Water ionization and pH
The ionic product, Kw
Variation in Kw with temperature and pressure
The ionic product, Kw
Water ionization occurs endothermicallyd due to electric field fluctuations between neighboring molecules. Dipole librations ,
resulting from thermal effects and favorable localized hydrogen
bonding , cause these fluctuations. The process may be facilitated by exciting the O-H stretch
overtone vibration . Once formed (at an average concentration of about 0.9 M H2O-H+···OH- ),
the ions may separate by means of the Grotthuss mechanism but normally (>99.9%) rapidly recombine.
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 . The pair of ions
(H+, OH-) hydrate independently and
continue their separate existencea for about 70 μs (this lifetime
also dependent on the extent of hydrogen bonding, being shorter
at lower temperatures). They tend to recombine when separated
by only one or two water molecules.
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 consequential changes in the tiny concentrations
of hydrogen ions have absolute importance to living processes.
Hydrogen ions are produced already hydrated (that is, as oxonium ions, H3O+; also called
oxonium or hydroxonium ions) and have negligible existence
as naked protons in liquid or solid water, where they interact extremely strongly with electron clouds. All three hydrogen atoms in the oxonium
ion are held by strong covalent bonds and are equivalent (that is, C3v symmetry). The thermodynamic properties of the dissociation at 25 °C and 100,000 Pa are ΔU = 59.5 kJ mol-1, ΔV =21.4 cm3 mol-1, ΔH = kJ mol-1, ΔG = 79.9 kJ mol-1, ΔS = -77.2 J K-1 mol-1 .
The above equations are better written
H3O+ + OH-
Kw = [H3O+][OH-]
Both ions are ionic kosmotropes, creating order and form stronger hydrogen
bonds with surrounding water molecules. The concentrations of H3O+ and OH- are normally 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.
H5O2+ + H3O2-
The concentration of oxonium and hydroxide
ions produced is therefore equal to the square root of the
ionization constant (Kw).
Aqueous OH- does not ionize further as (O2- + H2O 2OH-,
K > 1022). [Back to Top ]
The oxonium ion concentration
(commonly called 'hydrogen ion concentration') is often given
in terms of the pH, where pH = Log10(1/[H3O+])
= -Log10([H3O+]) (that is, [H3O+] = 10-pH)f with the concentration of H3O+ in mol l-1. More precisely
pH = -Log10(aH) = -Log10(mHλH/m°)
where aH, mH, λH 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 low concentrations normally found,
the hydrogen ion concentration is close enough to 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, particularly at the extremes of pH . For more information and a list of primary pH standards see . Proof that the use of the equation pH = -Log10(H+) may give misleading results (and pH = -Log10(aH) is preferred) is easily shown as the pH of 0.1 M HCl decreases when it is diluted with 5% M LiCl
The pH scale was first introduced by Sørensen (as pH·) in 1909
 using colorimetric measurements and the hydrogen electrode, which gives an electrode potential
proportional to pH. The pH scale extends to negative numbers (for example, concentrated HCl has a pH of about -1.1) and to greater than 14 (for example, saturated NaOH has a pH of about 15.0) . There is a recent review of the pH of natural water . [Back]
In a similar manner pKw is defined by pKw = Log10(1/Kw) = -Log10(Kw),
utilizing concentrations in mol l-1.e [Back to Top ]
-log10(Kw ) [IAPWS]
Variation in Kw with T and P
Kw is very temperature
dependent, increasing with temperature (that is, from 0.001 x 10-14 mol2 l-2 at -35 °C (pH 8.5) ,
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) ), to
10-12 mol2 l-2 at
300 °C (pH 6.0, ~50 MPa) 
in agreement with the high positive standard free energy.b There is a minimum at about 249 °C along the saturated pressure line for H2O and at about 257 °C for D2O (see right ). The pKw H2O minimum is about 0.74 lower than that for D2O . (see also conductivity maximum).
A theoretical treatment of this temperature dependence
is available .
Temperature and density dependence of ionization has been examined . Ionization depends on the pressure, with Kw doubling
at about 100 MPa; unsurprising in view of the negative ΔV associated with the
ionization, -18.1 cm3 mol-1 .
Ionization also varies with solute concentration and ionic strength; for example, 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 (with higher concentrations disrupting the hydrogen bonding). Ionization will also be different at interfaces; for example, it is greater at lipid membrane surfaces .
In ice, where the local hydrogen bonding rarely breaks to
separate the constantly forming and re-associating ions, the
ionization constant is much lower (for example at -4 °C, Kw = 2 x 10-20 mol2 l-2 ). [Back to Top ]
a This low occurrence
means that at neutrality (pH 7 at 25 °C)c,
similarly charged ions are, on average, separated by vast
distances (~0.255 μm) in molecular
terms and (for example) 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 of H2O (~55.5 M; increasing the absolute amount dissociated). The
mean lifetime of a oxonium 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 A bulk energy diagram
for the ionization in bulk water has been described .
c 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. [Back]
dIn a vacuum the
reaction H2O H+ + OH- requires over three times more energy (1.66 MJ mol-1)
than dissociation H2O H· + ·OH
(531 kJ mol-1). In water the hydration of the ions (H+ ΔG° hydration -1112.5 kJ mol-1, this includes H3O+ ΔG° hydration -461.1 kJ mol-1; OH- ΔG° hydration -437.6 kJ mol-1 ) reduces the ΔG° of the reaction
2 H2O H3O+ + OH- to +99.78 kJ mol-1 (These calculations assumes that the standard state of the solvent water is taken as 1.0 M. If the standard state of the solvent water is its mole fraction (= 1.0), the ΔG° is +79.907
kJ mol-1). The dissociated radicals (H·, ·OH) are also somewhat stabilized in liquid water, as shown by the occasional dissociation of water [1066, see equations]. [Back]
e The acidity constant
(Ka) of H2O is defined (as other acids)
by the equation H2O(+H2O)H+(aq)+OH-.
Therefore Ka= [H+][OH-]/[H2O]
= Kw/[H2O] = Kw/55.345 (at
25 °C) and pKa = pKw +1.743 (= 15.739 at 25 °C; compare pKas of H2Te, H2Se and H2S are 2.6, 3.89 and 7.04 respectively).
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]
f As Logarithms may only be taken of dimensionless numbers, all the concentrations (activities, partial pressures, etc.) in any Logarithmic expression are actually divided by unit values in the same units of that concentration (activity, partial pressure, etc.); thus, for example here [H3O+] (concentration of of H3O+ in mol l-1) is actually [H3O+]/(1.0 mol l-1).
The p in pH originated as the arbitrary choice for the naming of the electrode solutions 'p' and 'q' by Sørensen
[1036, 1891], but is now taken to mean the 'logarithm to the base 10 of the reciprocal of' (cologarithm) as in the function described above. [Back]