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 existencea for about 70 ms (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]=2.8x10-9 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+ + OH-

Kw = [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 DV 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. H5O2+ 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 equally-spaced 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 triply-hydrogen 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. -O-H···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 mm 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 inthe 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 H7O4- [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 H9O4+ 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 mm) 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=-Log10(aH)=-Log10(mHlH/m°) where aH, mH, lH 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].