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The Journal of Physical Chemistry, Vol. 83, No. 13, 7979
Communications to the Editor
COMMUNICATIONS TO THE EDITOR Standard States in the Thermodynamics of Transfer Publication costs asslsted by the National Science Foundation
mentally found to be almost ideal. One can visualize why this is so: if the Gurney procedure8 approximately accomplishes its intended goal of eliminating the cratic contribution from the potential (no one would seriously suggest that it does so exactly), and if solute-solvent interactions are of such short range that one can express experimental results in terms of unique contributions from groups as small as CH2,then it is reasonable to expect that the environmental interactions of, for example, an n-octane molecule at infinite dilution in n-hexane or n-decane should not be very different from the environmental interactions with other n-octane molecules in the pure state, and hence that in this case poL N los. Experimental data bear this out, at least for saturated alkanes, the only case where the equality is of practical i m p ~ r t a n c e The . ~ most accurate datalo are based on vapor pressure measurements, with careful correction for nonideality of the vapor, and they show that the difference between goL and p o s is only about 60 cal/mol at room temperature even when the difference in chain length between solute and solvent molecules is 10 carbon atoms! The difference between poL and y0s would be even smaller for the lesser range of hydrocarbon chain lengths for which transfer free energies to water are measurable, and it is insignificant in comparison with the transfer free energy, Le., the difference between p o H ~(POL or pas) and the standard potential (pow) in water. Ben-Naim criticizes those of us who try to deduce general chemical and biological principles from experimental data for using theoretical concepts “without taking the trouble of checking their validity”. One can be equally critical of those who dismiss work of this kind on the basis of second-order terms in theoretical equations without taking the trouble to give numerical values for these terms. As I have shown here the choice of standard state does not affect the most important results obtained from transfer studies related to the hydrophobic effect, but there are also more fundamental questions that can be answered only in terms of numerical values. How large is the difference between Ben-Naim’s “liberation free energy” and Gurney’s “cratic free energy”? Is the difference within or outside the uncertainty introduced by simplifications in the derivation of the equations? Acknowledgment. This work is supported by research grant PCM76-15240 from the National Science Foundation.
Sir: Ben-Naiml has enthusiastically advocated the use of the molar concentration scale when dealing with the thermodynamics of transfer of solutes from one solvent to another, and has harshly criticized solution chemists, biochemists, and biologists for employing other concentration scales and the standard states associated with them. I am not competent to comment on the validity of his preference, but do wish to respond to the criticism: the thermodynamic quantities that have been calculated from experimental transfer data, and have been the basis for gaining much insight into chemical and biological phenomena, are either rigorously independent of the choice of standard state or else do not depend on the choice because the factors that would make them dependent are experimentally insignificant. The thermodynamic quantities of greatest interest to many chemists, and especially to biochemists, are “group contributions”, which are the differences between the standard transfer free energies for two related organic molecules differing only by the addition of one chemical group to one of the molecules.2 The distribution of each solute is measured a t low concentration, and where concentration effects are important it is extrapolated to infinite d i l ~ t i o n .Each ~ measurement yields a value for the difference in standard potential (Aho) between the two solvents, and the group contribution is evaluated as the difference A(Apo) between the two compounds. Using the usual equation for the chemical potential of a solute in very dilute solutions, p = p o RT In C , where C is the concentration is any desired units, we can easily show4 that Apo depends on the concentration scale employed, whereas A(Apo) does not. The most remarkable experimental observation derived from transfer thermodynamics is that the addition of a CH2 group to an enormous variety of organic solutes changes Apo for transfer from a liquid hydrocarbon solvent to water by an almost constant ?~ amount, 850 f 40 cal/mol at room t e m p e r a t ~ r e . ~This measurement and similar results for CH2 group contributions to other thermodynamic parameters6 constitute the foundation on which our conceptualization of the hydrophobic effect rests. The result is clearly independent of the concentration scale and standard state employed. The same is true for attempts to relate the hydrophobic effect to the surface area of contact between References and Notes solute and solventa6The slope of a plot of Apo vs. surface area is independent of the choice of standard state; only (1) A. Ben-Naim, J . Phys. Chem., 82, 792 (1978). (2) S. S. Davis, T. Higuchi, and J. H. Rytting, J . Pharm. Pharmac., 24, the intercept would be affected. Suppl. 30P (1972); Adv. Pharmaceutlcal Sci., 4, 73 (1974). Ben-Naim correctly points out that the equation p = po (3) For example, R. Smith and C. Tanford, Prm. mtl. Acad. Sci. U.S.A., RT In C applies only to very dilute solutions and em70, 289 (1973). (4) Let C I Aand C,,Ebe the equilibrium concentrations of solute i in a phasizes the fact (surely well known to all solution distribution experiment between two solvents A and B, expressed chemists) that the standard potential of a substance in the in molar units, and let XI,Aand Xis be the same concentrations, pure state cannot in general be the same as the standard expressed in mol fraction units. I n ‘very dilute solutions, the relatlon between the two concentration scales involves only the number of potential derived from dilute solution data. He specifically of solvent in 1 L of pure solvent ( N Aand NB,respectively). criticizes the use in publications from this l a b ~ r a t o r y ~ , ~ ~ moles I f molar units are used, the free energy of transfer is Afioyc) = RT of the single symbol boHcto represent both the standard In (Ci,A/C,,B), and if mole fraction units are used, we have A/.L’~~) = RTln (X,A/XiE).The two quantities are not the same, Le., Awol(c) potential of a hydrocarbon in the pure liquid state ( p ’ ~ ) = Afioi(x) 4 R f l n ( N A / N B ) .In a second experiment, using solute and the standard potential (hypothetical unit concenj in the same two solvents, we have llkewise A/.boXc)= AfiOd(,) + tration) for very dilute solutions in another hydrocarbon RTln (NA/NB).When we evaluate the difference between Afi I and Abo,, the factor RTln (MAINE)disappears, Le., A(Afi’) = A f i 0 ~ c ) (los This ) . is, however, an exceptional system, experi-
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0 1979 American Chemical
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The Journal of Physical Chemistry, Vol. 83, No. 13, 1979
Communications to the Editor
- Awoyc, = Apoyx, - 4woYx,.The equality is rigorously true if experimental distribution ratios have been extrapolated to infinite dilution. C. Tanford, “The Hydrophobic Effect”, Wiley, New York, 1973. One of the earliest is the demonstration of a unique CH, group contribution to the heat capacity of transfer. See J. T. Edsall, J. Am. Chem. SOC.,57, 1506 (1935). (a) M. J. Harris, T. Higuchi, and J. H. Rytting, J . Phys. Chem., 77, 2694 (1973); (b) R. B. Hermann, J. Phys. Chem., 76, 2754 (1972); Proc. Natl. Acad. Sci. U.S.A., 74, 4144 (1977); (c) J. A. Reynolds, D. B. Gilbert, and C. Tanford, Proc. Natl. Acad. Sci. U . S . A., 71, 2925 (1974). There is a controversy as to whether or not a linear relation should be expected and it is therefore important to note that the choice of standard state does not affect the data per se. R. W. Gurney, “Ionic Processes in Solution”, McGraw-Hill, New York, 1953; Dover, New York, 1962; p 90. The procedure is discussed in ref 1 and 5. The reason it is important is that accurate data exist for transfer from pure hydrocarbon to aqueous solution. There are no comparable data for direct calculation of f i o s - wow. M. L. McGlashan and A. G. Williamson, Trans. Faraday Sac., 57, 588 (1961); A. J. B. Cruickshank, B. W. Gainey, and C. L. Young, ibid., 64, 337 (1968); C. P. Hicks and C. L. Young, ibid., 64, 2675 (1968). Whitehead Medical Research Institute and Depaiiment of Biochemistry Duke University Medical Center Durham, North Carolina 27710
Charles Tanford
Received September 5, 1978
Reply to C. Tanford’s Comments Concerning Standard States in the Thermodynamics of Transfer
Sir: I disagree with the views expressed by Dr. Tanford in ref 1. In my paper,2I have demonstrated that some of the standard free energies of transfer (SFET) may diverge to f infinity, so how can one claim that these quantities “do not depend on the choice because the factors that would make them dependent are experimentally insignificant”? In my paper I have emphasized the fundamental misconceptions that were propagated in the literature, not the numerical differences between various choices of SFET. Further numerical examples are presented in a book which is now in press.3 In my paper I have also demonstrated that the relation pi = p*i + kT In pi may be used for any concentration of the component i, including pure i. This is a subtle point which has obviously been overlooked by Tanford in discussing only the applicability of this relation to very dilute solutions. As was demonstrated in my paper,2 there is a fundamental conceptual error in the interpretation of the quantities used by Tanford which are referred to as “unitary” quantities. I still believe that many authors do use these quantities “without going to the trouble of checking their validity”. I found the oddest comment in his last paragraph which refers to the “second-order terms in theoretical equations”. Nowhere in my paper have I discussed the “order” of the terms. The differences between various SFET may range from zero to infinity, and that cannot be regarded as “second-order terms”. I should like to reply to Tanford’s last two questions. (1)The difference between the “liberation free energy” and the “cratic free energy” can be anything between zero and infinity. These are two f u n d a m e n t a l l y different quantities, but are unfortunately often discussed as being only a variation of the same quantity in different units. (2) The “uncertainty introduced by simplifications” is only ap0022-3654/79/2083-1803$01 .OO/O
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parent. As I have demonstrated, thermodynamics alone does not lend sufficient meaning to some of the SFET used in the literature. The implication of this question is that the difference between various SFET might be small and therefore one should prefer the simplest one. As I have pointed out above, different SFET might differ appreciably in their magnitude depending on specific circumstances. In special cases where their numerical values are similar, one could indeed prefer the simplest one, which is &LOP, rather &Ox recommended by Tanford. In footnote 4 Tanford presents one example where it makes no difference which concentration units are chosen. This comment has no effect on any of the conclusions of my paper. In the first place because my paper discussed the SFET, Apoi of a single solute in a solvent, and not differences in Apoi. Secondly, in most research articles one compares values of Ahai for the same solute in different solvents, not for different solutes in the same solvent. Thirdly, as noted by Tanford himself, the particular example given in footnote 4 is valid for very dilute solutions. In my paper I have discussed also the general case of concentrated solutions of A in B, and even pure liquid A. In these cases the argument presented in the footnote are not valid. In conclusion, in my paper I presented general arguments in favor of the choice of Apop as a SFET. One cannot criticize a general statement by showing that in some particular cases the difference between different standard states is small or even zero. Furthermore, if Tanford really believes that the choice of concentration units is of no importance, why does he so enthusiastically advocate the use of mole fractions? References and Notes (1) C. Tanford, J. Phys. Chem.,preceding communication in this issue. (2) A. Ben-Naim, J . Phys. Chem , 82, 792 (1978). (3) A. Ben-Naim, “Hydrophobic Interactions”, Plenum Press, New York, in press.
Department of Physical Chemistry The Hebrew University Jerusalem, Israel
A. Ben-Nalm
Received October 2, 1978
Negative Activation Energy for the Self-Reaction of HO, in the Gas Phase. Dimerization of HO,’ Pubhcabon costs assisted by Argonne National Laboratory
Sir: The hydroperoxyl radical, HOz, is an important intermediate in a variety of chemical systems, e.g., photochemical air pollution, combustion processes, and stratospheric chemistry. The self-reaction of HOz has been the subject of several recent s t u d i e ~ . ~The - ~ importance of the presence of water vapor (or NHJ, which complexes the HOz and results in an acceleration of the self-reaction, has been pointed outs4 Knowledge of the temperature dependence of the reactions of HOz is important to the subjects mentioned above. Cox5 has recently reported on the temperature dependence of the self-reaction, the rate exp[(3300 f 410)/RT] constant being (1.4 f 0.7) X cm3 molecule-l s-l. This report deals with our measurements of this rate constant over the temperature range 276-400 K, using a pulse-radiolysis technique which has been described earlier.* Briefly, a 50-ns electron pulse of about 2-MeV incident energy in a system of 1200 torr of H,and 5 torr of O2 creates H atoms which are entirely converted to H02 0 1979 American
Chemical Society
