Orr, R. J.; Valvani, S. C. Ind. Eng. Chem. Fundam. 1979,18, 351. Suzuki, T. J . Cornput.-Aided Mol. Des. 1991, 5 , 149. Mackay, D.; Mascarenhas, R.; Shiu, W. Y.; Valvani, S. C.; Yalkowsky, S. H. Chemosphere 1980,9, 257. Nirmalakhandan, N. N.; Speece, R. E. Enuiron. Sei. Technol. 1989, 23, 708. Wakita, K.; Yoshimoto, M.; Miyamoto, S.; Watanabe, H. Chem. Pharm. Bull. 1986, 34, 4663. ~~
Received for review July 14, 1992. Revised manuscript received October 5,1992. Accepted October 6,1992. We are grateful to the Swiss National Science Foundation (FNRS)for partial financial support (Grant 3100-34227.92).
