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
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The Journal of Physical Chemistry, VoL 83, No.
13, 1979
Communications to the Editor
Ei -11.2
-
-11.3-
-11.7r
I
-‘I 9;1.5
/‘
‘2:s 2:;
218
2:9
310 T-I
3il
x lo3 (
3.2 0
~
~
313 ~
3j4
3:5 3:s
’
)
Flgure 1. Arrhenius plot of the experimentally observed values for k , .
within a few microseconds. The slower disappearance of the HOz radical is followed over ca. P ms by kinetic spectrophotometry at 230 nm. Use of the known value for the HOz absorption cross section C T ~ &= 2.17 X cm2 molecules-’, base e ) , allows the determination of the absolute rate constant for the overall reaction HO2 + HO2 ---* HzOz 0 2 (1) The results are plotted in Arrhenius form in Figure 1. The result of a standard linear least-squares analysis, with the error limits given as plus or minus one standard deviation, is kl = (1.14 f 0.16) X W3exp[(2100 f 90)/RT] cm3 molecule-‘ s-l, which corresponds to the solid line. The dashed line represents the result of COX,^ which has already been mentioned. The negative activation energy for reaction 1 can be explained on the basis of an unstable dimer intermediate, H204,and the following mechanism:
+
H 0 2 + HOz
k $ -HZ04
(The dimer species may have a cyclic structure with two hydrogen bonds, and calculations on the stability of such a structure are being carried out.) Applying the steadystate approximation to H204,one finds
+
Therefore, k , is equivalent to k,k4/(k3 k4),and one can show that the overall activation energy, El, is given given bY
Ez + (k3/[k3 + h])(E4 - E31
(11)
For El to be negative, it is necessary that E, > E& Because the activation energy (Le., E,) for a radical combination reaction is expected to be near zero, the condition E 3 > E4 would be likely to lead to a negative value for El. If El is negative, eq I1 implies that E , would become more negative with increasing temperature because the ratio k 3 / [ k 3+ k4] would become larger. Thus, for the stated mechanism, the experimentally observed activation energy is seen to be an “average” activation energy over the temperature range studied. A good fit with the experimental data in Figure 1can be obtained by using k 2 = A2. ~XP(-EZ/RT)and h / k 4 = [ A ~ / A ~ I [ ~ X-P&I/RT)I, ([~ with A, 1.3 X cm3 molecule-l s-l, E2 400 cal mol-l, A3/A4 3 X lo3,and E4- E , -5000 cal mol-,. The main insight to be gained from this is that reaction 4 is required to have a much smaller preexponential factor than reaction 3. This is not unreasonable in view of the rearrangement necessary for reaction 4 to proceed. The presence of water vapor or ammonia has been previously observed4to increase the rate of reaction 1. The effect of temperature on these systems is also being investigated, and the results will be described in a future publication. Negative activation energies are also observed when water vapor or ammonia are present. The results will provide experimental information related to the stabilities of the complexes, e.g., H20--H02,which have been proposed on the basis of previous kinetic4 and theoretical studies.6
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- -
References and Notes (i) Work performed under the auspices of the Office of Basic Energy Sciences of the U S . Department of Energy. (2) S. N. Foner and R. L. Hudson, Adv. Chem. Ser., No. 30,34 (1962). (3) T. T. Paukert and H. S. Johnston, J. Chem. Phys., 50, 2824 (1972). (4) E. J. Hamilton and R. R. Lii, Int. J . Chem. Kinet., g, 875 (1977). (5) R. A. Cox, presented at the joint assembly of the International Association of Geomagnetism and Aeronomy and the International Association of Meterology and Atmospheric Physics, Seattle, Wash., 1977. (6) E. J. Hamilton, Jr., and C. A. Naleway, J . Phys. Chem., 80, 2037 (1976). (7) Faculty research participant from Department of Chemistry, Malcolm X College, Chicago, Ill. 60612. (8) Scientific Research Laboratory, Ford Motor Company, Dearborn, Mich. 48121. Chemistry Division Argonne National Laboratory Argonne, Illinois 60439
Received March 5, 1979
Ruey-Rong L11’ Robert A. Gorse, Jr.* Myran C. Sauer, Jr.” Sheffleld Gordon
