Self-ionization of water
The self-ionization of water is an ionization reaction in pure water or in an aqueous solution, in which a water molecule, H2O, deprotonates to become a hydroxide ion, OH−. The hydrogen nucleus, H+, immediately protonates another water molecule to form hydronium, H3O+. It is an example of autoprotolysis, and exemplifies the amphoteric nature of water.
Equilibrium constant
has an electrical conductivity of 0.055 µS/cm. According to the theories of Svante Arrhenius, this must be due to the presence of ions. The ions are produced by the water self-ionization reaction, which applies to pure water and any aqueous solution:Expressed with chemical activities, instead of concentrations, the thermodynamic equilibrium constant for the water ionization reaction is:
which is numerically equal to the more traditional thermodynamic equilibrium constant written as:
under the assumption that the sum of the chemical potentials of H+ and H3O+ is formally equal to twice the chemical potential of H2O at the same temperature and pressure.
Because most acid–base solutions are typically very dilute, the activity of water is generally approximated as being equal to unity, which allows the ionic product of water to be expressed as:
In dilute aqueous solutions, the activities of the solute particles are approximately equal to their concentrations. Thus, the ionization constant, dissociation constant, self-ionization constant, water ion-product constant or ionic product of water, symbolized by Kw, may be given by:
where is the molarity of hydrogen or hydronium ion, and is the concentration of hydroxide ion. When the equilibrium constant is written as a product of concentrations it is necessary to make corrections to the value of depending on ionic strength and other factors.
At 25 °C and zero ionic strength, Kw is equal to. Note that as with all equilibrium constants, the result is dimensionless because the concentration is in fact a concentration relative to the standard state, which for H+ and OH− are both defined to be 1 molal. For most practical purposes, the molal and molar concentrations are equal near the ambient temperature and pressure. The molal concentration scale results in concentration values which account for density changes with temperature or pressure changes; therefore, it is the scale used in precise or nonambient applications, e.g., for seawater, or at elevated temperatures, like those in thermal power plants.
We can also define pKw −log10 Kw. This is analogous to the notations pH and pKa for an acid dissociation constant, where the symbol p denotes a cologarithm. The logarithmic form of the equilibrium constant equation is pKw = pH + pOH.
Dependence on temperature, pressure and ionic strength
The dependence of the water ionization on temperature and pressure has been investigated thoroughly. The value of pKw decreases as temperature increases from the melting point of ice to a minimum at c. 250 °C, after which it increases up to the critical point of water c. 374 °C. It decreases with increasing pressure.| Temperature | Pressure | pKw |
| 0 °C | 0.10 MPa | 14.95 |
| 25 °C | 0.10 MPa | 13.99 |
| 50 °C | 0.10 MPa | 13.26 |
| 75 °C | 0.10 MPa | 12.70 |
| 100 °C | 0.10 MPa | 12.25 |
| 150 °C | 0.47 MPa | 11.64 |
| 200 °C | 1.5 MPa | 11.31 |
| 250 °C | 4.0 MPa | 11.20 |
| 300 °C | 8.7 MPa | 11.34 |
| 350 °C | 17 MPa | 11.92 |
With electrolyte solutions, the value of pKw is dependent on ionic strength of the electrolyte. Values for sodium chloride are typical for a 1:1 electrolyte. With 1:2 electrolytes, MX2, pKw decreases with increasing ionic strength.
The value of Kw is usually of interest in the liquid phase. Example values for superheated steam and supercritical water fluid are given in the table.
Isotope effects
, D2O, self-ionizes less than normal water, H2O;This is attributed to oxygen forming a slightly stronger bond to deuterium because the larger mass of deuterium results in a lower zero-point energy, a quantum mechanical effect analogous to the kinetic isotope effect.
Expressed with activities a, instead of concentrations, the thermodynamic equilibrium constant for the heavy water ionization reaction is:
Assuming the activity of the D2O to be 1, and assuming that the activities of the D3O+ and OD− are closely approximated by their concentrations
The following table compares the values of pKw for H2O and D2O.
Ionization equilibria in water–heavy water mixtures
In water–heavy water mixtures equilibria several species are involved: H2O, HDO, D2O, H3O+, D3O+, H2DO+, HD2O+, HO−, DO−.Mechanism
The rate of reaction for the ionization reactiondepends on the activation energy, ΔE‡. According to the Boltzmann distribution the proportion of water molecules that have sufficient energy, due to thermal population, is given by
where k is the Boltzmann constant. Thus some dissociation can occur because sufficient thermal energy is available. The following sequence of events has been proposed on the basis of electric field fluctuations in liquid water. Random fluctuations in molecular motions occasionally produce an electric field strong enough to break an oxygen–hydrogen bond, resulting in a hydroxide and hydronium ion ; the hydrogen nucleus of the hydronium ion travels along water molecules by the Grotthuss mechanism and a change in the hydrogen bond network in the solvent isolates the two ions, which are stabilized by solvation. Within 1 picosecond, however, a second reorganization of the hydrogen bond network allows rapid proton transfer down the electric potential difference and subsequent recombination of the ions. This timescale is consistent with the time it takes for hydrogen bonds to reorientate themselves in water.
The inverse recombination reaction
is among the fastest chemical reactions known, with a reaction rate constant of at room temperature. Such a rapid rate is characteristic of a diffusion-controlled reaction, in which the rate is limited by the speed of molecular diffusion.
Relationship with the neutral point of water
Water molecules dissociate into equal amounts of H3O+ and OH−, so their concentrations are equal to at 25 °C. A solution in which the H3O+ and OH− concentrations equal each other is considered a neutral solution. In general, the pH of the neutral point is numerically equal to pKw.Pure water is neutral, but most water samples contain impurities. If an impurity is an acid or base, this will affect the concentrations of hydronium ion and hydroxide ion. Water samples that are exposed to air will absorb some carbon dioxide to form carbonic acid and the concentration of H3O+ will increase due to the reaction H2CO3 + H2O = HCO3− + H3O+. The concentration of OH− will decrease in such a way that the product remains constant for fixed temperature and pressure. Thus these water samples will be slightly acidic. If a pH of exactly 7.0 is required, it must be maintained with an appropriate buffer solution.