J . Phys. Chem. 1986, 90, 4224-4233
4224
excited-state results and the present ground-state results. These are given in Figure 4. The surfaces in Figure 4 help to document the complex photochemical and photophysical properties of lepidopterene but they do not provide the insight into the very large spectral shift which characterizes the anthracene-ethylene exciplex, the region covered by the butterfly angle, a,and the mean interchromophore distance, d, being only schematic. This large shift is a puzzle, particularly as the absorption and fluorescence spectra of the A180 conformation show such good spectral overlap. Also, we have carried
out studies of the absorption and fluorescence of [2.2]- and [3.3](9,10)anthracenoparacyclophanes and we found little or no Stokes shift for these materials.8 Perhaps the lack of two constraining bridges in the lepidoterene exciplex allows a much closer approach of the ethylene chromophore than is possible for the cyclophanes. (8) Ferguson, J.; Puza, M.; Robbins, R. J.; Wilson, G. J., submitted for publication to J . Phys. Chem.
FEATURE ARTICLE Molecular Aspects of Ionic Hydration Reactions G. W. Robinson,*+P. J. Thistlethwaite, Department of Physical Chemistry, University of Melbourne, Parkville 3052, Victoria, Australia
and J. Lee Picosecond and Quantum Radiation Laboratory, Texas Tech University, Lubbock, Texas 79409 (Received: February 18, 1986)
Photokinetic experiments on ultrafast time scales have suggested that the integrity of the quasi-tetrahedral oxygen structure of liquid water sets the stage for both electron and proton hydration in aqueous media. Acid dissociation, and the attendant ion as a direct kinetic product. The parallel electron process gives proton hydration, produces the much discussed H904+ This may be the hydration product of a distorted water anion H20-, such as an rise to a similarly constituted ion, H804-. OH--H30 semi-ionic pair, and bears on the solvated-electronproblem in radiation chemistry. In Eigen's rate measurements of acid/base neutralization, the reactions were diffusion controlled. With newly developed mixed-solventmethods, the reverse dissociation process can span the gap between a 'diffusion-controlled" regimetranslation of water molecules to satisfy the local concentration requirement-and a "reaction-controlled" (*hydration-controlled")regimerotational diffusion of water molecules to satisfy the local structural requirement. Hydration rates of these 'elementary ions" in the hydration-controlled regime parallel dielectric and spin-lattice relaxation, shear viscosity, and other physical phenomena in pure liquid water where large amplitude rotations of water molecules play a dominant role. The necessary hydrogen reorientational motions thus limit the rates of these electron and proton hydration processes to STD-', where T~ is the Debye relaxation time. The role of the longitudinal relaxation time T~ (((713) in ion hydration is also discussed. Comparisons between photon-initiated acids, such as the excited states of 1- and 2-naphthol, and normal weak acids are made. These proton precursors are further compared with electron precursors. Free energy diagrams are introduced to help understand these correlations, with emphasis on the entropic contribution, which often dominates enthalpy terms. Equilibrium populations of states in the transition region quantitatively explain the rate phenomena. New absolute rate expressions for acid dissociation/recombination processes, which incorporate 7D-I and thermodynamic data, directly follow. A hydrogen/deuterium isotope rate factor of approximately 2.511 arises from purely entropic effects because of the stiffly structured nature of the hydrated proton or electron.
1. Introduction
The existence of "electrically conducting particles" in aqueous solutions of acids, bases, and salts has held a fascination for chemists since the early 1800s.'~* Modern concepts of spontaneous ionic dissociation were launched into their current form 100 years ago with the theory of A r r h e n i ~ s . ~Yet, the molecular nature of ion hydration reactions, particularly the structural role played by the surrounding solvent and the relevant scales of time, is still a subject of considerable speculation. The electron and the proton are ubiquitous chemical entities. The electron in water has engendered considerable research activity because of its importance in oxidation-reduction reactions4 and in radiation ~hemistry,~' while the proton in water is a major entity in analytical,* i n ~ r g a n i co, ~r g a n i ~ , ~and , ' ~electrochemistry."-'3 Permanent address: Texas Tech University.
These elementary ions also play a central role in biological energy transport.14 Current reasoning attributes specific s t r u c t ~ r e s , ' ~ J ~ - ~ ~ (1) Faraday, M. Experimental Researches in Electricity; 1839, Vol. I ; 1844, 1849, Vol. 2; 1855, Vol. 3. (2) For a good historical review, see: Partington, J. R. A History of Chemistry; Macmillan: London, 1964; Vol. 4. (3) Arrhenius, S. Z . Phys. Chem. 1887, 1, 630-648 (1887); In Nobel Lecutres in Chemistry, 1901-1921; Elsevier: Amsterdam, 1966; pp 43-61. (4) Taube., H. In Bioinorganic Chemistry ZI; Raymond, K. N., Ed.; American Chemical Society: Washington, DC, 1977, Ado. Chem. Ser. No. 162, pp 127-144. (5) Hart, E. J.; Anbar, M. The Hydrated Electron; Wiley-Interscience: New York, 1970. (6) Papers presented at Colloque Weyl IV, Michigan State University, East Lansing, MI, June 30-July 3,1975; J. Phys. Chem. 1975,79,2789-3079. Proceedings of the International Conference on Electrons in Fluids, Banff, Canada Sept. 5-11, 1976; Can. J . Chem. 1977,55, 1795-2277. (7) Freeman, G. R. Annu. Rev. Phys. Chem. 1983, 34, 463.
0022-3654/86/2090-4224$01 SO10 0 1986 American Chemical Society
Feature Article
H904+and H70,, to the hydrated proton and the hydrated OHion. Until the introductiona of picosecond spectroscopic techniques into the study of chemical kinetics, the direct observation of ionic dissociation in water and of the accompanying ion hydration step was not possible. In order to measure the rates of electron and proton solvation in pure solvents and to uncover any important structural constraints affecting these reactions, picosecond studies using water/alcohol solvent mixtures were initiated in our laboratory in 1976. The mixed solvent afforded a technique whereby the environment of an ion hydration reaction could be probed at the molecular level. The earliest experiments in mixed-solvent systems concerned electrons.21 Many early attempts2* to analyze these data in a convincing way were not completely successful, and it was only quite recently that a kinetics scheme describing simultaneously the rate processes and the quantum yield data could be formulated.23-25 The connection with proton hydration26 came to light after analysis of the electron experiments. For acceptance of these elementary ions, it was concluded that water molecules in the normal liquid had to reorganize rotationally within specific structural environments. The present paper analyzes a variety of new concepts based on these findings: (1) the Debye rotational correlation rate 7D-l as a multiplicative factor in electron and proton dissociation == hydration * recombination rates; (2) emphasis of electron and proton dissociation/hydration rates on local solvent structural properties, rather than on dielectric considerations; (3) confirmation of H904+ as a specific kinetic product in acid dissociation; (4) suggested H804- structure for the hydrated electron; (5) quantitative correspondence between equilibrium thermodynamic variables and classical rate parameters for AGO k 0 electron and proton dissociations into water; (6) domination by entropy in certain ion dissociation rates, free-energy minima not coinciding with energy minima; (7) entropy-dominated isotope effects; (8) water as a simple liquid.
The Journal of Physical Chemistry, Vol. 90, No. 18, 1986 4225
2. Water as a Hindered Rotor The uniqueness of water among liquids depends mainly on two properties: its small physical size and its propensity to retain tetrahedral structural integrity" through highly specific hydrogen bonding with its neighbors. The small mass of the H atom and the absence of a complicated molecular structure allow rapid reorientational motions in the liquid phase. Cooperativity within the hydrogen bonding network causes a lowering of the effective hindering potential with increasing t e r n p e r a t ~ r e . ~Therefore, ~.~~ as the temperature is raised, not only do higher energy states become increasingly more populated but anomalously in liquid water the number of available states in any energy range also increases. Anomalies in liquid water can be traced to this H-bond cooperativity,28while the hindered rotational motions set the stage for important kinetic and thermodynamic properties of water in the pure state and as a polar solvent. Dielectric relaxation,% shear v i ~ c o s i t y ,and ~ ~ -other ~ ~ rotational correlation phenomena33depend on the same type of mechanism. Thus, the hindered rotations of water molecules are central to its thermodynamic and kinetic properties. To describe the various dynamical processes, an analytical approximation to a temperature-dependent rotational rate parameter K(T)in pure liquid water was outlined in earlier work.28 In the case that applies throughout the supercooled and room temperature regimes, eq 5 of ref 28 has a pseudo-Arrhenius form
where the prefactor KO was found to be remarkably insensitive to temperature over the range -40° to +lo0 OC. The rate K ( T )varies with temperature in a non-Arrhenius manner because of the decrease of AH,,,* with increasing temperature. It will be seen in section 9 that the Debye correlation time TD, which is proportional to K - I , enters directly into the dissociation/hydration and recombination reactions of the elementary ions e-, H+, and OH- in water. In addition, T D is related to various temperature-dependent quantities such as the shear viscosity q TD
(8)Kolthoff, I. M.; Rosenblum, C. Acid-Base Indicators; Macmillan: New ; I. M., York, 1937;In Treatise on Analytical Chemistry, 2nd 4.Kolthoff, Elving, P. J.; Eds.; Wiley: New York, 1979;Vol. 2,Part I. (9)Bell,R. P. The Proton in Chemistry, 2nd ed.; Cornel1 University Press: Ithaca, NY, 1973. (10)Taft, R. W. Prog. Phys. Org. Chem. 1983,14,247. (11)Conway, B. E.; Bockris, J. O'M.; Linton, H. J . Chem. Phys. 1956, 24, 834. (12) Conway, B. E. In Mod. Aspects Electrochem. Bockris, J. O'M., Conway, B. E., Eds.; Buttenvorths: London, 1964;Chapter 2, No. 3. (13)Erdey-Griiz, T.; Lengyel, S.Mod. Aspects Electrochem. 1977,12. (14)For recent reviews, see: Kadish, K. M., Ed. Electrochemical and Spectrochemical Studies of Biological Redox Components; American Chemical Society: Washington, DC, 1982;Adu. Chem. Ser. No. 201. DeVault, D. Quantum-Mechanical Tunnelling in Biological Systems, 2nd ed.; Cambridge University Press: Cambridge, 1984. (15) Wicke, E.; Eigen, M.; Ackermann, T. Z . Physik. Chem. (Munich) 1954,I , 34. Eigen, M.; De.Maeyer, L. Proc. R . Soc. London, A 1958,A247, 505. Eigen, M.; De Maeyer, L. In The Structure of Electrolytic Solutions; Hamer, W. J., Ed.; Wiley: New York, 1959;pp 64-85. (1 6) Bascombe, K. N.; Bell, R. P. Discuss. Faraday SOC.1957,24, 158. (17)DePaz, M.;Giardini, G.; Friedman, L. J. Chem. Phys. 1970,52,687. (18)Newton, M. D.; Ehrenson, S.J . Am. Chem. SOC.1971,93,4971. (19)Newton, M. D. J . Chem. Phys. 1978,67,5535. (20)Rentzepis, P. M. Chem. Phys. Lett. 1968,2, 117. Netzel, T. L.; Struve, W. S.; Rentzepis, P. M. Annu. Rev. Phys. Chem. 1973, 24, 473. (21) Robinson, G. W.; Robbins, R. J.; Fleming, G. R.; Morris, J. M.; Knight, A. E. W.; Morrison, R. J. S . J. Am. Chem. SOC.1978,100, 7145. Robbins, R. J. Ph.D. Thesis, University of Melbourne, Melbourne, 1980. (22)See, for example: Robinson, G. W.; Auerbach, R. A,; Synowiec, J. A. Chem. Phys. Lett. 1977,5, 228. (23) Robinson, G. W.; Lee, J.; Moore, R. A. In Ultrafast Phenomena IV; Auston, D. H., Eisenthal, K. B. Eds.; Springer, Verlag: New York, 1984; pp 3 13-316. (24)Lee, J.; Robinson, G. W. J . Chem. Phys. 1984,81, 1203. (25)Moore, R. A.; Lee, J.; Robinson, G. W. J . Phys. Chem. 1985,89, 3648. (26) Lee, J.; Griffin, R. D.; Robinson, G. W. J. Chem. Phys. 1985,82, 4920.
= AvVMq/T
(2)
where VMis a molecular volume, the NMR spin-lattice relaxation times TI for nucleus X (3) and the dielectric relaxation times TD
Td
= AdTd
(4)
Commonly used theoretical relationship^^^ between T D and Td indicate that Ad lies in a range between -0.68 and 1.0. At 25 OC, Td(H2O) = 8.1 PS and Td(D20) = 10.2 PS. In Section 9 rD(H20)is shown to be equal to the OH-(aq) H30+(aq) recombination rate.31 This yields ~D(H20,298K) = 7.0 ps, so that Ad is 0.87. Using this same constant for the D 2 0 data gives T ~ ( D ~298 O , K) = 8.9 ps. The other A constants can be obtained from these T D values and published experimental Av(H20) = 1.30 X 10-8; A,,(D20) = (20 + 18) X Av(H20);AN(H20, l70)= 4.85 x w 4 ; A N ( D ~ Ol70) , = Ap~(H20,l 7 0 ) ;
+
(27) Bernal, J. D.; Fowler, R. H. J. Chem. Phys. 1933,1, 515. (28) Robinson, G.W.; Lee, J.; Casey, K. G.; Statman, D. Chem. Phys. Lett. 1986,123,483. (29) Bassez, P. M.-P.; Lee, J.; Robinson, G. W. in preparation. (30) Hasted, J. B. Aqueous Dielectrics; Chapman and Hall: London, 1973;Chapters 2 and 3. (31) Eisenberg, D.; Kauunann, W. The Structure and Properties of Water; Oxford University Press: New York, 1969;pp 224-227. (32) Kell, G. S. In Water, A Comprehensiue Treatise; Franks, F., Ed.; Plenum: New York, 1973;Vol. 1, Chapter 10. Osipov, Y. A.; Zheleznyi, B. V.; Bondarenko, N. F. Trawl. Shur. Fis. Khim. 1977,51, 1264. (33) Lang, E.; Liideman, H.-D. J. Chem. Phys. 1977,67,718.Lang, E.; Liideman, H.-D. Ber. Bunsen-Ges. Phys. Chem. 1980,84,462.Lang, E. W.; Liideman, H.-D. Ber. Bunsen-Ges. Phys. Chem. 1981,85, 603. (34)Weast, R. C., Ed. Handbook of Chemistry and Physics, 62nd ed.; CRC Press: Boca Raton, FL, 1981-1982,pp F-4,F-5,F-42.
4226
Robinson et al.
The Journal of Physical Chemistry, Vol. 90, No. 18, 1986
D) = 3.9 X when all data are expressed in cgs units. The time T~ is also related through a constant factor A , = 5.6 X to exp[+AfZ,*/RT] of eq 1. Reference 28 gives specific values for AHw*(T). Thus, a variety of methods are available for calculating temperature-dependent T ~ ’ for S use in the analysis of reaction rates. 3. Debye and Longitudinal Relaxation One of the results to be described in this paper is that the elementary ions e-, H+, and OH- near threshold energies hydrate on the time scale of T ~ while , large ions or energetic small ions are more likely to hydrate on the time scale of T ~the , longitudinal relaxation time. P ~ t t e l ’states ~ that in pure water T~ depends on “small reversible shifts ( 13) and higher bonding to H30+ does not contribute significantly. In this assumed hydration process, three strong primary and nine weaker secondary bonds to H30+form, while 12 normal water bonds break. The enthalpy change is thus
into water. This transient is most likely an H20- anion, distorted in some way so that it can be hydrated in an analogous manner as OH-. The most recent a b initio calculation^^^ of negatively charged water have employed the five-cluster geometries of Newtoms6 However, RayS7in 1971 suggested a pentameric structure consisting of a water anion H20- surrounded by four effective dipoles representing neutral water molecules. A recent experimental papers8 estimates the heat of formation of gaseous H20as -(8 f 4) kcal mol.-’ Combining this value withs9 AHf0(298 K) for H and 0-indicates that H20-, compared with H + H + 0-, is 136.5 kcal mol-’ more stable. That is, the 0-H bond energy in gaseous H20- is reduced by -40% from that in neutral water. The electronic ground state of H20- would also be stable with respect to dissociation into H OH- (-26 kcal mol-’) or H2 0-(-32 kcal mol-’). The stability of H20- to autoionization can be obtained directly from the AHfo for H 2 0 (-57.8 kcal mol-’)@ and the above AH? estimate for H20-: H20(g) e-(g) = H20-(g), AH = +SO kcal mol-I. This substantial negative electron affinity of H 2 0would lead to spontaneous ionization of HzO- in the gas phase. AH(hydration) = 9E(secondary) + 3E(primary) In aqueous solution the thermochemistry of H20- is modified. 12AH(normal) (5) However, it is unlikely that an electron attached to an otherwise undistorted water molecule is the intermediate we seek. In fact, giving E(secondary) = (-109.5 69 - 67.9) + 9 = -12.0 kcal a little reflection about the possible pathways for dissociation of mol-’, if AH(norma1) is taken as -5.66 kcal m01-I.~’ The -12.0 H20- leads to the conclusion that the energetically most probable kcal mol-’ value is not far from the ones reported in ref 46 ( n = path in the water solvent would yield OH-(aq) + H(aq). This 4, 5, and 6). is mainly because of the extremely favorable (-101 kcal mol-’) Evidence existsI8 also for tightly bound H704-, as the primary AGhydof OH-.s3 In addition, the thermochemistry of hydrated hydration shell of OH-, though this evidence is not as compelling oxonium H 3 0 is becoming known,61and hydration of this elecas that for H904+. The similarities in the thermodynamic trically neutral radical would also affect the thermochemistry. properties of hydrated H30+and OH-’7*5’and in the electrical Thus, a transient intermediate in the transformation, H20-(aq) conductance properties of the H+ and OH- ions”*12in liquid water OH-(aq) H30(aq), would seem to be a prime candidate for are central to the issue of hydration structure and favor the H704the H80; structure. We tentatively propose a hydrated “semiform. ionic pair” [(OH--H30).2H20] (aq), which also can be interpreted as a hydrated H20- anion with one OH bond highly distorted. 5. Hydrated Electron A reverse Grotthuss transfer” of a H+ from H30to OH- recreates H20- at an adjacent “site” leading to a mechanism for e- mobility The small enthalpy of hydration of the electron (-38 kcal in water similar to that for OH- mobility. An interesting side compared with that of the proton (-276 kcal mol-’)53 light is that through this diffusional process two such entities can restricts the number of electron ionization reactions in aqueous temporarily combine as a solvent-separated pair. This would be media compared with proton dissociation reactions. In those cases, the hydrated dielectron,62which reacts with itself, OH-...H30 + e.g., Na aq Na+(aq) e-(aq), where spontaneous electron OH-.-H30 = 20H-(aq) + H2(g). This is a well-known ionization can occur from a ground-state precursor, rapid sec“bimolecular” reaction of hydrated electrons in radiation chemondary reactions prevent a conventional kinetics study of the istry.’ Supporting this picture further is the fact that the process. “unimolecular dissociation” of the hydrated electron, OH--H,O Experimental results of the type shown in Figures 2-5 indicate OH-(aq) H(aq), is known5 to be extremely slow, the that the structure of the hydrated electron must be closely related equilibrium lying far to the left. More will be said about these to the structure of the hydrated H+ and OH- ions. There is also in a separate p ~ b l i c a t i o n . ~ ~ a similarity between the mobilities of e- and OH- in ~ a t e r , ~ ~ ~ideas ’ From these results, a near-molecular picture for these supsuggesting that a reverse Grotthud’ transfer of H+ to the negative posedly complex reactions of elementary ions in water is emerging ion may be playing a role in each case. Therefore, even though there is little previous evidence for the existence of an entity HsO5 cal K-’ mol-’.64965 Thus, in the case of a strong acid, AHio must be sufficiently negative to counteract the reaction-inhibiting decrease in entropy. Harned and Owen, in their chapter on weak electrolytes,66 review how various thermodynamic quantities may be obtained from ionization constant measurements over a range of temperatures, usually from 0 to -70 O C . The K,(T) values are first fit to a power series in T
log K , = - A * / T
+ D* - C*T
(8) valid within the experimental temperature range, with parameters A*, D*, and C* all positive. Using standard thermodynamic relationships, one then obtains AGiO = A ’ - D‘T
+ C‘p
ASio = D ’ - 2C’T
(9) (11)
where A’= ( R In 10)A*, etc. Note that for weak acid dissociations in water, both AHi’ and T M i 0decrease as the temperature rises. These types of data show that at -298 K in many weak univalent acids, Le., acetic, AHi’ is near zero, in fact somewhat negative, and a purely entropic barrier ASi’ = -20 cal K-’mol-’ stands in the way of acid dissociation.66 This is backward from simple gas-phase dissociation reactions, which normally have positive Mio.For our purposes, it is to be noted that this “normal” weak acid behavior has certain similarities to the case of photon-initiated acids, such as the naphthol^,^^,^^,^^.^^ and parallels electron dissociation^^^-*^ as well.
7. Free-Energy Curves In aqueous media one can imagine discrete stages of elementary ion dissociations: (M) neutral molecule, (CT) intramolecular charge transfer or another type of dipolar state, (IP) solvent-shared ion-pair state, (4C) four-cluster state coupled (weakly) to the hydrated precursor ion, and (D) the four-cluster fully dissociated from its precursor ion. These stages evolve as the interionic distance r increases. A conjecture about the behavior of Hio,Sio,and Gio as the dissociation proceeds along the reaction coordinate r is illustrated in Figure 6 for the univalent strong acid and Ynormal”weak acid cases near 298 K. For clarity, the values of Sio,Hio,and Gio have been taken to bk zero for the fully dissociated ions. In addition, it has been assumed that ASi’ = -15 cal K-’ mol-’ for both the strong acid and ”normal” weak acid cases, realizing of course that this value represents a range from --5 cal K-l mol-’ to --25 cal K-’ mol-’. The figure also assumes that each discrete “bonded” stage in the dissociation process possesses its own enthalpy min(64) Reference 9, Table 9, p 91. (65) Harned, H. S.; Owen, B. B. The Physical Chemistry of Electrolytic Solutions, 3rd ed.; Reinhold: New York, 1958. (66) Reference 65, Chapter 15, p 758. (67) Webb, S. P. Ph.D. Thesis, University of California, Berkeley, CA, 1985. (68) Webb, S. P.; Yeh, S . W.; Philip, L. A.; Tolbert, M. A,; Clark, J. H. J . Am. Chem. SOC.1984, 106, 7286.
‘.‘..
0
.8000 I
qT
IP
-r
4c
D
Figure 6. Top curve: hypothetical Hio(r)for a strong acid. Lower curve: hypothetical -TSio(r)for all acids. The broken curve represents the sum of these two curves: Gio(r) = Hio@) - TSio(r), for the dissociation of a strong acid. The ordinate units are cal mol-’, so the conventional pK, (measured between M and D) of the strong acid represented by these diagrams would be -5.5. For a ground-state weak acid with Mio 0, Le., acetic acid, Gio(r)follows the lower curve and the barrier for dissociation is totally entropic. In the case pictured, the pK, of the weak acid would be +3.3. This value is lower than that for acetic acid (pK, = 4.76), since in that case Mio = -22.1, while the diagram uses Mio = -15.0.
imum, the intermediate r values exhibiting maxima. Thus, the potential energy function defining the enthalpy of the ionization reaction is “cascadian” in nature, in contrast to the double-minimum potentials69usually imagined for charge-transfer processes. In a similar way, Slois expected to be more negative for the structured stages of the dissociation process. Its downward path toward ion dissociation is also cascadian, yielding -TSlo maxima and minima out of phase with the HIo extrema. In other words, the Hlo and TS,O contributions to GIo work against one another as in the conventional compensatory p i c t ~ r e . ’ ~For acids where IAHloI dominates (TASlol,the Glo minima tend to occur at the structured (bonded) stages along the dissociation path, while for acids where (TASlo(dominates, the GIominima favor the intermediate (nonbonded) regions where the structure is broken up in preparation for forming an adjacent structured stage. Thus, in this picture, the properties of acids, weak or strong, depend on the thermodynamic properties of a complicated equilibrium mixture of fully and partially dissociated species.
8. Electrons and Photon-Initiated Acids “Charge delocalization” in the form of more extended electronic orbitals or weaker intramolecular binding of the proton, is expected in electronically excited states. This can cause the free energy minimum for a weak acid in water to move outward from the neutral form, giving greater stability to more polar forms upon excitation. The polar properties, as measured by solvent shifts, of certain molecules in their excited states are known to depend crucially on the dielectric properties of the surrounding solvent medium.” However, what we are saying here goes somewhat beyond this, namely that the free-energy minimum can place itself a t various points along the interionic reaction coordinate-one limit being the neutral molecule, the other limit the fully dissociated ions. In water, ground-state weak acids lie near the former limit, while ground-state strong acids lie in the latter. Apparently, however, an entire range can occur when electronically excited species, such as electron precursors or photon-initiated acids, are considered and when a range of solvents is used. Figure 7 represents one such case-entropically dominated thermodynamics with the Glo minimum between the CT and IP forms. With reference to Table I, this case will be seen to be (69) Newton, M. D.; Sutin, N. Annu. Rev. Phys. Chem. 1984, 35, 437. (70) Lumry, R.; Rajender, S . Biopolymers 1970, 9, 1125. (71) See, for example: Kosower, E. M. Acc. Chem. Res. 1982, 15, 259.
4230 +3000
The Journal of Physical Chemistry, Vol. 90, No. 18, 1986
lh
-6000
I
I
I
I
CT
IP
4C
D
r-
Figure 7. “Entropy-driven” proton or electron dissociation from photoexcited precursor. Top curve: hypothetical Hio(r). Lower curve: hypothetical -TSio(r), the same as in Figure 3 but scale X2. The broken curve represents Gio(r). Notice that the -TSio(r) wells, which occur for the unstructured intermediatestages of dissociation, determine the Gio(r) wells and therefore the most probable equilibrium character of the undissociated state. In the case shown, the most stable state is between an intramolecular charge-transfer state (CT) and a solvent-shared ion-pair state (IP). The AH‘ would be zero in a rate measurement of the dissociation process, while there is a -1700 cal mol-l (-590 cm-I) contribution to the Stokes shift of the emission vs. absorption spectrum. If extended to negative values of r, the curves represent a well and barrier.
TABLE I: Activation Properties and Freauency Factors ‘
system indole AN
AH*dia,
1.7 X 1OIo 0 2.5 X 1O’O 0.79 X lolo 2.4 8.5 X IO9 2.2 X lo9
with solvent molecules, particularly if a locally structured system is formed, these entropy effects must be carefully considered. A knowledge of the temperature dependence is essential for an unambiguous interpretation of such data. In pure water, the deprotonation rate of 1-naphthol is insensitive to temperature (AH* = 0), while that of 2-naphthol exhibits an activation energy of about 2600 cal The pKa* values for the excited states of both naphthol^^^-^^ are known near the standard temperature of 25 OC: 0.4 f 0.2 for 1-naphthol and 2.73 f 0.10 for 2-naphthol. With these pKa* results, the AGio values for the dissociations are +(545 f 270) and +(3720 f 100) cal mol-], respectively. These numbers are consistent with a picture where AH*di,= AHio(for AHio > 0), but AHtdi, = 0 (otherwise), and A S * d i s = Sio. From the above data, these Sio values are -1.8 and -3.8 cal K-’ mol-’ for 1- and 2-naphthol, respectively. In the deuterated cases, the entropies decrease further to -3.7 and -6.2 cal K-I mol-’. Prefactors for the proton dissociation rates in 1- and 2-naphthol have of 2.5 X 1Olo and 0.85 X 1O1O s-’, respectively. Using the above entropies and dividing the two prefactors by e~p[+AS*~~,/l?] give “basic rates”: 6.2 X 1Olo and 5.8 X 1O’O s-’ respectively for protonated 1- and 2-naphthol. In the deuterated systems, the prefactors are 7.9 X lo9 and 2.2 X lo9 s-I, and the basic rates are 5.1 X loioand 5.0 X 1O’O s-I. The concept of the basic rate is confirmed as being equal to the rate at which a proton with no activation barrier or entropy restrictions leaves a large precursor molecule and is trapped by the water solvent. The reciprocals of these basic rates are roughly equal to the Debye rotational times 7 D for pure H 2 0 and DzO. This similarity supports a model where a rotational “bottleneck” in the solvent stands in the way of the overall ion hydration reaction.
M*dina
kcal mo1-I ko, s-l cal K-l mol-’ H b Db H D H D 10.4 10.8 5.0 X I O l 5 2.9 X 10I5 (+23.5) (+23.0) 0 0 2.4 X lo8 0.8 X lo8 -9.9 -11.6 o o 4.0 x 109 1.3 x 109 -4.4 -6.1
ANS TNSC 0 I-naphthol 0 2-naphthold 2.6
Robinson et al.
-1.5
-1.9
-3.7
-3.8
-6.2
“From eq 12, AS* = R In ( 0 - I k O ~ D where )r T~ is the rotational (Debye) correlation time in pure H 2 0 or D20 taken to be 7.0 X and 8.9 X s, respectively. The case of indole does not fit in with the other molecules studied, the large ko and positive &s*d,s being symptomatic of the difference. It is felt that the electron-transferreaction in the case of indole must be determined by intramolecular effects. b H signifies H20solvent, while D signifies D20 solvent. CD experiments not performed. dFrom new measurements. See ref 45 similar to that of 1-naphthol or the ANS derivatives in their excited states, where the activation enthalpy A P d , for proton (or electron) dissociation is zero. For excited 2-naphthol, M * d s is positive for the proton dissociation reaction, giving rise to a qualitatively different GIo curve. A feature of Figure 7, which was also observed in Figure 6 for the weak acid case, is the possibility of a free-energy minimum occurring near an enthalpy maximum, that is, at an intermediate, enthalpically less stable stage of the dissociation process. The result is a system whose initial state tends to “sit on top of an enthalpy hill,” causing AH*dlsto vanish. These initial states, as discussed in section 3, come into equilibrium with their surroundings on the time scale of 7L. In water T~ is not rate limiting in the dissociation/hydration of the elementary ions and normally one need not consider the attainment of equilibrium around the precursor ion as part of the acid dissociation kinetics. Thus, when entropy dominates, free-energy differences depend on the nature of the energy “hills” rather than the commonly supposed “bonded valleys.” Such concepts violate the intuition built up over the years concerning the connection between gas-phase spectroscopic states, spectral shifts, and reactions of excited states in the condensed phase. Spectroscopic data and energy-level discussions alone may therefore be inadequate for arriving at explanations of rate results. When either a reagent or a product species can interact specifically
9. Rates of Ion Dissociation Rate parameters for some H+ and e- dissociations are listed in Table I. If the forward and reverse reaction rates can be expressed in the Arrhenius form, then Mio= [AH*dis- AH*,,]. This is an identity and is nothing new or very interesting. However, if the naphthol results are general for univalent weak acids, then specific relationships exist between the rate parameters AH*dis or AH*,, and the thermodynamic quantity AHi’. In this case the above identity immediately becomes more interesting. Since ASio is always negative for acid dissociations in water, then analogous to the AH* vs. miorelationships, it would be suspected that U * d i s = Sio and AS*,== 0. This idea is borne out by three observations: the agreement between the basic rates in 1- and 2-naphthol, consistency with the results of Eigen et al.,75976 and the agreement with expectations based on 7D-I arguments. Thus, it would appear that very direct and simple relationships connect the thermodynamic quantities AHi’ and ASi’ with the kinetic quantities AH*dh, W,, ils*dis, and AS*,,for weak acid (AGio 2 0 ) dissociations in water: Case I: Sio and AHio are both negative (moderately weak acid) AH*dis = 0 AS*dis
AH*r, = -AHio
= Mio
AS*,,,= 0
Case 11: Miois negative but AHi’ is positive (very weak acid) AG*,jis = AGiO
Actrec = 0
Quantitative absolute rate expressions for weak acid dissociation and recombination rates can be formulated with the above (72) Webb, S. P.; Philips, L. A,; Yeh, S . W.; Tolbert, L. M.; Clark, J. H. J . Phys. Chem., submitted. (73) Harris, C. M.; Selinger, B. K. J . Phys. Chem. 1980, 84, 891. (74) Harris, C . M.; Selinger, B. K. J . Phys. Chem. 1980, 84, 1366. (75) Eigen, M. Angew. Chem. Int. Ed. Engl. 1964,3, 1. A summary has been given in: Crooks,J. E. In Comprehensiue Chemical Kinetics, Proton Transfer; Bamford, C. H., Tipper, C. F.H., Eds.; Elsevier: Amsterdam, 1977;
_.
Vnl R .
(76) Eigen, M.; Kustin,
K. J . Am. Chem. SOC.1960, 82, 5952
Feature Article
The Journal of Physical Chemistry, Vol. 90, No. 18, 1986 4231
TABLE II: Self-Consistent Rate Parameters for Some Weak Acids a
K,(298 K)b
H20
1.81 X 2.0 x 1047 7.0 x 10-4 5.75 x 10-8 5.62 X 1.76 x 10-4 1.75 x 10-5 1.38 x 10-3 (4.0 X lo-') (1.6 X lo-') 1.89 x 10-3 7.6 x 10-4
D20
HF
HIS NH4+
HFm HAC HClAc 1-N(H) 1-N(D) 2-N(H) 2-N(D)
AG*rw =
AG*djs E AH*db TAS"jc
-
n-lkdjt
0 0
[21.48] [22.78] [4.31 [9.88] [12.62] [5.12] +6.59 +5.06 +0.5 +1.1 [3.72] [4.31
0 0 0 0
0 0 0 0 0.10 1.16 0 0 0 0
2.5 x 2.2 x 1.0 x 8.2 x 8.0 X 2.5 x 2.1 x 2.7 x 5.6 X 1.8 X 2.4 X 8.4 x
10-5 10" io8
103 10' 107 io6
107 1O1O 1O1O lo8 107
krwg
kdhf
(2.5 x (2.2 x (7.0 x (4.3 x (2.4 X (1.1 x (7.9 x (1.2 x 2.5 X 7.9 x 1.1 x 3.8 x
10-5) 10") 107) 103) lo1) 107) 105) 107) 1O'O 109 108 107
1.4 X (1.1 x 1.0 x 7.5 x 4.3 x (6.3 X 4.5 x (8.9 x 6.8 X 4.8 X 5.8 X (5.0 X
10" 10")
IO" 1010 1010 lolo) 1010
109) 1Olo 1Olo 1OIo lolo)
nh
1.o (1.0) 0.70 0.54 0.3 1 (0.45) 0.38 (0.45) 0.49 0.44 0.46 (0.45)
"HFm = formic acid, HAC = acetic acid, HClAc = monochloroacetic acid, I-N = excited 1-naphthol, 2-N = excited 2-naphthol, and H and D refer to H20 and D 2 0 solvents. bDimensionsof K. are mol L-' = M. Values in parentheses calculated from experimental kdis/kr, values. 1-N, 2-N from ref 67, 72, and 73, others, ref 66. CInkcal mol-'. Values in square brackets correspond to positive Miosystems and are derived directly from In K, = -AGio/RT with AG*dis (298 K) = AGio;others are for Mio< 0 systems, in which case AH*dis = 0 and h S * d i s (298 K) = aio. See section 9. kcal mol-I, assuming for negative AHi"that AH*rE(298 K) = IMi'l,See section 9 and ref 66. 'In s-I; all values calculated from eq 12 using T ~ - I = 1.4 X 10'' s-' (H20), 1.1 X 10" s-' (D20),and AGtdis in column 3. fIn s-'. Values in parentheses calculated from relationship K, = kdia/kra; using column 7; otherwise measured values from ref 45, 67, and 73. gIn M-' s-I. Values in parentheses calculatedwith k,, = nkD and estimated Q in column 8; otherwise, measured values (see, for example, ref 67, 73, 75, and 76). An unpublished result of J. Lee and G . W. Robinson on k, at 298K for 2-naphthol was used. Values in parentheses estimated; otherwise obtained from columns 5 and 6. thermodynamic connections. Not to be confused with conventional absolute rate expressions, these are
where ASi'' is assumed always negative, Q is a mobility/steric factor introduced by Eigen and K ~ s t i nand , ~ ~the standard-state conditions require unit molarities throughout. The prefactor 0 ~ D - l appears in both eq 12 and 13. This is required because of detailed b~lancing'~ and provides a reciprocity78 between the forward rate of charge hydration and the reverse diffusional recombination rate, two seemingly different physical processes. One-notices too the absence of the classical k T / h factor in these equations. The temperature dependence of the prefactor for small ion dissociations in water lies in 7 D - l and reflects the cooperativity of hydrogen bonding discussed in section 2. Because barriers are surmounted in the rotational diffusion process, 7D-l is much slower than kT/h. The mobility contribution to Q can be estimated from the Debye expression for ion r e c o m b i n a t i ~ n . ~At ~ .constant ~~ temperature and solvent permittivity, this formula states that the recombination rate of two ions is proportional to the sum of their mobilities, (p+ + b-) = (D+ D - ) / k T , where D+ and D- are the diffusion coefficients of the ions. When an elementary ion is one of the partners and the other ion is relatively massive, the recombination rate is approximately proportional to the mobility of the small ion. Relevant mobility data for elementary ion dissociation/recombination reactions are5s3Ie-(H20) = 2.0 X H+(H20) = 3.6 X cm2 V-ls-l . V alues and OH-(H20) = 2.0 X in D20should scale as 7 D - l . Thus, compared with the dissociation of H 2 0 into H+ and OH- ions, the mobility factor would tend toward 3.6 f (3.6 + 2.0) = 0.64 for proton dissociation and 2.0 + 5.6 = 0.36 for electron dissociation from a large molecule. The steric factor in Q arises from the fact that, in the case where one of the ions is fairly large, the full 4 r solid angle is not available for ion recombinati~n~~ or for the ion dissociation process.4s This factor approaches 0.5 in the case of an infinitely large dissociating molecule with accessible ionization site. The observed value of 0 ( H 2 0or D20),which contains both steric and mobility factors, is -0.45 for large proton precursors. See Table 11. Because of the above relationships, it can be seen that the careful measurement of the equilibrium constant K, as a function of
+
~~
~
(77) Fowler, R. H . Statistical Mechanics, 2nd ed.; Cambridge University Press: Cambridge, 1966; pp 659-660. (78) Benson, S. W. Thermochemical Kinetics, 2nd ed.; Wiley: New York, 1976; p 14. (79) Debye, P. Trans. Electrochem. SOC.1942, 82, 265.
temperature, followed by the conventional evaluation of AHi" and ASi" from such gives virtually all the required information for the interpretation of rate data in weak acid dissociation. The only additional unknown quantity is the mobility/steric factor Q, which lies between narrow limits and can be estimated fairly accurately. These points are illustrated in Table I1 for a number of ground-state and photon-initiated weak acids. The connection between 7D-l and the prefactors is confirmed by the H20 = H+(aq) + OH-(aq) dissociation process, where Q is unity. Note that, for the cases of acetic and monochloroacetic acids, a small A H * , should occur for the recombination reaction. For strong acids, AH*r, is expected to be large, and the recombination process is strongly inhibited. Though there is considerable entropy gain in all the recombination reactions, it does not contribute to the recombination rate in the form of positive AS*=.Thus, the data suggest a very simple behavior for these reactions: in the transition region, forward and reverse reactions have the same velocities (detailed balancing); these velocities are given by the rotational rates 7D-I of the water solvent multiplied by a steric/mobility factor 0.25 < Q I1.0; overall reaction rates are equal to these velocities multiplied by equilibrium populations in the transition region as given by conventional thermodynamics. It is interesting that the ordinary compensation effect70 is entirely absent for highly endoergic acid dissociations that occur in H20and NH4+,their entropies lying within a normal (negative) range. This fact, together with the near constancy of the entropically based deuterium effect (see section lo), gives further evidence that, while AHi" depends on specific molecular binding and hydration properties of neutral and dissociated species, ASj" and thus atdis depend mainly on the formation of the H904+ (or H804-) structure. An interesting corollary is that as the initial state lies farther toward dissociation along the r coordinate, the less negative are ASi" and AS*dis.This implies that the excited equilibrium states of the naphthols (also ANS and TNS) in water correspond to a very highly dissociated complex even before the proton (electron) "comes completely off." In spite of the seeming beauty of the above results, the discerning reader will have already noticed a flaw. It has been seen in sections 2 and 6 that the parameters in eq 12 and 13 are themselves temperature dependent! In order to fit experimental data to these equations, one must therefore know and incorporate the temperature dependence of TD-', Mio,and AH,'. If these temperature effects are ignored, as has apparently been done both here and in ref 45, the data fit will surely give meaningless results. However, the situation is saved by a coincidence. What apparently happens is that the activation energy AHw*for rD-'decreases with increasing temperature at about the same rate that AC," increases
4232
Robinson et al.
The Journal of Physical Chemistry, Vola90, No. 18, 1986
with increasing temperature. A near-constant activation energy is the result. This allows a reasonably good correlation of the standard-state equilibrium parameters (298 K) with the temperature-dependent rate data. To illustrate how this works, consider the case of 1-naphthol. Here AH*,,,shas supposedly been measured to be However, according to eq 12 there should be a further temperature dependence of kdlscaused by s," (eq 11) and by AH,.,* of 7 6 ' (eq 1). How meaningful then is the data fit? Referring to ref 66, one notices that AS,"for most weak acids decreases an additional -8 cal K-' mol-] from 0 to -80 "C. This is mainly a result of the high-frequency modes in Hg04'. These vibrations do not appreciably contribute to the entropy even at the higher temperatures, while the entropy of pure liquid water continues to increase. The combined factor 7D-I exp[AS,"/R] thus has a value &' exp[s,O(O "C)/R][17.9 x 10-'2]-' at 0 "C and Ad-' exp[AS,"(O "C)/R][3.0 X 10-12]-1exp[-8.O/R] a t 80 "C, where experimental dielectric relaxation times3' and the relation 7 D = Ad7d have been used. Thus, while the variations in 7D-l and in exp[AS,"/R] with temperature are both large, they are in opposite directions, giving overall values of 5.95 X 10l0(const) at 0 "C and 5.59 X 101O(const)at 80 "C for the above combined factor. The difference is not large enough to pick up experimentally, so that the data fitting gives a zero temperature dependence for kd.. This cancellation effect is not expected to be general, though it may hold approximately for all weak acids and electron precursors. This is no reflection on the validity of eq 12 and 13, only in their application when the full temperature dependence of all the required parameters is not available. 10. Deuterium Effects A general deuterium effect, whose magnitude is reflected by
ApK, = pK,(D) - pK,(H) has been known for a long time in acid dissociation.8O In D,O acids are measurably weaker than in H20. When AH,"I0 for a weak acid then AIPh = 0, and the enthalpic isotope effect on kdlsvanishes. However, a deuterium effect arises from an entropy contribution caused by the low-frequency modes in liquid water, lower for D 2 0 than H 2 0 , and the ''loss'' of such modes in the stiffly hydrated H+ or D+ ion. This behavior is unlike that for many organic reactions, where the prefactor is supposed not very sensitive to isotopic substitution and the activation energy reflects both a zero-point contribution and a tunneling effect.s1 To understand the source of these isotope effects in greater detail, we refer to the paper of Wehry and Rogerss0 on deuterium effects in protolytic dissociations. Figure 1 of that paper indicates that ApK, ranges in a nearly linear fashion from about +0.4 for moderately weak acids (pK, = 2) to about +0.6 for very weak acids (pK, = 10). Considering case I of section 9, AH*dls for moderately weak acids should be near zero. This means that the deuterium effect on kd. can arise from only two sources, one from 7 D - l ~the other from exp(+AS,"/R). Furthermore, in these cases the deuterium effect on k,, derives mainly from 7 D - l . These deuterium effects on kdls,k,, and thus pK, are therefore readily calculated, providing of course that AH*dls is indeed -0. This is certainly the case for 1-naphthol. Taking the case of 1-naphthol specifically (see Table I) and using eq 12 and 13, we find that Ka(D)/Ka(H) = exp[AS,"(D) - AS,"(H)]/R = 0.404
(14)
From this, the value of ApK, is +0.39, in essentially exact agreement with the compilations in Figure 1 of ref 80 for the moderately weak acid case (pK, = 2). Furthermore, since ASl0(D) - AS,"(H) is near -2 for all weak acids irrespective of their pK, (electron dissociations as well), the entropy change will always give a -+0.4 contribution to ApK,. As AH,"becomes more positive and the acids become weaker, a zero point energy contribution to ApK, must also be considered. For 2-naphthol, we see that this zero-point effect is "backward", ~
~~~
(80) Wehry, E. L.; Rogers, L. B. J . Am. Chem. SOC.1966, 88, 351. (81) Melander, L.; Saunders, W. H., Jr. Reaction Rates of Isotopic Molecules; Wiley: New York, 1980.
probably because of the detailed shape of the cascadian curves for the thermodynamic functions. Small shifts of the GIo minimum along these curves can give rise to this backward effect. Aside from the 2-naphthol case, a normal zero-point effect on AH,"is expected to give the upward trend of ApK, values shown in ref 80 for acids of decreasing strength. Even when pK, is around 10 and AH,"is -6 kcal mol-', the additional zero-point contribution to ApK, is only -0.2. This corresponds to a difference AH,O(D) - AHlo(H) of about +280 cal mol-'. The separate deuterium effects on the rates of dissociation and recombination reactions (eq 12 and 13) are also of interest. The isotope effect on 7 6 ' enters in both of these cases, but the overall effect is different for forward and reverse reactions. This difference has been confirmed experimentally for 1-naphthol by Webb et a1.72
11. Conclusions In this paper we have brought together various common aspects of electron and proton dissociations in aqueous media, including ground-state acids, and have thrown new light on a number of long-standing problems. Eigen and his co-workersS2studied the rates of recombination of the hydrated proton with various parent anions. This is the reverse of the acid dissociation reaction. Their work showed that the recombination reaction rate depends on the time required for the ions to diffuse to one another's vicinity. The diffusion of ions in these reactions is adequately described by the equation proposed by D e b ~ e .Even ~ ~ though dissociation rates can be obtained by combining the recombination rate data with the acid constant K,, little information about the molecular details of ion hydration was derived from these measurements. For instance, the special structural requirement of four water molecules is a molecular feature that would have been difficult to characterize through the recombination reaction. Though H904+ has been implicated in transport, thermodynamic, and structural studies,' 1 ~ 1 2 ~ 1 5 we ~ 1 6 believe that the demonstration of the direct dynamical participation of this four-cluster species in the hydration of protons (H804for electrons) is an important advance in the understanding of this type of condensed-phase chemical reaction. Our work thus far has dealt only with weak acids (pK, 2 0), and it is here that the H904+structure is essential for the proton dissociation process. If AGio is very negative in a water solvent, it may also expected to be somewhat negative in certain nonaqueous solvents. Proton dissociations in such solvents cannot involve the H904+ species, so it will be of interest in future work to see what structural constraints, if any, are required in these other systems. If AH,"is sufficiently negative, what structural requirements remain even for water? With this excess energy does the water still have to surmount the AH,* barrier on the T ~ time - ~ scale, or can proton hydration in these cases take place on the 7L time scale? Suggestive correspondences between the thermodynamic variables and the rate parameters for weak acid dissociation reactions is an important new feature of these studies, which needs to be documented more extensively. In many cases, entropy is the dominant factor. The importance of entropy, though ~ e l l - k n o w n ~ ~ in the thermochemistry of acid dissociations, has not been appreciated for rate processes. The introduction of entropy considerations may violate some of the intuition built up over the years concerning the connection between spectroscopic shifts and molecular processes in the condensed phase.71 Enthalpy differences may depend on the nature of the "nonbonding hills" rather than the commonly supposed "bonding valleys." Interestingly, isotope effects in electron and proton hydration rates were also traced to entropy. There is sometimes confusion about the role played by various relaxation times in chemical reactions, but in water at least the picture is becoming clear. This role is played by the Debye rotational correlation time 7 D for the elementary ions (H', e-, OH-), at least if they are not very energetic, but by the longitudinal relaxation time 7Lfor large ions. In water, elementary ions hydrate (82) See, for example, ref 75 and 76.
Feature Article more slowly than large ions. The rate of elementary ion hydration is therefore governed by the true viscosity of bulk water. Conversely, the "microviscosity" governing large ion hydration is a high-frequency viscosity and is much smaller than that of the bulk. An important comment can be made here about the difference between water and other solvents. In water, the high-static permittivity limits the range of Coulomb forces, and attention is thereby focused mainly on local molecular properties of the solvation reaction. When the dielectric constant of a solvent is small, interactions persist over a considerable volume, and the local molecular aspects tend to be lost in the averaging process. Thus, while continuum dielectric theories may be adequate for nonaqueous solvents, a molecular theory is demanded for water. As a corollary to this point, continuum dielectric properties of aqueous solutions are bound to give an incomplete picture of rate processes and spectroscopic observations. Conventional concepts in reaction rate theories, such as the k T / h factors3 and the parabola crossing are absent in the derivation of the hydration rate expressions. A number of modern aspects of condensed-phase chemical reactions seem also to be missing. For example, though tunneling84of electrons and protons undoubtedly occurs in the hydration process, the details of this quantum mechanical process are lost, since tunneling is apparently too fast to be rate limiting. The main quantum mechanical features concern state density considerations and the presence of zero-point effects, which affect both entropies and enthalpies of the reaction and also carry over to the activation parameters. It would seem that these effects in water and aqueous solutions can be estimated adequately without the need for a full-scale quantum treatment of the liquid. The use of frequency-dependent frictions5 seems not to be required in the water problem. Perhaps this is a bit surprising because of the small mass of the hydrogen atom. However, strong-mode coupling among intermolecular librational motions in associated liquids, particularly water, destroys motional memory during extremely brief time spans, causing a near perfect fit of the viscosity and rotational correlation data to conventional hydrodynamic expressions. As long as there are no high, steeply peaked potential barriers to (83) Glasstone, S.; Laidler, K. J.; Eyring, H. The Theory of Rate Processes; McGraw-Hill: New York, 1941. (84) DeVault, D. Quantum-Mechanical Tunnelling in Biological Systems, 2nd ed.; Cambridge University Press: Cambridge, 1984. ( 8 5 ) Grote, R. F.; Hynes, J. T. J . Chern. Phys. 1980, 73, 2715.
The Journal of Physical Chemistry, Vol. 90, No. 18, 1986 4233 surmount,85classical expressions for dynamical motions in water should be valid. The disagreement divulged here between the picture of a hydrated electron as obtained from threshold ionization experiments and that from radiolytic data5-52is a bit surprising. Since our methods give an excellent picture for proton hydration, we have confidence that it is also correct for the electron hydration problem. The parallels in the four-cluster structure, entropy, deuterium isotope effects, ionic mobilities, and the correspondence with q, seem too far reaching to be cast off as coincidences. The range of ASdi, (H20 and DzO)in Table I for the series of AN electron precursors suggests a standard ASo for electron hydration that is negative and roughly the same as that for the hydrated proton. The strong structure-making properties implied by this negative entropy change are specifically at odds with some current which concludes that the electron is a structure breaker. However, those views are based on a thermodynamic cycle86containing two contributions that are not known with certainty. Though water is usually classed as a difficult solvent, and ionic reactions in water are considered particularly intractable, we feel that the work described here on elementary ions in water is giving for the first time a good look at the details of an important solvent role in chemical reactions. Reactions involving these ions, from the molecular level to the thermodynamic level, are now, we feel, the best understood of any chemical reaction in the condensed phase. In future work, such reactions can be used as an embarkation point for the study of condensed-phase chemistry involving larger ions, general mixed solvents, and nonaqueous solutions. We realize that many complications will arise when the transition to these systems is attempted. The problem described here can be thought of as a limit, a narrow limit at that, but one which we feel is a bit more specific than other ion solvation models currently proposed.36 Acknowledgment. Financial support at the PQRL has been shared jointly by the National Science Foundation (Grant No. CHE8215447) and the Robert A. Welch Foundation. G.W.R. wants particularly to thank M.-P. Palmyre Bassez for suggesting a number of important changes in the paper. Thanks also go to Cheryl Starkey for the many hours spent perfecting the final draft of the manuscript. Registry No. D1,7782-39-0. ~
~~
(86) Jortner, J.; Noyes, R. M. J . Phys. Chem. 1966, 70, 770.
