Thus, for liquids x = l/y, since f R = f L , and for solids x = In terms of I.L mol/L, the correlating parameters used by Chiou can be related to x; hence, y for dilute solutions as: (fs/fR)/?w.
S = 55.5 x x lo6 pmol/L or
S = 55.5 X 106/y, (liquids) or 55.5 X
lo6 ( f s / f R ) / y , (solids)
The partition coefficient K in units of g or mol/L ratio can be obtained from the fugacity equation written as Figure 1. Photostationary state group as a function of standard deviation u of mixing fraction 7 between source-rich and background urban
air of 1.78 at u = 0.5, whereas a t [NO212 = 0.2 ppm and [NO12 = 0.02 ppm, 0 reaches 1.43 at u = 0.5. The effect of the intensity of the fluctuations in the mixing fraction 7 on the ratio 0 is understandable because this level of fluctuations determines how greatly 0 differs from ( O ) , Le., unity.
Literature Cited (1) Calvert, J. G., Enuiron. Sci. Technol., 10,248 (1976). (2) Hampson, R. F., Jr., Garvin, D., Eds., Chemical Kinetic and Photochemical Data for Modelling Atmospheric Chemistry”, NBS Tech. Note 866,1975. (3) O’Brien, R. J., Enuiron. Sci. Technol., 8,579 (1974). (4) Eschenroeder, A. Q., Martinez, J. R., Nordsieck, R. A., “Evaluation of a Diffusion Model for Photochemical Smog Simulation”, Final Rep. of General Research Corp., Santa Barbara, Calif., to EPA Contract No. 68-02-0336, 1972. ( 5 ) Eschenroeder, A. Q., “Los Angeles Reactive Pollutant Program (LARPP) Summary of Data Management Activities”, Environmental Research and Tech. Inc. Document P-165613, 1976.
John H. Seinfeld Chemical Engineering California Institute of Technology Pasadena, Calif. 91 125
f
= x,y,fR
where subscripts w and o refer to the water and octanol phases. The reference fugacities f R cancel, regardless of whether the solute is solid or liquid at the system temperature. Now C, is x, 55.5 mol/L, and C, is 6.36 x,. Since the density of octanol is 827 g/L and its molecular weight is 130, 1L of octanol contains 6.36 mol. Thus,
K = C,/C,
= 6.36 x,/55.5 x,
f
= xy,fR
where x is the mole fraction of the compound in water, y, is its activity coefficient in aqueous solution, and f R is the reference fugacity, i.e., the fugacity of the pure liquid compound at the system temperature. For liquid compounds f R is simply the liquid vapor pressure f L . For solids f R is the extrapolated liquid fugacity (below the triple point), not the solid fugacity (or vapor pressure) f S . However, the ratio f R / f S can be estimated by standard techniques (2).
= 0.115 y,/yo
A correlation between log K and log S is thus a correlation between (log y, - log yo - 0.94) and (-log y, log ( f s / f R ) 7.74). Since y, varies from a value of about lo3for chloroform to about IO9 for 2452‘4‘5’ PCB, its variation dominates the correlation. If yo and ( f S / f R )were constant, the correlation illustrated in Figure 1 by Chiou would be a line of slope -1. This is nearly true for liquids, as can be seen by the clustering of the points for liquid compounds at the right of Figure 1 about a slope of -1. In practice, for solid compounds as molecular weight and melting point increase ( f s / f R ) becomes smaller and yo increases as the compound exhibits more positive nonideality in the octanol phase, due in part to the increase in molar volume difference. By inserting the above definitions of K and S in Chiou’s correlation and rearranging it, it can be shown that
+
+
(fs/fR)Yo=
SIR: Chiou et al. recently obtained an empirical correlation between n -octanol/water partition coefficients and aqueous solubilities for a wide variety of compounds ( I ) . Since partition coefficient or solubility correlates with biomagnification, there is justification for using these purely physical-chemical properties as estimators of environmental and toxicological behavior. The authors omitted to mention that there is a physical-chemical basis for their correlation; indeed, both the partition coefficient and aqueous solubility are to a large extent functions of the same property, the aqueous phase activity coefficient of the compound, and as shown below the correlation is partly between that property and its reciprocal. The aqueous solubility of a hydrophobic compound in water can be expressed in terms of the fundamental equation in its fugacity f , using the Raoult’s law convention,
= X,7,fR
0.0158
This is an empirical relationship (equivalent to the Chiou correlation) which states that as molecular weight, melting point, and hydrophobicity increase, the fugacity ratio is observed to decrease and yo is observed to increase in proportion to the cube root of the decreasing solubility. If data were available for yo, melting point, entropy of fusion, and solid and liquid heat capacities, then the precise relationship between K and S could be calculated. Chiou’s work is entirely valid, and it will be useful as a means of overcoming a lack of physical-chemical data needed for interpretation of biomagnification and toxicity studies and for checking the “reasonableness” of K and S values. It is, however, noteworthy that part of the success of the correlation is attributable to correlating a quantity against its reciprocal. Finally, the quoted value for the solubility of benzene (820 ppm) is substantially lower than the more recent values which are about 1780 ppm (3).
Literature Cited (1) Chiou, C. T., Freed, V. H., Schmedding, D. W., Kohnert, R. L., Enuiron. Sci. Technol., 11 ( 5 ) ,475 (1977). (2) Prausnitz, J. M., “Molecular Thermodynamics of Fluid Phase Equilibria”, Prentice-Hall, Englewood Cliffs, N.J., 1969. (3) McAuliffe, C., J . Phys. Chem., 70,1267 (1966).
Donald Mackay Department of Chemical Engineering and Applied Chemistry University of Toronto Toronto, Canada M5S 1A4
Volume 11, Number 13, December 1977 1219
