journal of chemical education paul a_the great fallacy of the h+ ion and the true nature of h3o+

8/10/2019 Journal of Chemical Education Paul A_The great fallacy of the H+ ion and the true nature of H3O+

1/5

P a u l A. Giguere

Universit6 Laval

Quebec

IK

7P4

The Great Fallacy of the H Ion

Canada

and the True Nature of H30

Th e term hydrogen ion a nd the symbol H+ are s t il l cu r -

rently used to designate the entity characteristic of acids

(BrQnsted's definition), especially in aqueo us systems. Y et,

th a t formulation has been a p erennial source of confusion, not

only in teaching, bu t also in interpreting ex perimenta l results.

Even am ong modern chemistry textbooks one f inds an in-

credible diversity, if not discrepancy on this most fund am enta l

quest ion. M ost au thors d o acknowledge a more complex

species than the over-simple H+ . They call i t var iously hy-

drated proton (protonated water would he more logical ) ,

proton hyd rate, "wet" proton, oxonium ion, and more ap-

propriately, hyd roniu m ion'. As for th e formula, beside the

right one, H30+, authors use any of the following: H+.,,

H+(HzO),, H+ (H20)4. (H 8.3 Hz 0) +, HgOqt, etc. In a recent

"comprehensive" monograph

2)

H s0 + is barely mentioned

as such But there is no longer any excuse for such uncertainty.

We now have suff icient data, exper imental and theoret ical ,

to get a clear picture as

I

intend to show hereaf ter.

Historical Background

The question originated with the theory of electrolytic

dissociation (A rrhenius, 1887). Since all comm on acids contain

hydrogen, which the y give up readily, i t was logical to identify

them w ith the H + ion, the coun terpart of the OH- ion in bases.

Th e invention of th e pH scale (SQrensen, 1909) established

definitely that practice. However, when physicists began

probing th e structure of the atom, it was soon realized tha t H+

is no ordinary ion. In fac t , s trict ly speaking, i t is not an ion

according to th e def ini t ion th at an ion is "an atom , or group

of atom s tha t carries a positive or negative electric charge"

I ) .

Th e symbol H+ represen ts , no t an a tom, h u t a subatomic

particle, the proton.

Th e proton is unique in chemistry by vir tue of i ts atomic

mass an d electronic size. Because of the la t ter i t exer ts an

intense electr ic f ield on i ts surrounding. Therefore, i t cannot

remain free under o rdinary conditions. In th e case of aqueous

acids i t mu st he combined with the solvent , and H 30t is the

simplest possible en tity. Now, the concept of H30 + got a bad

star t when i t was f irs t mentioned, a t the turn of the century,

in a paper dealing with organic compounds of..

.

quadrivalent

oxygen

3).

Th e fo rmula OHsOH and the name oxonium hy-

droxide were suggested for it by analogy with ammonium

hydroxide, NHqOH. S oon afterwa rds, physical chem ists rec-

ognized various indire ct evidenc e for H:iO+ in aque ous acids:

for instance f rom acid catalysis (Goldschmidt and Udby,

1907),cryoscopy (Hantzsc h, 19081, molecular volume (Fajans,

19211, and refractivity (Faja ns an d Joos, 1924) (Cf. Bell (4)

for a review). Following the discovery of X-ray diffraction by

crystals, V olmer

5)

showed that the sol id monohydrate of

perchloric acid (M.Pt. 50C) is isomorphous with am mo -

nium perchlorate. From th is he concluded rightly that i t is an

ionic compound, HsO+C104-, not a molecular hydrate,

HC IOcH 20, as it is still often considered. Definite identifi-

cation of H 30 + ions finally cam e with th e discovery of nmr.

In 1951 wo independ ent groups (6) showed that in the crys-

talline hydra tes of strong mineral acids the th ree protons are

equivalent. Shortly after, the fundam ental vibrations of H 30+

ions were identified in frozen acid solutions 7).

Sti l l , f rom al l tha t evidence one could not infer the natu re

of the ion in aqueous acids. Indeed, due to t he much greater

mobility of liquids the association of a proton with a given H 2 0

molecule could well be too short-lived to vield a distinct

chemical enti ty . T ha t seemed al l the more l ikely as a num ber

of early attem pts to de tect th e vibrations of HnO+ had failed.

But ,

s

explained below, these ea rly studies, mostly by Ram an

spectroscopy, were doomed t o failure. Infrared spec tra turned

ou t to he m uch m ore revealing as we reported some twenty

years ago 8 ) .Our assignment of the fund amenta l hands of

HsO+ in aqueous aciddwas disputed by some (9,10) hut later

on definitely confirmed (11,1 2). Finally, an elaborate X-ray

and neutron dif f ract ion s tudy of hydrochlor ic acid 13)has

given Hs 0 + the consecration of direct experime ntal proof. Yet,

in spi te of al l this evidence, i t is a safe bet that al l the

"doubting Thom ases" will not he convinced.

T h e

Thermodynamics

Viewpoint

I t is in the realm of thermodynamics tha t the H+ on con-

ce pt seem s particularly fallacious, and even a bsurd . As early

as 1919 Fajans (14) est imated the proton aff ini ty of the H 20

molecu le a t 182 kcallmole, a remarkably a ccu rate value for

th e time. F rom t ha t he derived th e oreno sterous fieure 10-130

for the conc entration of free protons in water. In a more pic-

turesq ue vein Sidgwick (15) wrote th at "in loT0 niverses filled

with a 1

N

acid solution th ere would he only one unsolvated

hydrogen ion " Therefore, the equati on

Hz0 H+ +OH -

1)

still curren tly used to des cribe 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 a tom i t would require an enormo us energy:

387 kcal mole- ', to he exact. And even if tha t much energy

were provided, complete atomization would take place in-

stead

H 2 0 - 2 H + O

(2 )

since it requ ires only 221 kcal mole-'. Forma lly speaking, th e

ionization of water is a bimolecular orocess. which shou ld he

writ ten as such

2H20= HsO+,OH-

3)

Th e conventional excuse for the H + formalism is that i t stands

for

H 0 .

But experience shows it is not always

so.

ake, for

instance, the u h lr s of thermodvnum ic functions for hvd rati m

of ions (16). I t is customary to head th e list of ions with th e

'T he present state ul ron uiiun

is

wrll rxl*ml,lifird

, .

rulr

{ 14

of

the NwntncIature

o

Inr,ryanic ('he m ~st ry

f

the IL 1'.4CI

.

"The ion HgO ', uhleh is i n fact the monr.h\dn,ted

u n , t u n ,

s to hr

known as the

oxonium

ion when it is

believed

have tdis constitution,

as for example in H zO+C IOc,oxonium perchlarate. T he widely used

term hydronium should be kept for the

cases

where

it is

wished to

denote an indefinite degree

of

hydration o f the p roton, as, for example

in aqueous solution. If, however, the hydration is of no particular

importance to the m atter under consideration, he simpler term hy-

drogen ion may be used." (Italic s mine.)

And for good measure there is a footnote.

The

ommittees

concur in

oxonium or the ion H-Of. but see little

dration."

All this notwithstanding, hydronium sees preferable o

oxonium

which applies to a ll compounds of rival ent oxygen.

/

Volume

56,

Number

9

September

1979 1

571


2/5

object ionable H+. In the case of par t ial m olal volumes, the

accepted value,

VH+"

= -5.4 cm3 mole-I a t 25", refers ob-

viously to th e H3 0+ ion, not t o the b are proton. However ,

when i t comes to the enthalpy of hydration, this time th e given

value, AH

=

-270 kcal mol-', refers not to th e HaO+ ion, hu t

t u H ; hich explains why it is more t han twice as large as for

the oth er monovalent ions. Actually, that qu antity is the sum

ot'two quite different terms. P irrt i i the enthalpy of the gas-

phase react ion

H 2 0+ H +

-

30+

AH

= 166

kcal mole-

4)

also known as th e proton a ffinity of HzO. It has been m easured

accurately, in particular by mass spectrome ter (17). (Cf. (18)

for a review). Clearlv. it does no t belona in the above tables

since reaction (4) is no t a hydration. In hy dratio n processes

the H z0 molecule retains essentially i ts s tructure. W hat we

have here, instea d, is a true chemical reaction, with forma tion

of a stronz covalent bond. Incidentally, th e O-H bonds in th e

free ~ ~ 0 :on, 130 kcal mole- ', are even strong er th an those

in H ~ 0 , 1 1 0cal mole-'. Th e other term, namely the enthalpy

of hydration of the gaseous H30 t, is not known so accurately.

Values ranging from -70 to -125 kcal mole-' have been re-

por te d for i t (16) . Th is wide uncer tainty may stem from th e

prese nt dichotomy . At any rate, the accepted value, -103 kcal

mole-', seem s reasonab le by com parison with -106 an d -101

kcal mole-I, resp ectively, for th e isochore Na+ and OH- ions.

In r e t rospect , the confus ion between H + and H30+ appear s

as a rem nan t of the tradit ional lack of concern of thermody -

namicists for things s tructural .

The Real H 3 t

T he above men tioned nm r studies (6) not only established

th e H 20 + ion as an en t i tv hu t a l so v ie lded some s truc tu ra l

~

- ~

information; i.e. th e nonhond ed H-H distan ce (Fig. 1). Be -

cause the O-H distance was not measurable by tha t tech-

nique it was not possible to decide between a flat tr iangle and

a shallow pyramidal s tructure. Th e lat ter , more probable by

analogy with the isoelectronic NH3 (19), was later confirmed

by neutron diffraction (20). In fact, the O-H bond s have th e

same length as in ice, and apex angles fal l generally between

110" and 115". This m eans a rath er f lat pyram id, 0 .25 to 0.3

A igh. Likewise, the dynamics of H30 + have been s tudie d in

various crystalline compounds, mostly by infrared (21). In-

deed, because of the ionic charge on the hydrogen atoms, the

HqO f ion is stronelv nolar. There fore, its vibrations (even the

.

parallvl ones) art: t w weak tu bc, detecte d ens dy V the Hamnn

effect. Th is accoun ts rm thr a h w e mentioned failure of mrly

studies. In liquid acids the overwhelming absorp tion of water

makes more difficult the observation of the HaO+ bands;

particularly th e two O-H stretch ing (Fig. 2). Still, th e weak

maximum aroun d 2900 cm-' clearly belongs to th e ion. Its low

frequency (compared to 3100 cm-I in watr r , is ind ~ rn ti w f

\ cry

s t rong hydrogen hm ding . The tu ,o bend ing m o d w I.,.

the sym mrtric , rentt nvl aruund 1200 cm-1, and u 1 . i t I X 0

Figure 1 Structure ol,the average H 3 t ion in various crystals.

572

1

Journal of Chemical Education

Frequency (cm-')

Figure2. Infraredabsorption spectra

of

thin films of the four hydrohalic acids.

Concentrations in mole per cent). Reproduced from 12 .

cm-' are muc h more obvious. Th e former, located in a "win-

dow" of the water absorption, can be de tecte d even in a 1M

solution: tha t is with some fifty water m olecules per hydro-

nium ion. Interestingly, the sa me lower limit holds for the 3610

cm-I Ram an hand of the OH- ion in alkal ine solutions

(22).

Finally, diffraction methods have provided direct confir-

mation of H3 0+ ons in liquid acids. Liquids always give rathe r

diffuse diffraction patterns from which structural information

is not easily extracted . Nevertheless, m uch progress has been

achieved by using these dat a to test theoretical models. In th e

case of water this had led to acc urate interatomic dis tances

(23) .

A

similar extensive investigation (1 3),using both X-ray

an d neutrons, has enabled measu rem ent of th e O-H (or

rathe r O-D) bond length of th e ion in con centra ted hydro-

chloric acid, 1.02 A More im porta nt, perhaps, is the O-H-0

dista nce, 2.52 (Fig. 3) , signif icantly sh or ter tha n th at in

water, 2.83 A (23). From these da ta a model , was proposed

(Fig. 4), in which H3 0+ s coordinated to four wate r molecules;

three of them linked by strdng H-bonds, th e fourth , by much

weaker cbarge-dipole forces. In short, the geometry of the

H:%0+on, whether in crystals or in liquid acid s, is now known

with same accuracy as tha t of H2 0 n l iquid water , ice, or the

hydrates.

The Average Lifetime

ol H3 0 +

Obviously, an important property of the HaO+ ion in

aqueou s acids is its average lifetime T I t has been the ob jec t

of mu ch spe culation a nd calculation. A first estim ate of 0.24

psec (lo-" sec) was calculated pr or by C onway, Bockris

and L inton (24) from their elaborate m easurem ents of proton

conductance. A higher value, by abo ut one order of magn itude,

was derived by Eigen (25 ) from his dielectric relaxation d ata.

Th e exact value, however, was found by m eans of nm r through


3/5


4/5

0 0

distance of 2.37 or less the notential curve of the nro-

ton is of t he single, symmetric-well type. This is reasonable

considerine the short distance involved. Therefore, it seems

that

tunnelling plays no significant rdle hericontrary

to curren t belief.

This, then, raises the question of why the protons spend

most of their time covalently bonded in H30+ ions? The an-

swer must be th at proton transfer in aqueous solutions is a

concerted process involving reorganization of the hydrogen

bond pat tern around the "excess or defect proton." Indeed,

th e 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 de-

crease in the heat of activation with temperature, from 2.5 kcal

mole-' at room temperature down toone tenth tha t value near

400K (32).

What about

H.04 ?

Th e H904+ ormulation often used in textbooks was first

postulated in 1954 on the basis of such indirect evidence as

s~e c if ic eat and entronv (33). Since then it has received

-

si pp or t from various sources, both experimental and theo-

retical (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 dis-

tributed 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 t he 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 exten t of hydration in this particular in-

stance. 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 in ir io calculations

(29), that the 0


5/5

waipnt

x

HF Wcigh1.l. HCi

F i g u r e 5. Boiling-point curves 01 the binary

systems

H20-HF and

H20-HCI.

Ion pairs of hydronium chloride and bromide had been de-

tected 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 tha t 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 H 3 0 t . . - ) 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- ons gradually

reolace the H,O moleculee which stabiliee the ion pairs. This ,

cdupled with ihe incipient formation of HF2- ions, increases

th e number of charged species, and the apparent strength of

th e acid. Thu s we see that , contrary to the heavier hydrogen

halides, H F behaves as a weak acid in aqueous solutions be-

cause the

F-

ion is a hetter proton acceptor than H20.

CohcluSIOnS

Th e present review may be summarized a s follows:

(1) The hydronium ion H30+ is just as real as its counter-

part , 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 neut ron diffraction in hydrochloric acid.

4) In aqueous acids the H30+ ion is strongly H-bonded to

three Hz0 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 1per cent of the

average lifetime of the H30+ ion.

(6)

Contrary to current theory HF is mostly ionized in

water like the other three hydrogen halides. I t behaves as a

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 n H30+.3H20. The term

hydrogen ion

is here tostay , of course, like other time-honored

misnomers in Science.

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(1) Weas%

R.

. , (Editor). '"Handbaok ofchem istry a nd Physic.," 55th ed. The Chemical

Ruhber Co. Cleveland, Ohio. 1975. pp. Bd 5. F-98.

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391

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~ . ~, ~,~

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~ h r n i . h y s .

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Letters.

37,569 (19761.

Volume

56

Number

9,

September 1979

1

575

journal of chemical education paul a_the great fallacy of the h+ ion and the true nature of h3o+

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