The hydrated hydronium ion - Journal of Chemical Education (ACS

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H. Lawrence Clever

I

-he Hydrated Hydronium Ion

M o s t students of chemistry are introduced to the concept of the hydrated in aqueous solution. The high charge to size ratio of the proton and its high force of attraction for water molecules is emphasized in most beginning textbooks. The monohydrated proton or hydronium ion, H30+, is usually the only species discussed. It is also an important. species in any discussion of the Rt6nsted theory of acids and bases. Recently the trihydrate of the hydronium ion, B30+.3H10or HSO4+,has been postulated to explain many observed properties of aqueous strong acid solutions. I t is the purpose of this brief review to cite and discuss some of the evidence for the existence of this trihydrated hydronium ion. The older evidence for the existence of the monohydrated proton, H30+, is outlined as a n introduction. More detailed discussions can be found in Wicke, Eigen, and Ackerman (1) and in Bell (8). Evidence for

+ HzO

The Hydrated Species Hs04+

Over the past 10-15 years considerable experimental evidence has accumulated which can hest be explained by a trihydrate of the hydronium ion, H30+.3Hz0(also represented by the formulas Hg04+ or H+(H10)4). Wicke, Eigen, and Ackerman (I) suggest, the structure of this unit of proton and primary water of H

H30+

Quite conclusive evidence for the hydronium ion in solids is hased on the nature of solid monohydrates of strong acids. The fact that ammonium perchlorate and perchloric acid monohydrate crystals are isomorphous and give similar X-ray patterns suggests an ionic H,O+ C104- structure (5). Nuclear magnetic resonance studies of solid HCIO1.HzO, HNO3.H2Oand HzS04.H,0 give spectra characteristic of three equivalent protons. This suggests either a planar or pyramidal H30+. Detailed consideration of observed prot,on-tnbroton distances leads to the conclusion that the hyjronium ion is a flat pyramid with H-0-H bond angles of about 11.5' (4). Infrared studies of hydro~alogenmonohydrate solids show four fundamental irequencies characteristic of a pyramidal H30+ ion (5). Estimates of the proton affinity of water based on the ?roperties of hydrohalogen monohydrate crystals after L logical estimate of their crystal lattice energy give ralues (6, 7) which agree with direct theoretical es,imates of the proton affinity (8). Direct confirmation of the presence of the hydronium n m d~lute . .aqueous solution of strong acids is difficult. ell (2) pomts out that the characteristic properties ~f the hydronium ion will diff'er littre from those of vater which is always present in large excess, and that he rate of exchange of the proton between water lolecules may he so rapid that the H,O+ lifetime is too hort to characterize its properties. Infrared spectra have heen obtained of thin films of oncentrated strong acids (Q), which contain three of he same four bands observed for the H30+in solids (5). Kinetic and electrolytic evidence for the hydronivm )n in solution comes from studies of nonaqueous solents containing small amounts of water. The reaction

b.

s ROH + H,O+ is part of a reaction scheme consistent with the rate of acid-catalyzed esterification reactions in alcohol containing small amounts of water (10). Other assumptions about the hydration of the proton do not fit the rate data. Liquid sulfur dioxide dissolves equimolar amounts of HBr and H20. Upon electrolysis one equivalent of water per equivalent of hydrogen is liberated a t the cathode (11), which suggests that the proton migrates into the cathode compartment as H30+. Ht(ROH)

H

~ 4 '

I

fH

H hydration to be a pyramidal hydronium ion hydrogen bonded to three moles of water. The H30+acts as a h w i s acid in reacting with three water molecules to form the H904+complex. To add a fourth water molecule to the H80' oxygen would require the complex to react as a Lewis base and if the Hl,Os+ formed, the fourth water would probably be much less strongly bonded than the other three molecules. Thus it seems reasonable to regard the H,O+.(HIO)*or Ego4+ as the primary hydrated species. The three hydrogen bonds are thought to be of greater than ordinary strength because the charge of the proton is directed along the three honds rather than being distrihuted uniformly over the surface of a sphere as is the charge of a metallic ion. Baughan (18) has worked out a cycle, hased on the properties of hydrogen halides, that results in a value of 283 kcal for the reaction H+ (8) HsO HsO+ ( a d This reaction is the sum of prot,on affinity, H a + (g) H+ (8) H*O (g) and hydration of the gaseons hydronium ion, HaOC(g) H1O HIO+ (ad The proton affinity is about 180 kcal (6, 7, 8). The difference of ahout 100 kcal can be assigned to the

+ +- -

+

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hydration step. The hydration energy is made up of contributions from the three hydrogen bonds in the HB04+structure and the additional hydrogen honds of secondary water of hydration to the primary hydration shell. If the three hydrogen honds in the H,04+ structure are responsible for more than 15-8 kcalof the 100 kcal hydration energy, they are stronger than conventional hydrogen bonds. The exprimental evidence to support the existence of the Hg04+ion comes from the following: Extraction studies on strong acids from water into basic solvents, Field emission and mass spectrometry of water vapor, The interpretation of the Hammett acidity function of strong acids, The infrared spectra of aqueous strong acid solutions, The activity coefficients of strong electrolytes, and The heat capacity of aqueous solutiom of strong acids

Both the extraction studles and the field emission and mass spectrographic studies give indirect evidence of the H,O,+ ion in aqueous solution since they indicate the existence of ions in non-aqueous liquids and it> water vapor, respectively. However, if the H901+ is a probable species under such conditions, it may well he a probable species in water solution. The other experimental studies were made on aqueous solution. The H,04+ existence depends on acceptance of the theoretical interpretation of the data obtained. Not all of the theories used have won universal acceptance but the evidence from 80 many diverse viewpoints seems convincing. Extraction Studies

Fairly strong evidence for the HB04+ion in nonaqueous liquids comes from the study of extraction of aqueous strong acids into basic solvents. The review of Marcus (31) on extraction contains a con~prehensive section on the distribution of strong acids between water and basic solvents. A particularly useful study is that of Tuck and Diamond (19) who have extracted strong aci.3~ from water into basic solvents l i e dibutyl Cellosolve, diisopropyl ketone and tri-n-hutyl phosphat.e. I n a typical experiment, five ml of aqueous strong acid solution is extracted with five rnl of the basic solvent in a graduated tube of small bore. If the total volume of the syst.em does not change, the decrease in volume of the water layer can be interpreted as water carried into the organic laycr with the acid. When perchloric acid is extracted into either dihutyl Cellosolve or diisopropyl ketone, the volume change in the water layer is linear with the amount of acid extracted and amounts to a little over four moles of water per mole of acid. If only the proton is hydrated in the water laver, this is good evidence of the II+(H,0)4 (or ~ ~ 0 ~ ~ ) . When HCl, HRr, or HCIOI is extracted into t,ri-nSutvl ~ h o s ~ h athe t e water volume carried with the acid is ];near with extracted acid to fairly high acid concentrations hut amounts to only three molecules of water pr acid molecule extracted. 'This is still consistent with the I-IB04+ion since water saturated tri-n-butyl phosphate (TRP) has one mole of water per mole TBP which results in a net exchange of only three moles of water per mole of acid during extraction. 638

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Journal of Chemical Education

This is confirmed by the work of Baldwin, Higgins, and Soldano (14) who have analyzed the acid-TBP layers for water by the K. Fisher technique and find water-toacid ratios of 4.1 and 4.6 for HC1 and HBr, respectively. Ext.raction of the strong acid HFeC14into diisopropyl ether carries 4 water molecules per molecule of acid. Electrolysis and ultraviolet spectra of the organic phase indicate that all of the water is associated with the H + and none with the anion (16,16). Extraction studies on nitric and trichloroacetic acid into dihutyl Cellosolve (19) are also consistent with the HgOa+ion if corrections for the dissociation of these acids in the water phase are made. Extraction studies also give evidence of the hydronium ion itself. Whitney and Diamond (30) finds that when perchloric acid is extracted into a less polar organic phase such as TBP diluted in some hydrocarbon only one mole of water is carried per mole of acid extracted. Field Emission and Mass Spectrographic Studies of Water Vapor

I n field emission studies of water vapor, Beckey (92) has observed HaO+.(H20),with n values of 0 to 10. Knewstnhb and Tickner (99) have studied the mass spectrometry of ions formed from the negative glow and Faraday dark space of discharges in water vapor and observed ions of the form HaO+.(H20). with n = 0--5. Their data indicates that the bond strength in the ion falls off sharply after n = 3, and that the H@r+ (m/e = 73) represents a particularly stable form. Knewstubh and Tickner made an approximate kinetic analysis of their data on the basis of the reaction scheme

They assumed that the measured ion currents could he taken as a measure of the ion concentration. The hydration reactions were treated as bimolecular reactions which obey first order kinetics. It was assumed that the ion bond strengths were such that thermal energy was not enough to cause an appreciable amount of reverse reaction. The rate constants were matched to data in the tail of the negative glow (2.0 to 3.5 cm from the cathode). Starting with 100yo H80+ in the vapor the calculation shows a fast build up of the H9O4+ion to better than 90% of the mixture with neither Hs02+or H703+being more than 20% of the mixture a t any time. Hommetl Acidity Function

Bascomhe and Bell (2, 17) have interpreted thc Hammett acidity function of strong acids like HC1 HBr, HC104, and HzSOI as evidence for the H,04' hydrate. They point out that salt effects on the activ. ity coefficient of a nonelectrolyte (18) often takes thc form

where f is the activity coefficient of the nonelectrolyte and C is the concentration of the salt. The constant A is a slope of about 0.1. Bascombe and Bell show the Hammett acidit,y function and water activity in strong acids solution gives such a result for the activity coefficient of the undissociated indicator base, B, if one assumes that the proton is hydrated with four molecules of water and that the activity coefficients of the hydrated proton and the indicator acid, BH+, are essentially equal. The Hammett acidity function is a measure of the transfer of a proton to an indicator base B + H+

+

BHf

and is formally defined as (19) aa+J~ Csn+ Ha = -log -= pICsa+ - log f~a+ CB

If the defining equation is written to include the proton water of hydration, with h the protoil hydration number

broadens the normal water absorption bands. Sometimes this effect is obscured by a small absorption bond-strengthening effect due to the acid anion. Suhrmaun and Breyer and Wicke, Eigen, and Ackermann have calculated extinction coefficient as a function of wavelength between 1.4 and 2.3 fi for water assuming the measured extinction coefficientis the SUICI of a contribution from "free" water molecules plus one from hydrated molecules. Their equation is K.

=

hqKb

+ ( 1 - hq)K,

where K , is the measured extinction coefficient of the solution, K, is the extinction coefficient of free water, K , is the extinction coefficient of bound water, h is the bound water molecules, and q is the ratio of protons to water molecules present in the solution. When h is unity, the calculated plot shows an incorrect minimum at about 1.95 p, while the use of h = 4 gives a qualitative reproduction of the experimental curve. Activity Coefficients of Concentrated Electrolytes

The Hammett acidity function becomes

If one can assueme fk+ = f ~ ~which t , is reasonable for similar size ions such as is the case with the hydrated proton and the indicator acid ion, the last term becomes log fe and upon rearrangement log f~ = -Ho

- log Cx+ + h log an%o= AC

+

when h is given the value 4.0, plots of i-Ho-log Ca+ 4 log a ~ , o against ) C are linear and have slopes of about 0.1 for HC1, HClO,, and HzSO,, up to molalities of a b o u t 8.0. Another approch by Bascomhe and Bell that does not require knowledge of the water activity in strong acid solution is to write the Hammett acidity function as Ho = -log

Ca+

+ h log C B , ~-

They assume that in addition to f H + = J"BH+, t h a t f ~= I'k*, thus the last term is zero. They substitute for CH+the acid molarity and for CHI0a function of acid molarity and molality which includes the reduction in the amount of free mater by hydration. Their final equation (2), which assumes h = 4, -Ho

=

log m - 4 log ( 1 - 0.072 m )

+ 3 log ( 1 + 0.032 m)

very satisfactorily predicts the observed Ho values of HC1, HBr, HCIOn,and H2SOnup to molalities of 8.0. Infrared Spectra of Strong Acid Solutions

Wicke, Eigen, and Ackermann (1) have interpreted the infrared data of Snhrmann and Breyer (20) for HCI and HzSOasolutions as evidence for the H+(HzO), ion. In aqueous solutions of neutral salts the water aborwtion is strenethened due to a partial dewolvmerizaion of the water structure. I n Btrong ac;d ~olutions here is a structure-forming effect due to the primary vdration shell around the proton which weakens and '

6"""" I

-

Glueckauf (23) has developed an expression for the activity coefficient of an electrolyte in concentrated solution that is in part a function of the hydration number of cation plus anion. His treatment is a refinement of the earlier work of Stokes and Robinson (24) in which he takes into account the effect of ionic sizes on the covolun~eentropy effect. His expression for the Gibbs free energy of a solution of electrolyte 1 in a solvent 2 is

r,

The partial volumes, are treated as concentration independent, and the chemical potential obtained by taking the derivative with respect to nl a t constant total mater. Glueckauf's final equation is m r ( ~+ h - V ) + 0.018 2.3 V (1 . +. 0.018 m;) + h h-V log (1 log (1 + 0.018mr) -

log r* = log re'

--

- 0.018 mh).

where h is the hydration number of the electrolyte, r is the apparent molar volume divided by the molar volume of pure water, V is the sum of positive and negative ions from the electrolyte, and m is the molality. When the equation is applied to the observed activity coefficients the values of h are 4.7, 4.7, and 4.0 for HC1, HBr, and HI, respectively. Thermodynamic considerations cannot determine hydration values of cations and anions separately but reasonable assumptions about the hydration of individual ions leads to a value of about 0.9 for the halide ion and 3.9 for the proton. Eigen and Wicke (21) have developed a theory of activity coefficients of electrolytes for high concentrations. Their theory takes into account electrostatic interactions by an ingenious modification of the distribution equation used by Debye and Huckel, space requirements of the hydrated ions in the ionic atmosphere, and incomplete dissociation of the electrolyte at high concentration. The theory has been critized because of overemphasis on cloud-cloud exclusion and oversimplification of anion-cation exclusion in the cloud Volume 40, Number 12, December 1963

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639

\vhicIi leads t sonic tnuthrmatical inconsisrency 1%. and bt:cau*c thedisio(:intion c o ~ ~ ~ t ar~nuired nts to'fit experimental data are not always consistent'with K's from %man spectral studies (3%). The final equations of Eigen and Wicke can be fitted to the experimental activity coefficients, heats of dilution and apparent molal heat capacities of many strong electrolyte solutions. Their activity coefficient equation fits (1, 22) both HC1 and LiCl activity coefficient data up to 2.0 molal when they assume complete dissociation and a hydration number of 6 A for both electrolytes. This implies, but does not prove, that in this case the similar activity coefficient behavior may mean similar hydwtion of H+ and Li+ ions.

ably have won little acceptance. However, when all of the available evidence from many experiulental approaches is considered the Ho04+ion must he reckoned with as a species of considerable importance in aqueous acid solution. Although the extraction and Hammett acidity interpretations assume no contribution of anion water of hydration, fractional increases over the 4.0 moles of water are ascribed to anion effects. In the thermodynamics approaches of activity coefficientand specific heat some arbritrary decision is made that separates cation and anion contributions. Although the anion water of hydration does complicate the interpretatiou the importance of the HgOn+ ion is evident.

Heat Capacily of Strong Acids

Other Evidence

The initial evidence for the trihydrated hydronium ion comes from the specip heat measurements of aqueous strong acid solutious by Wicke, Eigen, and Ackermann (1). Experimentally they have measured the specific heat of aqueous HC1 solutions of concentrations of ahout 0.5, 1.0, and 2.0 molal a t 8 to 10 different temperatures between 10 and 130°C. The apparent molal heat capacity of HCl was calculated, plotted against m"' and extrapolated to get the apparent molal heat capacity of HC1 in aqueous solution a t infinite dilution at 10' intervals between 10 and 130°C. The apparent molal heat capacity a t infinite dilution is separated into a contribution of H + and C1- by a technique worked out by Eigen and Wicke (25). The H+ contribution to the partial molar heat heat capacity a t infinite dilution is fitted to the detailed model of Eucken (26) which allows hydration numbers to be estimated from the temperature dependence of apparent molal quantities. Eucken's theory assumes that the hydrated ion affects the properties of water in two ways. The first is a partial depolymerization of the water which causes a negative contribution to the apparent molal heat capacity and apparent molal volume of the solute. The second is a temperature-dependence to ion hydration. The hydration water is absorbed in two layers. The primary layer does not change with temperature and gives a further negative contribution to the apparent molal volume. A secondary hydration layer decreases with temperature and gives a positive contribution to both apparent partial molal volume and .. heat capacity. The hydrated H + contribution to the partial molal heat capacity is fitted best with a temperature independent ~ r i m a"r vlaver of four water molecules. the H&+ . . " unit; and a secondary hydration layer t&t decreases from 4 moles of water a t 0" to 1 mole a t 130°C. The hydrated H + contibution to the limiting value of apparent molal volume is fitted by the same hydration model. The Eucken model (26) of aqueous solution pictures liquid water as an ideal solution composed of H,O, (HSO)~,(HeO)a, and (H3O)a species in equilibrium. The (H20)8species is assumed to be quite ice-like. Properties of liquid water and aqueous solution are interpreted in terms of displacement of this association equilibrium. The model has not been generally accepted and is contrary to other modern viewpoints (34, 36). If the heat capacity interpretation was the only evidence of the H0O4+ion,its existence would prob640 / Journal o f Chemical Education

The hydroxide ion is also hydrated. Gluckauf (23) gives a hydration number of 4.0 from his activity coefficient approach. Ackermann (22) fits the infrared data of concentrated KOH solutions with h = 3. Ackermann (22) interprets his specitic heat and specific volume data on aqueous NaOH in terms of the Eucken model and gets the best fit with a primary hydration layer of 6 moles of water and the temperature dependeut secondary layer decreasing from 7 moles of water a t 0' to 3 moles of water a t 130°C. The three molecule hydrate of the hydronium ion is not a rigid structure that migrates through solution. There is a continuous migration of positive charge withim the primary hydration unit; and when the group is properly oriented with respect to secondary waters of hydration, the charge migrates with a new water molecule coming in and an old water molecule being ejected from the primary Hood+unit. Eigen (27) has explained protonic charge transport and fast protolytic reactions by a two step mechanism that is consistent with the HOOP+structure. The mechanism involves the formation of a structure with favorable orientation and the charge transfer within a hydrogeu bond. Eigen believes that the first is the rate determining step in liquid water and that the latter is the rate determining step in ice. Conway, Bockris, and Linton (28) discuss conductivity evidence for HaO+ in water organic mixtures and discuss the mechanism of proton migration in solution. Although they do not mention the Ho04+ion, their mechanism of proton transfer does not appear to rule out the possibility of such a unit. The continuous realignment and exchange of water between primary and secondary waters of hydration is consistent with the kinetic viewpoint of hydration oi Samoilov (29). He believes hydration is a matter o the time of coutact between the water molecule anc the ion. The water molecules around a highly hydratec ion have a longer time of contact with the ion than the3 do with neighboring water molecules. He postulate! that the water molecules around slightly hydrated ion! actually have a shorter time of contact with the ior than with neighboring water molecules. Literature Cited (1) WICKE,E.. EIGEN,M., A X D ACKERVANX, TH.,Z. Physzk C h a . iFrmkfur'l. 1.340 (1954). (2) BELL,R.P., " ~ k P e ~ &inI 'Chemistry," Cornell Universit: Preas, Ithaca, 1;.Y., 1959, Chaps. 3 and 6. (3) VOLMER, A., Ann. Chenc., 440, 200 (1924).

RrcaAnus, R. E., AND SMITH,J. A. S., Tram. Faraday Soc., 47, 1261 (1851).

BETHELL,I). E.,

SHEPPARD, N., J . Chem. Phys., 21, 1421 (1953); and FERRISCO, C. C., AND HORNIG,D. F., J . Chem. Phys., 23, 1464 (1955). GRIMM.H. G.. Z. Electrochem.. 31.474 (1925). SHERM*N, J., hem. ~ e u .11, , i64(193i). FAJANS,K., Ber. deulcher phys. Geaell, 21, 709 (1919). FALK,M., AND GIOUERE,P. A., Can. J . Chem., 35, 1195 AND

(1957).

GOLDSCHMIDT, H., A N D UDHY,O., Z. Physik. Chem., 60,728 (1907); GOI~SCHMIDT, H., Z. Electmehem., 15, 4 (1909). BAGSTER, L. s., AND COOLING, G., J . them. A% ,. 1920, 693. BAUGHAN, E. C., J. Chem. Soc., 1940, 1403. TUCK,0 . G.,A N D I~IAMOND, R. M., J . Phys. Chem., 65, 193 (1961).

BALDWIN, W. H., HIGGING,C. E., AND SOLDANO, B. A., J . Phya. Chem., 63, 118 (1959). TUCKA N D I)IAMOND, Op. kt., refs. 24,26. FRIEDMAN, H. L., J . Am. Chem. Soe., 74,5 (1952). BASCOMBE, K. N., AND BELL,R. P., Discussim Faraday Soc., 24, 158 (1957). LONG.F. A,. AND MCDEVIT,W. F.. Chem. Reu., 51, 119 (1952).

HAMMETT, L. P., A N D DEYRUP,A. J., J. Am. Chem. Soe., 54, 2721 (1932). A recent detailed review is PAUL,M. A., and LONG,F. A , , Chem. Rev., 57, l(1957).

R., AND BRETER,F., Z. Phy~ik.Chem. BZ3, (20) SUHRMANN, l- -m- (lQ23). (21) EIGEN,M., AND WICKE,E., J . Phys. Chem., 58,702 (1954); WICKE, E., AND EIGEN, M., Z. Electrmhem., 57, 319 (1953). (22) ACKERMANN, TH., Discassions Faraday Soc., 24,180 (1957). E., Trans. Faraday Sac., 51, 1235 (1955). (23) GLUECKAIIF, R. H., A N D ROBINSON, R. A., J . Am. Chem. Soe., 70, (24) STOKES, 1870 119481. (2.51 R&N. , M.. AND WICKE. ~-., . , E.., Z. Electroehem.. 55. 354 (19511. (26) EUCKEN, A,, Z. Electrochem., 51, 6 (1948). (27) EIGEN,M., Proc. ROY.Soe., 247A, 505 (1958). B. E., BOCKRIS,J. O'M., AND LINTON,H., J . (28) CONWAY, Chem. Phys., 24, 834 (19.56). 0 . YA., Di~cussion~ Faraday Soc., 24,141 (1957). (29) SAMOILOV, R. M., J . P h w . Chem., 67, (301 . . WHITNEY.D. C., AND DIAMOND, 209 (1963). Y., Chem. Rev., 63, 139 (1963). (31) MARCUS, (32) BECKEY, H. D., Z. h7aturjorseh., 14A, 712 (1959); 15A, 822 \ - - - - , ~

~

--~. ~~~

. .

.

(\i-m-n-) . ,~

(33) KNEWSTUBB, P. F., A N D TICKNER, A. W., J . Chem. Phys., 38, 464 (1963). (34) SCATCHARD,G., J . Phys. Chem., 58,713 (1954). (35) (a) FRANK, H. S., A N D TSAO,M. S., Ann. Rev. Phys. Chew&., 5,61-8 (1954); and ( b ) REDLICH,O., AND JONES,A. C., Ann. Rev. Phus. Chm?.,6, i2.78 (1955).

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