Paul A. Giguere Universit6 Laval Quebec GIK 7P4 Canada
I
The Great Fallacy of the H+ Ion and the True Nature of H30+
T h e term hydrogen ion and the symbol H + are still currently used to designate the entity characteristic of acids (BrQnsted's definition), especially in aqueous systems. Yet, that formulation has been a perennial source of confusion, not only in teaching, but also in interpreting experimental results. Even among modern chemistry textbooks one finds an incredible diversity, if not discrepancy on this most fundamental question. Most authors do acknowledge a more complex species than the over-simple H+. They call it variously hydrated proton (protonated water would he more logical!), proton hydrate, "wet" proton, oxonium ion, and more appropriately, hydronium ion'. As for the formula, beside the right one, H30+, authors use any of the following: H+.,, H+(HzO),, H+(H20)4. (H8.3Hz0)+, HgOqt, etc. In a recent "comprehensive" monograph ( 2 ) Hs0+ is barely mentioned as such! But there is no longer any excuse for such uncertainty. We now have sufficient data, experimental and theoretical, to get a clear picture as I intend to show hereafter. Historical Background The question originated with the theory of electrolytic dissociation (Arrhenius, 1887). Since all common acids contain hydrogen, which they give up readily, it was logical to identify them with the H+ ion, the counterpart of the OH- ion in bases. The invention of the p H scale (SQrensen, 1909) established definitely that practice. However, when physicists began probing the structure of the atom, it was soon realized that H+ is no ordinary ion. In fact, strictly speaking, it is not an ion according to the definition that an ion is "an atom, or group of atoms that carries a positive or negative electric charge" ( I ) . The symbol H + represents, not an atom, hut a subatomic particle, the proton. The proton is unique in chemistry by virtue of its atomic mass and electronic size. Because of the latter it exerts an intense electric field on its surrounding. Therefore, it cannot remain free under ordinary conditions. In the case of aqueous acids it must he combined with the solvent, and H30t is the simplest possible entity. Now, the concept of H30+ got a bad start when it was first mentioned, a t the turn of the century, in a paper dealing with organic compounds of.. . quadrivalent oxygen (3).The formula OHsOH and the name oxonium hydroxide were suggested for it by analogy with ammonium hydroxide, NHqOH. Soon afterwards, physical chemists recognized various indirect evidence for H:iO+ in aqueous acids: for instance from acid catalysis (Goldschmidt and Udby, 1907),cryoscopy (Hantzsch, 19081, molecular volume (Fajans, 19211, and refractivity (Fajans and Joos, 1924) (Cf. Bell (4) for a review). Following the discovery of X-ray diffraction by crystals, Volmer (5) showed that the solid monohydrate of perchloric acid (M.Pt. 50°C) is isomorphous with ammonium perchlorate. From this he concluded rightly that it is an ionic compound, HsO+C104-, not a molecular hydrate, HCIOcH20, as it is still often considered. Definite identification of H30+ ions finally came with the discovery of nmr. In 1951 two independent groups (6) showed that in the crystalline hydrates of strong mineral acids the three protons are equivalent. Shortly after, the fundamental vibrations of H30+ ions were identified in frozen acid solutions (7). Still, from all that evidence one could not infer the nature of the ion in aqueous acids. Indeed, due to the much greater mobility of liquids the association ofa proton with a given H 2 0
+
molecule could well be too short-lived to vield a distinct chemical entity. That seemed all the more likely as a number of early attempts to detect the vibrations of HnO+ had failed. But, explained below, these early studies, mostly by Raman spectroscopy, were doomed to failure. Infrared spectra turned out to he much more revealing as we reported some twenty years ago (8). Our assignment of the fundamental hands of HsO+ in aqueous aciddwas disputed by some (9,10) hut later on definitely confirmed (11,12). Finally, an elaborate X-ray and neutron diffraction study of hydrochloric acid (13)has given Hs0+ the consecration of direct experimental proof. Yet, in spite of all this evidence, it is a safe bet that all the "doubting Thomases" will not he convinced.
as
The Thermodynamics Viewpoint I t is in the realm of thermodynamics that the H+ ion concept seems particularly fallacious, and even absurd. As early as 1919 Fajans (14) estimated the proton affinity of the H 2 0 molecule a t 182 kcallmole, a remarkably accurate value for the time. From that he derived the orenosterous fieure 10-130 . . " for the concentration of free protons in water. In a more picturesque vein Sidgwick (15) wrote that "in loT0universes filled with a 1N acid solution there would he only one unsolvated hydrogen ion!" Therefore, the equation (1) Hz0 = H+ +OHstill currently used to describe the ionic dissociation of water is purely fictitious. Even in the gas phase this process is physically impossible. Because of the high ionization potential of the hydrogen atom it would require an enormous energy: 387 kcal mole-', to he exact. And even if that much energy were provided, complete atomization would take place instead (2) H20-2H+O since it requires only 221 kcal mole-'. Formally speaking, the ionization of water is a bimolecular orocess. which should he written as such (3) 2H20= HsO+,OHThe conventional excuse for the H+ formalism is that it stands for H 0'.But experience shows it is not always so.Take, for instance, the uhlrs of thermodvnumic functions for hvdratim of ions (16). I t is customary to head the list of ions with the
'The present state ul ronfuiiun is wrll rxl*ml,lifirdI,). rulr .{ 14 of the NwntncIature of Inr,ryanic ('hem~stryof the IL!1'.4CI 1 1 ,. "The ion HgO', uhleh is in fact the monr.h\dn,ted un,tun, 1s to hr known as the oxonium ion when it is believed have tdis constitution, as for example in HzO+CIOc,oxonium perchlarate. The widely used term hydronium should be kept for the cases where it is wished to denote an indefinite degree of hydration of the proton, as, for example in aqueous solution. If, however, the hydration is of no particular importance to the matter under consideration,the simpler term hydrogen ion may be used." (Italics mine.) And for good measure there is a footnote. "Thecommittees concur in oxonium for the ion H-Of. but see little dration." All this notwithstanding, hydronium sees preferable to oxonium which applies to all compounds of trivalent oxygen. /'
Volume 56, Number 9. September 1979 1 571
objectionable H+. I n the case of partial molal volumes, the accepted value, VH+" = -5.4 cm3 mole-I a t 25", refers obviously to the H30+ ion, not to the bare proton. However, when it comes to the enthalpy of hydration, this time the given value, AH = -270 kcal mol-', refers not to the HaO+ ion, hut t u H7; which explains why it is more than twice as large as for the other monovalent ions. Actually, that quantity is the sum ot'two quite different terms. Pirrt i i the enthalpy of the gasphase reaction H 2 0 + H+
-
H30+ AH0 = 166 kcal mole-'
(4)
also known as the proton affinity of HzO. It has been measured accurately, in particular by mass spectrometer (17). (Cf. (18) for a review). Clearlv. .. it does not belona in the above tables since reaction (4) is not a hydration. In hydration processes the H z 0 molecule retains essentially its structure. What we have here, instead, is a true chemical reaction, with formation of a stronz covalent bond. Incidentally, the O-H bonds in the free ~ ~ ion, 0 130 : kcal mole-', are even stronger than those in H ~ 0 , 1 1 kcal 0 mole-'. The other term, namely the enthalpy of hydration of the gaseous H30t, is not known so accurately. Values ranging from -70 to -125 kcal mole-' have been reported for it (16). This wide uncertainty may stem from the present dichotomy. At any rate, the accepted value, -103 kcal mole-', seems reasonable by comparison with -106 and -101 kcal mole-I, respectively, for the isochore Na+ and OH- ions. In retrospect, the confusion between H + and H30+ appears as a remnant of the traditional lack of concern of thermodynamicists for things structural. The Real H 3 0 t
The above mentioned nmr studies (6) not only established the H-~"2 -0- + ion as an entitv hut also vielded some structural ~ - information; i.e. the nonhonded H-H distance (Fig. 1). Because the O-H distance was not measurable by that technique it was not possible to decide between a flat triangle and a shallow pyramidal structure. The latter, more probable by analogy with the isoelectronic NH3 (19), was later confirmed by neutron diffraction (20). In fact, the O-H bonds have the same length as in ice, and apex angles fall generally between 110" and 115". This means a rather flat pyramid, 0.25 to 0.3 A high. Likewise, the dynamics of H30+ have been studied in various crystalline compounds, mostly by infrared (21). Indeed, because of the ionic charge on the hydrogen atoms, the HqOf ion is stronelv .. . nolar. . Therefore, its vibrations (even the parallvl ones) art: t w weak tu bc, detected ensdy IIV the Hamnn effect. This accounts rm thr a h w e mentioned failure of mrly studies. In liquid acids the overwhelming absorption of water makes more difficult the observation of the HaO+ bands; particularly the two O-H stretching (Fig. 2). Still, the weak maximum around 2900 cm-' clearly belongs to the ion. Its low frequency (compared to 3100 cm-I in watrr, is i n d ~ r n t i wof \.cry strong hydrogen hmding. The tu,o bending m o d w I.,. the symmrtric, rentt!nvl aruund 1200 cm-1, and u.1 .it I X 0 ~
Frequency (cm-')
~
Figure 2. Infrared absorption spectra of thin films of the four hydrohalic acids. (Concentrations in mole per cent). Reproduced from ( 12).
cm-' are much more obvious. The former, located in a "window" of the water absorption, can be detected even in a 1M solution: that is with some fifty water molecules per hydronium ion. Interestingly, the same lower limit holds for the 3610 cm-I Raman hand of the OH- ion in alkaline solutions (22). Finally, diffraction methods have provided direct confirmation of H30+ ions in liquid acids. Liquids always give rather diffuse diffraction patterns from which structural information is not easily extracted. Nevertheless, much progress has been achieved by using these data to test theoretical models. In the case of water this had led to accurate interatomic distances (23). A similar extensive investigation (13), using both X-ray and neutrons, has enabled measurement of the O-H (or rather O-D) bond length of the ion in concentrated hydrochloric acid, 1.02 A. More important, perhaps, is the O-H-0 distance, 2.52 A (Fig. 3), significantly shorter than that in water, 2.83 A (23). From these data a model, was proposed (Fig. 4), in which H30+ is coordinated to four water molecules; three of them linked by strdng H-bonds, the fourth, by much weaker cbarge-dipole forces. In short, the geometry of the H:%0+ion, whether in crystals or in liquid acids, is now known with same accuracy as that of H 2 0 in liquid water, ice, or the hydrates. The Average Lifetime ol H 3 0 +
Figure 1. Structure ol,the average H30t ion in various crystals.
572 1 Journal of Chemical Education
Obviously, an important property of the HaO+ ion in aqueous acids is its average lifetime T . I t has been the object of much speculation and calculation. A first estimate of 0.24 psec (lo-" sec) was calculated a priori by Conway, Bockris and Linton (24) from their elaborate measurements of proton conductance. A higher value, by about one order of magnitude, was derived by Eigen (25) from his dielectric relaxation data. The exact value, however, was found by means of nmr through
various methods. Meiboom (26) first used the 170-induced proton relaxation to measure the rate of the acid-catalyzed proton exchange reaction in water and very dilute acids:
More accurate measurements (27) have yielded a rate constant k, = 7.9 X lo9 1mole-' sec-' a t 25°C. The half-life of that bimolecular reaction, 1 to5 = - =
k.c
1 = 2.2 psec 7.9 X lo9 X 55.35
(6)
is, therefore, the average lifetime of H30+, T. Now, a most significant corollary to these measurements, which has been generally ignored, was the determination of the rate of the base-catalyzed proton transfer, HzO
+ OH- SOH+ H20
(7)
I t turns out that this reaction is about half as fast as its acid counterpart; namely k b = 4.5 X lo9 1mole-' sec-'; hence tos = 4.0 psec! It is an ironic observation that the OH-ion in water has an average lifetime barely double that of HaO+, yet its reality has never been questioned. Incidentally, this ratio of
0
1'
.-
0
0
-I
r c l 160
HCi 8.20 H20 -I
HCi 399 H20 -I
1:2 was already known from the excess mobility of these two ions, as pointed out by Conway et al. (24). Short as these lifetimes may be, they are sufficient for both ions to vibrate as discrete chemical entities. For instance, the lowest frequency in the spectrum of HaO+, 1200 cm-', requires a minimum lifetime of only 0.03 psec. The corresponding figures for the other vibrations are listed in Table 1. Obviously, as the concentration of the acid increases, so does the average lifetime of the HaO+ ions, while that of the Hz0 molecule decreases. The numbers in Table 2 are based on Eieen's anproximate relationship between lifetime and concentration (28). It is not often realized that because of the fast uroton exchange, the average lifetime of a given Hz0 molecule in water is less than one millisec. at ordinary temperature.
-
The M e c h a n i s m of Proton Transfer
Proton transfer reactions are among the fastest and most common reactions. They are important not only in solution chemistry, but also in the gas phase and in biological systems (for instance in carrying electric charges within proteins as zwitterions). In condensed phases, proton transfer obviously takes olace t h r o u-~ bhvdroaen . - bonds. The latter. then.. mav. be regarded as a preliminary stage. On the basis df their conductivitv measurements Conwav. Bockris and Linton (24) concludkd that the rate-determining step could not be a classical proton migration, nor quantum mechanical tunnelling, hut rather rotation of the water molecules that accept the proton. Intuitively, we can picture as follows the most favorable situation: (a) the three O-H-0 nuclei are co-linear, (b) the 0-0 distance is a t a minimum, and (c) the 0-H stretching is maximum. Since the actual transfer occurs via stretching of the O-H bond, its period is roughly the same sec). Note that (Table 11, about 10 fsec (1 femtosec = this takes only 0.2% of the average lifetime of H30+. The hvdroeen bond distance. 0-0. is a most imuortant parameter, of course. Originally, it was assumed that the potential curve for oroton transfer was of the double-well tvue. Given the experimental distance of 2.52 A,and an O-H boid leneth of 1.02 A (13).this leaves less than 0.5 A for a uotential hairier. I n fact, quantum mwhanicnl ralnrlntions 13i1shuu,ed that in that case the "wress urnton" w i ~ ~ tw l d trar111tv1inn single asymmetric potential well. However, the abobe 0-0 distance is an equilibrium distance. One must also take into account the thermal vibrations of atoms. In liquid water and ice the root-mean-square amplitudes of H and 0 atom vibrations are of the order of 0.2 A (30). Interestingly enough, Newton (29) has found by ab initio calculations that for an Table 1. Approximate Values of the Vibrational Frequencies, Periods, and Number of Vibrations (N) ot the H,0+ Ion in Water and Dilute Acids.
Figure 3.Correlation functions from Xqay diffraction paitern of hydrochloric acid ~oiutions,reproduced from Triaio and Narten (13). O-H stretch. HOH bend. (asym.) HOH bend. (sym.) Libration Translation Table 2.
pH
u Figure 4. Model illustrating the average coordination of H30i ions in dilute aqueous acids, redrawn from ( 13).
TS
3000 1700 1200 800 300
0.01 0.02 0.03 0.04 0.1
200 100 75 50 20
Average Lifetime T of a Given H,O Molecule in Aqueous Acids and Bases at 25% ras
7..
rm
hall-llfe due to add-catalyzedproton transler.
vb. half-lifedue to base-catalyzedproton transfer.
Volume 56. Number 9, September 1979 1 573
0-0 distance of 2.37 A or less the notential curve of the nroton is of the single, symmetric-well type. This is reasonable considerine the short distance involved. Therefore, it seems tunnelling plays no significant rdle hericontrary that to current belief. This, then, raises the question of why the protons spend most of their time covalently bonded in H30+ ions? The answer must be that proton transfer in aqueous solutions is a concerted process involving reorganization of the hydrogen bond pattern around the "excess or defect proton." Indeed, the short lifetime of HsO+ (and OH-) is comparahle to the lifetime of the hydrogen bond (31). This model, which relates proton transfer with thermal agitation, can account for the anomalies of proton conductance; in particular the large decrease in the heat of activation with temperature, from 2.5 kcal mole-' at room temperature down to one tenth that value near 400°K (32). What about H.04+?
The H904+formulation often used in textbooks was first postulated in 1954 on the basis of such indirect evidence as s ~ e c i f i cheat and entronv Since then it has received .-(33). . sipport from various sources, both experimental and theoretical (10). Eigen (281, with whom it has become identified, looked upon it as the hydration complex of H30+ (primary hydration shell); that is, essentially, as in the abovemodel (Fig. 4). Nevertheless, the Hg04+ formulation is misleading because it does not distinauish between the covalent O-H bonds of H30+ and the hy&ogen bonds to the three water molecules. Furthermore, i t suggests that the ionic charge is evenly distributed over the whole complex. Chemical intuition tells us, on the contrary, that it must rest mostly on the central H30+ ion. Actually, Newton and Ehrenson (29) have calculated that in the free H904+ species, only 7% of the positive charge is transferred to each of the three water molecules. In other words, the various building blocks in this complex largely retain their identities. A better formulation would be H30f :iH20. But even this is not always correct; as, for instance, in very concentrated acids where there is insufficient water for complete hydration of the H3Of ions. At any rate, there is no need to specify the extent of hydration in this particular instance. Here again the OH- ion provides a valid term of comnarison. Because of its neeative charee it is a strona .. hv. drugen Iwnd ucreptor. 111 fact, there is conrlusiee widt!nre, tanh from mass snertrumetrv (18) and o b inirio calculations (29), that the 0 < - . 3 ~ z 0 complex is particularly stable, with hydrogen bonds nearly as strong as those in H30t.3Hz0. But we never formulate the aqueous OH- ion as H70r-. Why, then, write Hg04+ in lieu of H30+? What about H502+?
The H502+ ion, variously called proton dihydrate or diaquohydrogen ion, was suggested first by Huggins (34) to account for the abnormal mobility of the proton in water. He pictured it as a strong, symmetric hydrogen bond linking two water molecules (HzO.H.OHz)+. So far, however, HsOzt ions have been observed onlv in the solid state (20. 21 1. Their characteristic is a very ihort 0-0 distance (2.41-2.45 A). Otherwise, their aeometrv varies considerably from one tcr theo;her depending on th(.irsurro&dinc in the wmpo~~nrl cr\fstal lattice. This is true, in particular, of the luration of the excess proton, which ranges from a centrosymmetric HsOz+ to the hydrate H30f.He0 (35). Clearly, the HsOzt ion is an uncommon species which requires stabilization by the crystal field. In spite of this, the concept of "H50zf grouping" in aqueous acids (and conversely, H302- in bases) is still advocated by Zundel and coworkers (10,36). Its main feature is said to he "an easily polarizable hydrogen bond;" in other terms, the nroton fluctuatine verv r a ~ i d l vbetween two water molecules which retain t h z r idkntiiy, ior between two OH- ions in HaOz-). But this is contrary to experimental evidence, hoth 574 / Journal of Chemical Education
from spectroscopic and diffraction data. The three water molecules in the H30+.3Hz0 complex must he equivalent on the average, except during the fast proton transfer. And this, in the final analysis, is what these "Hs02+ and H30zgroupings" refer to; namely the activated complex, or transition state of the proton transfer reaction. Like all activated complexes they dissociate a t the first vibration. As a consequence, the 0--H stretching band of the proton donor is broadened considerably towards low frequencies. In fact, this so-called "continuum'~occursalso in no;-aqueous acid solutions, e.g. CH30H (lo), and in the H-X hands of supersaturated hvdrohalic acids (37). In short. there are nodistinct H5O2+ions or groups in aqueous acids The Strange - Case of Hydrofluoric Acid
A typical example of the errors engendered by the HC ion fallacy is the current theory of hydrofluoric acid. Chemistry textbboks tell us that hydrogen fluoride in dilute aqueous solution is a weak acid, like formic and acetic acids. This is a most surprising observation considering that the other three hydrogen halides are very strong acids. The "accepted" value of the pK, based on electrochemical measurements, is 3.2 for HF, compared with -7.4 for HCI, -9.5 for HBr, and -10 for HI (38). . . Now. what could be the reason for such an enormous difference-more than 101O-between the dissociation constants of H F and HCI? That riddle has long challenged the imaginations of chemists. Back in 1912 Pick (39) put forward an hvpothesis which has endured ever since. Essentially he pos&iated that the dissociaiion is a two-step process:
HF-?IH++F-
(8)
2
HF + F- HF2(9) The first equilibrium, kl, which must be rewritten thus, H20 + HF + HaO++ F(10) would lie far to the left (the dissociation amounting to only 2% in dilute solution), and the second one, kz, slightly to the right. But, that hypothesis raises some serious objections. First, chemical intuition tells us that the H-F bond, which is nearly 50% ionic in character (40), cannot remain undissociated in a strong ionizing solvent like water. More concretely, Pick's hypothesis cannot account for certain properties of hydroflnoric acid. For instance, contrary to ordinary weak acids, H F in water seems to become more and more dissociated with increasing concentration. So much so that in the pure state it is near& as strong as sulfuric acid, judging from the Hammett acidity function (41). Likewise, the vapor pressure and boiline-. noint curves of the H9O-HF hinarv ~rovide " svstem " clear evidence against Pick's model. Hydrofluoric acid, like the other three hydrohalic acids, shows strong negative deviations from Raoult's law leading to a maximum boiling azeotrope (Fig. 5). This can only mean that the solute is largely ionized over that concentration range. Otherwise, undissociated H F would lower the boiling point of water. The Key to the Riddle
The apparent contradiction between the electrochemical, and the other nhvsio-chemical nro~ertiesof hvdrofluoric acid has been resoivld thanks to infrared spectrbscopy (42). As may be gathered from Figure 2 the absorption spectra of the four hydrohalic acids show great ressemblance. The major difference in the case of H F is a large shift of the strong vr band to about 1830 cm-I. Such a large shift (100 cm-I) is uncommon for an OH bending mode. I t is indicative of an exceptionally strong H-bond. ~ogically,it must he related to the electrolytic anomalies mentioned above. A suitable model to that effect is the strongly hydrogen-honded ion pair, or proton transfer complex, .. . H---H+.. .F-
weak acid because of the limited dissociation of the strongly H-bonded ion pairs, H30+-F-, the predominant species in dilute solutions. (7) The erroneous H+ ion formulation, and names such as "proton hydrate" should he abandoned to avoid confusion. Likewise, there is no need, in gerneral, to indicate the extent of hydration of the hydronium ion as in H30+.3H20. The term hydrogen ion is here tostay, of course, like other time-honored misnomers in Science. Literature Cited
waipnt
x
Figure 5. Boiling-point H20-HCI.
HF
Wcigh1.l.
HCi
curves 01 the binary systems H20-HF
and
Ion pairs of hydronium chloride and bromide had been detected previously in liquid sulfur dioxide (43). Normally, one would not expect them in measurable concentration in aqueous solutions. However, the case of hydrofluoric acid is unique in that the F- ion is the strongest proton acceptor known, as shown by the remarkable stability of the HF2- ion. This, coupled with the strong proton donor nature of &0+, explains the great strength of these ion pairs. Therefore, the dissociation process should be represented as follows:
+
H 2 0 HF
-
(H30t..
.F-)
+ H30+
+ F-
(11)
Judging from the freezing-point lowering (41) only about 15 oer cent of the ion oairs are dissociated at infinite dilution. As the concentration of HF increases, the F- ions gradually reolace the H,O moleculee which stabiliee the ion pairs. This, cdupled with ihe incipient formation of HF2- ions, increases the number of charged species, and the apparent strength of the acid. Thus we see that, contrary to the heavier hydrogen halides, H F behaves as a weak acid in aqueous solutions because the F- ion is a hetter proton acceptor than H20. CohcluSIOnS The present review may be summarized as follows: (1) The hydronium ion H30+ is just as real as its counterpart, the hydroxide ion OH-. (2) In water and aqueous solutions both ions are equally short-lived due to rapid proton transfer. Their average lifetime a t 25OC are respectively 2.2 and 4.0 psec, as measured by nmr. (3) The existence of discrete H30+ ions, first detected hy infrared spectroscopy, has recently been confirmed directly hy X-ray and neutron diffraction in hydrochloric acid. (4) In aqueous acids the H30+ ion is strongly H-bonded to three H z 0 molecules, with 0-0 distances (2.52 A) much shorter than in pure water (2.83 A). (5) Proton transfer between H30+ and water (or water and OH-) is a concerted process accompanied by rearrangement of the H-bond network. It takes less than 1 per cent of the average lifetime of the H30+ ion. (6) Contrary to current theory H F is mostly ionized in water like the other three hydrogen halides. I t behaves as a
(1) Weas% R.C., (Editor). '"Handbaok ofchemistry and Physic.," 55th ed. The Chemical Ruhber Co. Cleveland, Ohio. 1975. pp. Bd5. F-98. (2) Franks, F., (Edilnrl. "Water. A Comprehensive Tieatire." Val. 3, "Aqueous Solutions oiSimple Electrolytes.'' Plenum P ~ e r sNPW , Ymk, 1973. (3) Collie, J.N.,andTickle,T., J . Chrm. Soe, 75.710 118991. (4) BeI1.R. P.;'TheProtonin Chemistry,'(2nd ed.Curn~ilUniversity Pross,NewYork, 1973. I51 Volmer,M.,Ann. Chem., 440,200i19241. (6) (a) Richards, R. E., and Smith. J . A. S., Trans. Farodoy Soc, 47, 1261 (19511. lhl Kakiuchi, Y., Shomo. H.. Komatsu, H.. and Kigmhi. J.. J. Chem. Phya.. 19. 1069 119511. (7) (a1 Bethell, D. E..and Sheppard. N., J . Chem. Phys.. 21,1421 1195:l); lbl Ferrin0.C. C..and Harnig,D. F., J.Amm Chem Soc.. 15,4113 l195?l:lcl J . Chsm. Phya., 23. 1464 (1955); Id) Taylor, R. C.. and Vidaie, G. L.. J. Am., Chem Soc.. 78. 5999
1969. ( I l l Downing, H. D.,snd Williamr,D., J . P h y s Chrm., 80.1640(1976). I121 Giguire, P.A..andTurrell,S.. Con. J . C h m . , 54,8477 119761. (131 Triola, R.. and N8rten.A. H.. J . Chem. Phys.. 63.3624 i1975l. (141 Fajans, K.,Rrr., 21.709 (19191. 1151 Sidgwiek, N. v.,"The Chemical Elements and theircompounda." Oxford University PIOSI. London. 1950. p. 19. I161 Friedman.H. L..and Klisnan. C. V..Chapter 1 of ref 121. (171 la) Keharie. P., J . Chem Phyq., 5.3, 2129 (19701. (h! de Pa%,M.. Ehrensan, S., and Friedman. H. L.. J . Chrm. Phir.. 52,3362 11970). (I81 H8pler.L. G., and Wuo1l~y.E.M..Chapter 3oirei. (21. I191 Giguire, P.A.,Reu. Chim. M i n , 3.627 119661. (201 Schuifer. P.. Zundel, G., and Sandorfy. C.. IEdilors!. "The Hydrogen Bond."NorthHdlsnd Publishing Co. Amsterdam, 1976.Chapter 10. Lundgren, J. O..and Olovson, I. p. 471. (211 Williams, J. M.. Chaptw 14 iriret I201 p. 655. 122) Turre1l.S.T.. Unpublished results. (231 (a1 Narten.A.H..andLeq.H. A.,Srieocr. 165,447(19691.lhlNarten.A.H.J . Cham. Phys., 56.568 119721. (24) Conway, B. E., Boekris, J.O. M.,and Linton.H.. J Chpm Phys.. 24,834 119561. (25) Eigen, M., An~riu.Chem.. 75,489 11963). (2fiI Meihuom.S.,J. Chrm. Phyn.. 34.376 119fill. 1271 (a! G1ick.R. E..andTewari, K.C.. J Chcm. Phus., 44.546(196fi). (hlRahidesu.S.W.. and Hetch, H.G., J . Chrm. Phyr., 67.544 119671. I281 Eigen. M.. and De Maeyer. I. .. Proc. Rny. Soe.. A247. 505 119581. 1291 la! Newtun. M. D..and Ehrenran,S.,J. Amrr. ChemSnc.. 9Z,(49711, ihl Newt0n.M. D.. J . Chsm. Phys. 67,5586 119771. (30) Eisenherg. D.. and Kauzmann. W., "The Structureand Pmwrtier ofWater."Oiford University P i e s . London, 1969.p. 77. (31) M
