The ionic product, Kw
The bare hydrogen ion (a proton) readily hydratesf and cannot exist freely in solution. Initial hydration forms the oxonium ion (H3O+) (sometimes called the hydrogen ion).d This has a flattened
trigonal pyramidal structure (calculated gas phase
values O-H bond length 0.961
Å, H-O-H angle 114.7°;e compare with the significantly different calculated liquid values of O-H bond length 1.002 Å,
H-O-H angle 106.7° ) with C3v symmetry and equivalent protons. H3O+ has an effective ionic radius of 0.100 nm , somewhat less than that of the H2O molecular radius (0.138 nm). Its molar volume is -5.4 cm3 mol-1 due to electrostriction . It forms the core of the 'Eigen' cation,a described later.
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
clusters. H3O+ is also found in
the monohydrates of HCl, H2SO4and
HClO4, for example, [H3O+]2[SO42-].b All the occupied molecular
orbitals of H3O+are on another page.
It has been shown that H3O+ can donate three hydrogen bonds (but accepts almost none); the strength of these donated hydrogen bonds being over twice as strong as those between H2O molecules in bulk water . This effectively means that the H3O+ cation can be considered as H9O4+ in solution. The polarization causes these first shell water molecules to also each donate two further hydrogen bonds (but also accept little) with strengths still somewhat higher than bulk water . Second shell water molecules also donate two hydrogen bonds (but also accept only one with a rather weak hydrogen bond) with strengths still fractionally higher than bulk water . The bias towards donated hydrogen bonds, within the two-shell H21O10+ ion cluster, requires that it must be surrounded by a zone of broken hydrogen bonds. This is confirmed by infrared spectra that show that the presence of an H3O+ ion extends to affect the hydrogen bonding of at least 100 surrounding water molecules .
The oxonium ion binds strongly to another water molecule in two possible manners. Opposite are shown
the two H5O2+ dihydronium ions with closely matched energies, where the proton is asymmetrically (top) or symmetrically (bottom) centered between the O-atoms.e The asymmetric structure (top) of H5O2+ is found to be more stable using
the 6-31G** basis set. However, other more thorough ab
initio treatments have found the symmetric hydrogen-bonded
structure (bottom), with a slightly shorter hydrogen bond, to be the global minimum of by about 0.6
kJ mol-1 .
In this symmetric form (the 'Zundel' cation, shown bottom opposite), all O-H bonds are the same length (0.95 Å)
except the two involved in the hydrogen bond, which are covalent and equally-spaced
(1.18 Å; similar to that in ice-ten,
and as found by neutron diffraction in some crystals mid way between the oxygen atoms [118a], such as the dihydrates of HCl and HClO4, for example, [H5O2+][ClO4-]). There is localized but low
electron density around the central hydrogen atom. The vibrational
spectrum of H5O2+ shows
a strong sharp peak (at 1090 cm-1) for its shared
proton, similar to H3O2-. As expected, these spectra are much broadened,
shifted and poorly resolved in bulk liquid water.
occupied molecular orbitals, found using the 6-31G** basis
set, of H5O2+ are on another page.
H5O2+ may be fully hydrated, also with an equally spaced
central hydrogen bond, with one water molecule hydrogen bonded
to the four free hydrogen atoms as H13O6+. 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 very quickly (< 100 fs, ) between the extremes of triply-hydrogen
bonded H3O+ (H9O4+,
'Eigen cation') ions through symmetrical H5O2+ ions ('Zundel cation')a , with the low potential energy barriers washed out by the zero-point motion of the proton .
Note that the small movement of the proton gives rise to a much greater movement of the center of positive charge. Preference for the Zundel cation structure occurs when its
outer hydrogen bonding is approximately symmetrical as in
H13O6+ (right) , although the O····O separation may be greater than expected for the lone H5O2+ Zundel ion .
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 ),
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 ).
Once correctly oriented, the potential energy barrier to proton
transfer is believed to be very small .
However, the hydrated oxonium ion (opposite; the 'Eigen' cation)e may be
the most stable hydrated proton species in liquid
water, being slightly more stable than the symmetrical dihydronium ion, due to electronic delocalization
over several water molecules being preferred over the nuclear delocalization.
In acidc solutions, there will be many contributing structures giving
rise to particularly broad stretching vibrations associated
with the excess protons (for example, magic
number ions). It has been determined from studies
of freezing point depression that H3O+(H2O)6 (that is, H15O7+) is
the mean structural ion in cold water .
H7O3+ and H9O4+ are both also found in HBr.4H2O, i.e. [H9O4+][H7O3+][Br-]2.H2O.
The central (positively charged) hydrated proton interacts very much more strongly with the oxygen of neighboring water molecukes rather than any weakly forming hydrogen bonds; H2O···OH3+(H2O)3 being a much stronger link than the hydrogen bond HO-H···OH3+(H2O)3 . This causes rotations in the neighboring water molecules as a hydrogen ion moves through the solution so disrupting the hydrogen bonded network. This O···O attraction even exists between H3O+ species as in more concentrated acid solutions (~0.5 - ~3 M) with the hydrated protons appearing to form contact ion pairs, with the oxonium lone-pair sides pointing toward one another and the oxygen atoms only about 0.34 nm apart.. This unusual “amphiphilic” behavior minimises the disruption to the water's hydrogen bond network caused by the strong hydration of the protons . A similar effect may occur at the surface of concentrated acid solutions, causing the lone pairs to point towards the (hydrophobic) gas phase.
As hydrogen ions can be readily stripped from aqueous surfaces , by themselves, as constituents of small clusters or as aerosol, there may be a build -up of positive charge within clouds and negative charge on Earth that leads to thunder and lightning.
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a The hydration of 'Eigen' (H9O4+) and 'Zundel' (H5O2+) ions has been investigated . [Back]
accepts protons from stronger acids to form H3O+ and H3O+ donates protons to the bases
of weaker acids. The acidity constant (Ka) of H3O+ is defined (as other acids) by the equation H3O+(+H2O)H+(aq)+H2O.
Therefore Ka= [H+][H2O]/[H3O+]
and as [H+] is the same as [H3O+],
Ka = [H2O] = 55.345 M (at 25 °C),
and pKa = -1.743 (at 25 °C).
There is a difficulty that has been ignored in this definition as the Ka should be expressed in terms of activities rather than concentrations  and the activity of pure H2O is defined as unity whereas that of solutes is defined relative to their standard state (1 mol kg-1). [Back]
c Note that acid-base neutrality
only occurs when the concentration of hydrogen ions equals
the concentration of hydroxyl ions (whatever the pH). Neutrality
is at pH 7 only 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. [Back]
d The term 'oxonium ion' should be reserved for the H3O+ ion with the term 'hydronium ion' now obsolete. The term 'hydrogen ion' may refer to any of the group of protonated water clusters including H3O+. [Back]
e The oxonium ion and small hydrated hydrogen ion clusters shown on this page were drawn using ab initio calculations using the 6-31G**
basis set. Where not otherwise referenced, bond distances, angles and atomic charges are derived from these calculations. [Back, 2, 3]
f H+ + H2O H3O+ (ΔG° = -651.4 kJ mol-1) , this is followed by H3O+ + aq H3O+(aq) (ΔG° = 461.1 kJ mol-1; ~260 nm) giving an overall H+ + aq H3O+(aq) (ΔG° = -1112.5 kJ mol-1). These calculations assume that the standard state of the solvent water is taken as 1.0 M. ). [Back]