Environ. Sci. Technol. 1990, 24, 1755- 1756
CORRESPONDENCE
Comment on “Temperature Dependence of the Aqueous Solubilities of Highly Chlorinated Dibenzo-p-dioxins”
Table I. Molar Free Energy, Enthalpy, and Entropy Changes for the Dissolution of PCDDs at 299 K“ congener AG, AGf
SIR: In a research paper (I) that appeared in this journal, Friesen and Webster reported the water solubilities of some highly chlorinated dibenzo-p-dioxins (PCDDs) over a temperature range of 7-41 “C. From the solubility data and their temperature dependence, they calculated the molar free energy, enthalpy, and entropy changes associated with the solution of solid PCDDs and the corresponding subcooled liquids. Their calculations of these thermodynamic functions are summarized as follows: The molar enthalpy change for solution of solid PCDDs (AH,) is computed from the temperature dependence of the solid solubility by In X = -AH,/RT
+C
(1)
where X is the mole fraction aqueous solubility of the solid, T is the absolute temperature of the system, R is the gas constant, and C is a constant. The molar free energy change for solid dissolution (AG,) a t temperature T is obtained from
AG, = -RT In X
(2)
and the corresponding entropy change by use of the relation AG, = AH, - TAS,
(3)
With AG, obtained from eq 2 for solid PCDDs, the molar free energy of solution for respective subcooled liquids (AG,) is obtained by relating the free energy changes of the solid and subcooled PCDD as
where AGf is the molar free energy of fusion of PCDDs. By relating the enthalpy of fusion (AHf) to the entropy of fusion (AS,) at the melting point as AHf = T,ASf
(5)
AGI = AS,(T, - T )
(6)
along with
where T , is the melting temperature, the AH,and TASl for respective subcooled PCDDs are obtained through AH, = AH, - AH,and TAS, = TAS, - TASP 0013-936X/90/0924-1755$02.50/0
TICDD PSCDD H&DD H7CDD a
0 0 0 0
8.4 9.2 13.3 13.5
AG, AH8 AHf AH, TAS, TASf TAS, -8.4 -9.2 -13.3 -13.5
39.8 47.5 45.5 42.2
25.3 26.0 30.2 30.4
14.5 21.5 15.3 11.8
39.8 47.5 45.5 42.2
16.9 16.9 16.9 16.9
22.9 30.6 28.6 25.3
All values in kilojoules per mole.
Whereas eqs 1 and 3-6 are quite proper, the use of eq 2 to express the molar free energy of solution for the solid compound appears to be in error; this affects the computation of the AG, and TAS, values for solid PCDDs and AGl and TASl values for the corresponding subcooled PCDDs. Equation 2 (with correction of sign, Le., AG = R T In X) applies properly for the molar free energy of solution of a liquid into an ideal solution a t mole fraction X (2),in which there is no equilibrium between the liquid and its (ideal) solution. By contrast, the free energy change associated with the solution of a solid (or a partially miscible liquid) into a saturated solution must be zero, as it is for all equilibrium processes at constant temperature and pressure. Given the very small mole fraction solubility of solid PCDDs, the error in AG, by using eq 2 (and the resulting error in AGl from eq 4) is therefore considerable. It appears that a similar error has been made in the work of Opperhuizen et al. ( 3 ) that was cited in the article of Friesen and Webster. Because of the interrelation of AG, AH, and TAS, the error in AG, and AG, results in incorrect TAS, and TASl values for solid PCDDs and their subcooled liquids. In the referred article (I), both AG, and AG, are large in magnitude and positive; the respective TAS, and TASl values are negative, with TASl being greater in absolute magnitude. Thus, by reference to the original data of the article, the authors concluded that “... for the subcooled liquid to aqueous solution step, both enthalpy and entropy changes are thermodynamically unfavorable”, “the large negative entropy change that accompanies the dissolution of the subcooled liquid appears to be more important in controlling the solubility of these solutes”, and “the entropy changes in the subcooled liquid to solution step limit the solubility of these compounds in water”. These conclusions are not consistent with the solubility effect of sparingly soluble compounds. Since AG, is zero, the AG1for the subcooled liquid of a solid PCDD is hence AG, = -AGf, which should give AG, a small negative value, since AGf is small but positive. This difference between AGI and AG, is attributed to the fact that the subcooled liquid is metastable below the melting point and would therefore have a higher free energy than
0 1990 American Chemical Society
Environ. Sci. Technol., Vol. 24, No. 11, 1990
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the solid. Correction of eq 2 and application of eqs 1 and 3-6 results in a set of new AG,, AG,, TA&, and TAS, values for solid and subcooled TCDDs. The new data at 299 K are given in Table I and lead to the following conclusions: 1. The molar free energies of solution of solid PCDDs (AG,) at the point of saturation in water are zero and of respective subcooled liquids (AGJ are slightly negative. Small negative AGl values are attributed to the transition of unstable subcooled liquids to stable solids below the melting point. 2. While AH, and AHl are positive (with AHs > AHJ, so are the values of AS, and AS,, with AS, > AS,, in favor of the dissolution. The larger AS, than AS, is a consequence of the greater loss of order of the solid when dissolved relative to its subcooled liquid. 3. The low solubility of PCDDs in water is a result of their large unfavorable endothermic heats of solution, which offset the favorable entropic driving force for dissolution. The above conclusions give a more realistic account of the dissolution effect of solid and liquid compounds in a
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solvent (water) in which the solutes exhibit sparing solubility. Registry No. H,O, 7732-18-5. Literature Cited (1) Friesen, K. J.; Webster, G. R. B. Enoiron. Sci. Technol. 1990, 24, 97-101. (2) Hildebrand, J . H.; Prausnitz, J. M.; Scott, R. L. Regular and Related Solutions;Van Nostrand-Reinhold: New York, 1970; pp 15-17. (3) Opperhuizen, A.; Gobas, F. A. P. C.; Van der Steen, J. M. D.; Hutzinger, 0. Enuiron. Sci. Technol. 1988,22,638-646.
Cary T. Chiou" US. Geological Survey Denver Federal Center, MS 408 Denver, Colorado 80225
Mllton Manes Professor Emeritus, Kent State University Amberson Towers No. 412, 5 Bayard Road Pittsburgh, Pennsylvania 152 13
