Ionization of Water
Water molecules ionize endothermicallyf due to electric field fluctuations caused by nearby
dipole librations [191] resulting from thermal effects, and favorable localized hydrogen
bonding [567]; a process that is facilitated by exciting the O-H stretch overtone vibration
[393]. Ions may separate by means of the Grotthuss mechanism (see below) but normally
recombine within a few femtoseconds. Rarely (about once every eleven hours per
molecule at 25°C, or less than once a week at 0°C) the localized hydrogen bonding
arrangement breaks before allowing the separated ions to return [191], and the pair of ions
(H+, OH-) hydrate independently and continue their separate existence a for about 70 s
(this lifetime also dependent on the extent of hydrogen bonding, being shorter at lower
temperatures). They tend to recombine when only separated by one or two water
molecules.
H2O
H+ + OH+
Kw = [H ][OH-]
Although the extent of ionization is tiny ([H+]/[H2O] = 2.8 x 10-9 at 37°C), the ionization and
changes in the tiny concentrations of hydrogen ions have absolute importance to living
processes. Hydrogen ions are produced already hydrated (i.e. as hydronium ions, H3O+;
also called oxonium or hydroxonium ions) and do not have any free existence as naked
protons. All three hydrogen atoms in the hydronium ion are held by strong covalent bonds
and are equivalent (i.e. C3v symmetry). The above equations are better written as:
2 H2O
H3O+ + OHKw = [H3O+][OH-]
Both ions create order and form stronger hydrogen bonds with surrounding water
molecules. The concentrations of H3O+ and OH- are taken as the total concentrations of all
the small clusters including these species. As other water molecules are required to
promote the hydrolysis, the equation below includes the most important.
4 H2O
H5O2+ + H3O2-
The concentration of hydronium and hydroxide ions produced is therefore equal to the
square-root of the ionization constant (Kw). The hydronium ion concentration (commonly
called 'hydrogen ion concentration') is often given in terms of the pH, where
pH = Log10(1/[H3O+]) = -Log10([H3O+]) (i.e. [H3O+] = 10-pH) with the concentration in mol l-1.b
In a similar manner pKw = Log10(1/Kw) = -Log10(Kw), also with the concentrations in mol l-1.
OH- does not ionise further (O2- + H2O
2OH-, K > 1022).
Kw is very temperature dependent, increasing with temperature (i.e. from 0.001 x 10-14
mol2 l-2 at -35°C (pH 8.5) [112], 0.112 x 10-14 mol2 l-2 at 0°C (pH 7.5), to 0.991 x 10-14 mol2
l-2 at 25°C (pH 7.0), to 9.311 x 10-14 mol2 l-2 at 60°C (pH 6.5) [87]), to 10-12 mol2 l-2 at 300°C
(pH 6.0, ~50 MPa) [456] in agreement with the high positive standard free energy.c A
theoretical treatment of this temperature dependence is available [763].
Ionization depends on the pressure with Kw doubling at about 100 MPa; unsurprising in
view of the negative V associated with the ionization, -18.1 cm3 mol-1.
Ionization also varies with solute concentration and ionic strength; e.g. Kw goes through a
maximum of about 2 x 10-14 mol2 l-2 at about 0.25 M ionic strength (using
tetramethylammonium chloride, where possibly the change in hydrogen bonding caused
by clathrate formation encourages ionization) before dropping to a value of about 1 x 10-16
mol2 l-2at 5 M (higher concentrations disrupting the hydrogen bonding).
In ice, where the local hydrogen bonding rarely breaks to separate the constantly forming
and re-associating ions, the ionization constant is much lower (e.g. Kw = 2 x 10-20 mol2 l-2
at -4°C).
Ab initio calculations show that the hydronium ion (H3O+, opposite showing a section
through the electron density distribution (ab initio calculation using the 6-31G** basis set;
high densities around the oxygen atoms have been omitted for clarity) has a flattened
trigonal pyramidal structure (O-H bond length 0.961 Å, H-O-H angle 114.7°; calculated gas
phase values. cf. O-H bond length 1.002 Å, H-O-H angle 106.7°; calculated liquid values
[709]). The structure can invert (like a wind-blown umbrella) with an activation energy less
than that of a hydrogen bond and this may occur as an alternative, or even preferred,
pathway to rotation within a dynamic hydrogen bonded cluster.
The O-H bond length of the OH- ion is calculated as 0.958 Å. All the occupied molecular
orbitals of H3O+ and OH- are on another page.
Opposite are shown the H5O2+ (left, where the proton is centered between the O-atoms)
and H3O2- (right, where the proton is off-center, giving rise to a low-barrier hydrogen bond)
hydrated ions. The hydronium ion is the most stable hydrated proton species in liquid
water, being slightly more stable than dihydronium (H5O2+, showing a section through the
electron density distribution; ab initio calculation using using the 6-31G** basis set with
high densities around the oxygen atoms omitted for clarity), due to electronic delocalization
being preferred over nuclear delocalization [102].
All O-H bonds are the same length (0.949 Å) except the one involved in the hydrogen
bond, which is equally-spaced (1.18 Å; similar to that in ice-ten, and as found by neutron
diffraction in some crystals [118a]) mid way between the oxygen atoms. Note the localized
but low electron density around the central hydrogen atom. H 5O2+ is also found in the
dihydrates of HCl and HClO4, e.g. [H5O2+][ClO4-]. It is also found fully hydrated, also with
an equally-spaced hydrogen bond and with one water molecule hydrogen bonded to the
four free hydrogen atoms as H13O6+. A slightly more stable form of H5O2+, involving a
longer O···O distance (2.40 Å) and hydrogen bond (1.32 Å), is found using the 6-31G**
basis set. However, other more thorough ab initio treatments have found the equallyspaced hydrogen-bonded structure (above left) to be the global minimum by about 0.6 kJ
mol-1 [118]. The presence of these three similar energy minima for the proton lying so
close between the two oxygen atoms is surely the major reason for the ease of transfer of
protons between water molecules; the proton moving between the extremes of triplyhydrogen bonded H3O+ (H9O4+, 'Eigen cation') ions through symmetrical H5O2+ ions
('Zundel cation') [161]. Preference for the Zundel cation structure occurs when its outer
hydrogen bonding is approximately symmetrical as in H13O6+ below right [815]. When the
extra proton is shared equally between more than one water molecule the approximate
structure can be deduced from a consideration of the resonance structures; for example,
the two shared protons in H7O3+ give rise to bond lengths half way between those in (H2O)2
and H5O2+ (the calculated minimum energy structure is shown [815]),
and the three shared protons in H9O4+ giving rise to bond lengths a third of the way
between those in (H2O)2 and H5O2+ (below; the calculated minimum energy structure is
shown [815]). Once correctly oriented, the potential energy barrier to proton transfer is
believed to be very small [161].
In acidd solutions, there will be many contributing structures giving rise to particularly broad
stretching vibrations associated with the excess protons (e.g. magic number ions). It has
been determined from studies of freezing point depression that H3O+(H2O)6 (i.e. H15O7+) is
the mean structural ion in cold water [250].
The tetrahedral ion H7O4-, see HO-··(HOH)3 opposite, is probably the most stable hydrated
hydroxide ion [541] being slightly favored over H3O2- (above right) [102]. There is
evidence of a much weaker hydrogen bond involving the OH - hydrogen atom (i.e. -OH···OH2), which may facilitate the OH- transport mechanism (see below) [650]. It is
possible that four water molecules may coordinate to the hydroxide ion as HO -(··HOH)4,
(all donating their hydrogen atoms) because the electron distribution around the hydroxide
ion is not directional [371]. Such an arrangement has been recently reported using neutron
diffraction, with empirical structure refinement, of concentrated NaOH solutions [698].
Spectroscopic studies, however, show the 4th H2O in HO-(··HOH)4 to be hydrogen bonded
to the other three forming a second shell [461].
The O···O distance in H7O4- and H3O2- are slightly greater (~2.67 Å and ~2.50 (2.467 Å
[337]) respectively) and the O-H slightly shorter (~0.98 Å and ~1.05 (1.125 Å [337])
respectively) than in H5O2+. The hydration of these ions reduce their chemical activity,
which may be a factor in their increased reactivity when subjected to hydrogen-bond
disrupting electromagnetic effects [454].
The hydrogen atom lies significantly asymmetrically in H3O2- where the energy barrier for
proton transfer has been calculated (~0.9 kJ mol-1) to be much lower than the available
vibrational energy, so allowing easy equilibration of the proton's position [337] as occurs
with H5O2+. The vibrational spectrum of H3O2- indicates that it behaves as a single
(vibrationally-averaged) species with no bend vibration (v2), both free O-H stretch
vibrations being equivalent and a very strong and sharp band at 697 cm -1, corresponding
to the vibration of the shared proton [755]; thus the shared proton hops between the two
minimum energy sites giving a quantum-averaged structure. The vibrational spectrum of
H5O2+ also shows a strong sharp peak (at 1090 cm-1) for its shared proton. As expected,
these spectra will be very much broadened, shifted and poorly resolved in bulk liquid
water. All the occupied molecular orbitals, found using the 6-31G** basis set, of both forms
of H5O2+ (129 KB) and H3O2- (56 KB) are on other pages. In crystal structures, H3O2- with a
symmetrical hydrogen bond may be found (e.g. O···O 2.41 Å; O···H 1.205 Å; O-H 0.733 Å
[380]).
It is generally thought that protons and hydroxide ions rapidly diffuse in liquid water [102],
with protons diffusing almost twice as fast (and seven times as fast as Na +). It should be
recognized that these diffusivities are determined from movement in an electric field (at
100 v m-1 ; H+ and OH- have mobilities of 32.5 and 17.8 m s-1 respectively)e, where the
special mechanisms described below are operational, and the true movements of the ions
may be somewhat less, as can be recognized by the proton diffusional limitations that take
place at the surface of some immobilized enzymes [103].
The Grotthuss mechanism (origin in [160]), whereby protons tunnel from one water
molecule to the next via hydrogen bonding, is the usual mechanism given for proton
mobility and is similar to that of autoionization, the mechanism causing the ions (H +, OH-)
to initially separate.
Note that aquaporin water channels deliberately re-orient water molecules to preclude
such sequential hydrogen bonding so preventing proton transfer. If further proton tunneling
through the same molecules and in the same direction is to proceed, it is clear that proton
movement must be followed by a reorientation of the hydrogen bonding.
A similar process can be given for hydroxide mobility:
In order to migrate the ions must be associated with hydrogen bonded clusters; the
stronger and more extensive the cluster, the faster the migration. Stronger hydrogen
bonding causes the O···O distance to be shorter, so easing the further shortening required
for transfer. A limiting factor in the mobility for both ions is the breakage of an outer shell
hydrogen bonds. As a first step, this enables the hydrogen to transfer from H3O+ or, as a
last step, the release of water by the newly formed hydroxide ion in H 7O4- [102] (see
below). Both transfers involve the additional energy requirements of stretching the outer
hydrogen bonds due to the contraction of the O···O distance.
Hydronium ion transport mechanism
The symmetrical structure during proton transfer (above right), involving a triangular
arrangement of water molecules [371], has also been found in the protonated trimer
(H7O3+, [138]). The presence of the fourth water molecule associated with the H 9O4+
cluster (shown above the charge above) is seen in a neutron diffraction study as oriented
but distant (3.2 Å, [697]). Proton transport may also occur using 'Zundel' dihydronium
(H5O2+) ions only, as below [490], which involves the concerted movement of two
molecules. Such proton jumps may be short (shown on left) or long (shown on right).
Hydroxide ions make use of an entirely different mechanism [371]. The hydrated hydroxide
ion is coordinated to four electron-accepting water molecules such that when an incoming
electron-donating hydrogen bond forms (necessitating the breakage of one of the original
hydrogen bonds) a fully tetrahedrally-coordinated water molecule may be easily formed by
the hydrogen ion transfer. The structure below left, HO -(··HOH)4, together with the more
distant oriented water molecule below it, has been seen using neutron diffraction, with
empirical structure refinement, of concentrated NaOH solutions [698]. The different
mechanism, involving extra hydrogen bond rearrangements plus re-orientations, is the
reason for the reduced mobility of the hydroxide ion compared with the hydronium ion.
Hydroxide ion transport mechanism
a
This low occurrence means that at neutrality (pH 7 at 25°C)d, similarly charged ions are,
on average, separated by vast distances (~0.255 m) in molecular terms and that bacteria
contain only a few tens of free hydrogen ions. Contributing to this effect are the high
dielectric constant (encouraging charge separation) and high concentration (~55.5 M;
increasing the absolute amount dissociated). The mean lifetime of a hydronium ion (1 ps;
about the same as that of a hydrogen bond) is such that the charge could be associated
with over 107 molecules of water before neutralization. [Back]
b More precisely pH = -Log (a ) = -Log (m  /m°) where a
10 H
10
H H
H, mH, H and m° are the
relative (molality based) activity, molality, molal activity coefficient and standard molality (1
mol kg-1) of the hydrogen ions. At the normally low concentrations, the hydrogen ion
concentration is close enough to the the relative (molality based) activity for its use for most
purposes. The molal activity of hydrogen ions cannot be determined directly but may be
determined using a glass electrode relative to the response of standard buffer solutions of
suitable ionic strength. Glass electrode-determined pH values are error-prone and
calculated hydrogen ion concentrations should be treated with caution. For more
information see [813].
c A bulk energy diagram for the ionization in bulk water has been described [604].
d Note that acid-base neutrality only occurs when the concentration of hydrogen ions
equals the concentration of hydroxyl ions (whatever the pH). This only occurs at pH 7 in
pure water when at 25°C. A solution is acidic when the hydrogen ion concentration is
greater than the hydroxide ion concentration, whatever the pH.
e Degassing may increase these values [711].
f In a vacuum the reaction H OH++OH- requires over three times more energy (1.66
2
MJ mol-1) than dissociation H2O H· + ·OH (531 kJ mol-1). In water the hydration of the
ions reduces the G of the reaction 2 H2O
H3O+ + OH- to 99.78 kJ mol-1.