SIR: In his correspondence to the editor, Mackay has offered some very useful arguments on the relationship between the octanol/water partition coefficient ( K )and water solubility (S)from thermodynamic considerations. It has to be recognized, however, that the relationship derived by Mackay is based on a simplified condition, namely, that the activity coefficient yw of an organic chemical in pure water (in the S term) and its value in the octanol-saturated aqueous phase yw/oct(in the K term) are identical. While yw may not differ significantly from yw/octfor some highly water-soluble compounds, they may be substantially different for compounds of low solubility such as those reported by Chiou et al. ( I ) . In other words, the solubility of a poorly soluble organic compound in pure water could be very different from that in an octanol-saturated water. Similarly, the solution behavior of a water-saturated octanol phase cannot be assumed to be the same as that of pure octanol (2).Because of these effects, the correlation between log K and log S as proposed by Mackay should be rewritten as: log K term
where yoctlwhas a similar meaning as yw/oct defined above. In the log K term, yw/OCt and yoct/&are used to replace yw and yo, respectively. Therefore, from strict thermodynamic considerations, the correlation between K and S reported by Chiou et al. ( I ) is not attributable to correlating a quantity against its reciprocal as claimed by Mackay. Indeed the slope of log K vs. log S would be closer to -1 for highly soluble liquid solutes since in this case it is expected that yw/oct/yw= l, log yoctIu = constant, and f s / f R = 1. For organic chemicals which exhibit positive nonideality in water, it is reasonable to believe that while y I Lis larger than ywloct,it also increases more rapidly than yw/octas the aqueous solubility decreases. The slope of log K vs. log S would then have a smaller negative value based on the above arguments since the variation of other
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terms, log yoct/wand log (f&), are relatively insensitive in comparison with the variation of yw and yU,loct.For example, when K = lo3,ywloct is already about four orders of magnitude higher than y O C t ~and u , the variation of f s / f R is relatively small in comparison with that of yw.The slope (-0.670) observed by Chiou et al. ( I ) agrees with this expectation. The basic principle presented by Mackay to relate K to S in terms of solute activity coefficients is undoubtedly valid and helps to pinpoint some thermodynamic parameters associated with the K - S relationship. It requires differentiations between yw and ywloctand between yo and yoctlwto be exact. Meanwhile, note that a relationship between log K and log S for organic liquids has been derived by Hansch et al. (3) using a similar treatment by assuming that water and octanol do not mutually solubilize in their mixture. The experimental results, nonetheless, showed some deviation from the predicted relationship. The authors are aware that no exact relationship between K and S in terms of thermodynamic parameters could likely be achieved without considering the solubility effect of octanol in water and vice versa. Empirical investigation of the relationship was therefore carried out before postulating the theoretical basis of the relationship. Finally, we appreciate the suggestion of a more reliable benzene solubility. L i t e r a t u r e Cited (1) Chiou, C. T., Freed, V. H., Schmedding, D. W., Kohnert, R. L., Enuiron. Sci. Technol., 11 (51, 475 (1977). (2) Leo, A., Hansch, C., Elkins, D., Chem. Reu., 71,525 (1971).
(3) Hansch, C., Quilan, J. E., Lawrence, G. L., J. Org. Chern., 33,347 (1968).
Cary T. Chiou Virgil H. Freed Department of Agricultural Chemistry Oregon State University Corvallis, Ore. 97331
