Correspondence Comment on “Influence of Soot Carbon on the Soil-Air Partitioning of Polycyclic Aromatic Hydrocarbon” In two recent publications (1, 2), the soot-air adsorption constant (Ki SA) of a given compound i has been estimated from its Henry’s law constant, (Ki AW) and its measured sootwater adsorption constant (Ki SW) using the thermodynamic cycle according to
Ki SA ) Ki SW/Ki AW
(1)
However, the thermodynamic cycle only works in cases where the involved phases or interfaces do not affect each other. It cannot work for an interface that consists of a solid surface and an adjacent liquid phase in one case and that consists of the same solid surface but an adjacent gaseous phase in the other case. The thermodynamic cycle is frequently used to estimate an unknown equilibrium partition constant of a compound i between two phases from its partitioning between other pairs of phases. As an introduction into the principal limitations of this approach, two examples from bulk-phase partitioning will be used before the application of the thermodynamic cycle to interfaces is discussed. Example 1. Octanol-air partitioning of compound i is commonly estimated from its octanol-water and air-water partition constants by the following approach:
Ki oa ) Ki ow/Ki aw
(2)
or equivalently (* indicates equilibrium conditions):
c/i octanol c/i air
)
c/i octanol c/i air / c/i water c/i water
(3)
Obviously, the idea behind this approach is that the term ci/ water in eq 3 cancels out. However, a closer look at the experimental values of Ki ow and Ki aw reveals that Ki ow describes the partitioning between an octanol phase saturated with water and a water phase saturated with octanol whereas Ki aw describes partitioning between air and pure water. Hence, to be correct, eq 3 must actually be rewritten as
c/i octanol satd with water c/i air
)
c/i octanol satd with water c/i air / (4) c/i water satd with octanol c/i water
It becomes clear now that the thermodynamic circle only works with some limitations: (a) eq 4 yields the octanol-air partition constant for wet octanol and not for dry octanol, and (b) eq 4 only works if the phase properties of water saturated with octanol are similar to those of pure water because otherwise the two terms concerning the water phase would not cancel out. Others have already discussed these details for the case of octanol partitioning (e.g., refs 3 and 4). Example 2. A situation where the thermodynamic cycle does not work is the attempt to calculate the water solubility of ethanol from its saturated vapor pressure and its Henry’s * E-mail:
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law constant. This calculation results in a water solubility of 0.15 g/L for ethanol at 25 °C. Obviously, this value is erroneous considering the well-known complete mutual miscibility of ethanol and water. In fact, the calculated number corresponds to the hypothetical solubility of ethanol in pure water, a situation that can never be achieved in practice because a water phase containing high concentrations of ethanol is not similar to a pure water phase any more. (Note that similar errors can occur if linear free energy relationships are used to predict a wide range of water solubilities for organic compounds. Ref 5, for example, reports estimated water solubilities of 1256 and 508 g/L for methanol and ethanol, respectively, although both are completely miscible with water.) The above examples have illustrated the principle problems for bulk phases. Much more severe errors, however, occur if the thermodynamic cycle is used to predict airsurface adsorption from water-surface adsorption or vice versa. Before getting to the theoretical considerations, it is instructive to take a look at some experimental data. Unfortunately such data are not available for a soot surface, but they are available for an R-Al2O3 surface. These data prove that eq 1 does not hold: the adsorption constant of naphthalene from water to R-Al2O3 at 20 °C is 7.6 × 10-10 (m3/m2) (6). The dimensionless Henry’s law constant of naphthalene is 0.013 (m3/m3) at 20 °C (7). Hence, eq 1 would yield a surface-air adsorption constant of naphthalene to R-Al2O3 of 7.6 × 10-10 (m3/m2)/0.013 (m3/m3) ) 5.8 × 10-8 (m3/m2). However, the experimental value (extrapolated to 20 °C) for exactly the same R-Al2O3 is 3 orders of magnitude larger: 6.1 × 10-5 (m3/m2) (8). (This value is for R-Al2O3 that is in equilibrium with 30% relative humidity in air and would be even higher at lower relative humidities). To understand the reason for this discrepancy, it helps to write down the applied thermodynamic cycle (eq 1) more precisely (for any solid surface insoluble in water):
c/i surface-air interface c/i air
)
c/i surface-water interface c/i air / / c/i water ci water
(5)
This equation can only hold if the surface-water interface was identical (or at least similar) to the surface-air interface. This is not the case. Similarity of two phases or interfaces with respect to the partitioning of an organic compound means that the compound exhibits similar interaction free energies when transferred to these interfaces from a reference state. However, a comparison of the relevant energy terms in the above cases immediately reveals that these interaction free energies must be quite different. When compound i is transferred to the surface-air interface, energy is gained from interactions between i and the surface (9, 10). The same is true if compound i is transferred to the surface-water interface. However, in the latter case an additional energy contribution comes from the water molecules that must be replaced by the adsorbing compound. The change in free energy of these water molecules that are originally adsorbed to the surface and then moved to the bulk water phase when i adsorbs contributes to the overall adsorption energy of i at the surface-water interface. Hence, eq 5 could only give correct results if the water molecules had a zero adsorption energy on the considered surface (i.e., if their interactions at the surface were the same as in the bulk water phase). This 10.1021/es0301370 CCC: $27.50
2004 American Chemical Society Published on Web 01/24/2004
situation is not likely to occur, and as the above example for a mineral surface shows, huge errors can arise. An example of a correct application of the thermodynamic cycle to interfacial adsorption is the calculation of the adsorption equilibrium between bulk water and the waterair interface (which determines the stripping efficiency of gas bubbles; 11) from the adsorption equilibrium between air and the water-air interface (for which literature data are available; 12). This thermodynamic cycle is shown in eq 6:
c/i water-air interface c/i water
)
c/i water-air interface c/i air
*
c/i air c/i water
(6)
Equation 6 works, in contrast to eq 5, because the considered interface is exactly the same on both sides of the equation. Other interesting examples on how to use the thermodynamic cycle correctly in order to gain information about partition processes can be found in ref 13.
Literature Cited (1) Ribes, S.; Van Drooge, B.; Dachs, J.; Gustafsson, O.; Grimalt, J. O. Environ. Sci. Technol. 2003, 37, 2675-2680. (2) Dachs, J.; Eisenreich, S. J. Environ. Sci. Technol. 2000, 34, 36903697.
(3) Beyer, A.; Wania, F.; Gouin, T.; Mackay, D.; Matthies, M. Environ. Toxicol. Chem. 2002, 21, 941-953. (4) Ko¨mp, P.; McLachlan, M. S. Environ. Toxicol. Chem. 1997, 16, 2433-2437. (5) Abraham, M. H.; Le, J. J. Pharm. Sci. 1999, 88, 868-880. (6) Mader, B. T.; Goss, K.-U.; Eisenreich, S. J. Environ. Sci. Technol. 1997, 31, 1079-1086. (7) Schwarzenbach, R. P.; Gschwend, P. M.; Imboden, D. M. Environmental Organic Chemistry; John Wiley & Sons: Hoboken, NJ, 2002. (8) Goss, K.-U.; Eisenreich, S. J. Environ. Sci. Technol. 1996, 30, 2135-2142. (9) Goss, K.-U. Environ. Sci. Technol. 1997, 31, 3600-3605. (10) Goss, K.-U. J. Colloid Interface Sci. 1997, 190, 241-249. (11) Hoff, J. T.; Gillham, R.; Mackay, D.; Shiu, W. Y. Environ. Sci. Technol. 1993, 27, 2174-2180. (12) Roth, C. M.; Goss, K.-U.; Schwarzenbach, R. P. J. Colloid Interface Sci. 2002, 252, 21-30. (13) Borisover, M.; Graber, E. R. Isr. J. Chem. 2002, 42, 77-87.
Kai-Uwe Goss* Swiss Institute of Environmental Science and Technology (EAWAG) U ¨ berlandstrasse 133 CH-8600 Du ¨ bendorf, Switzerland ES0301370
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