Variation in Kw with temperature and pressure
Hydrogen ions
Hydroxide ions
Grotthuss mechanism
Water ionization occurs endothermicallyd due to electric field fluctuations between neighboring molecules. Dipole librations [191], resulting from thermal effects and favorable localized hydrogen bonding [567], cause these fluctuations. The process may be facilitated by exciting the O-H stretch overtone vibration [393]. Once formed (at an average concentration of about 0.9 M H2O-H+···OH- [1984]), 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 [191]. 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.
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 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 [1938].
The above equations are better written as:
2 H2O
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.
4 H2O
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 [1890]. For more information and a list of primary pH standards see [813]. 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 [1107]. The pH scale was first introduced by Sørensen (as pH·) in 1909 [1036] 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) [1187]. There is a recent review of the pH of natural water [1712]. [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 ]
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) [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.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 [1865]). The pKw H2O minimum is about 0.74 lower than that for D2O [1865]. (see also conductivity maximum).
A theoretical treatment of this temperature dependence is available [763].
Temperature and density dependence of ionization has been examined [1321]. 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 [1964].
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 [604]. [Back]
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 [1067]) 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 [1188] 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]
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This page was last updated by Martin Chaplin on 15 April, 2013
