Chemically pure water 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:
: HO + HO  HO + OH
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 HO is formally equal to twice the chemical potential of HO 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 solutes (dissolved species such as ions) 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 K, may be given by:
where [HO] is the molarity (molar concentration) of hydrogen cation or hydronium ion, and [OH] is the concentration of hydroxide ion. When the equilibrium constant is written as a product of concentrations (as opposed to activities) it is necessary to make corrections to the value of  depending on ionic strength and other factors (see below).
At 24.87 °C and zero ionic strength, K 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 (= 1 mol/kg) when molality is used or 1 molar (= 1 mol/L) when molar concentration is used. For many practical purposes, the molality (mol solute/kg water) and molar (mol solute/L solution) concentrations can be considered as nearly equal at ambient temperature and pressure if the solution density remains close to one (i.e., sufficiently diluted solutions and negligible effect of temperature changes). The main advantage of the molal concentration unit (mol/kg water) is to result in stable and robust concentration values which are independent of the solution density and volume changes (density depending on the water salinity (ionic strength), temperature and pressure); therefore, molality is the preferred unit used in thermodynamic calculations or in precise or less-usual conditions, e.g., for seawater with a density significantly different from that of pure water, or at elevated temperatures, like those prevailing in thermal power plants.
We can also define pK  −log K (which is approximately 14 at 25 °C). This is analogous to the notations pH and pK for an acid dissociation constant, where the symbol p denotes a cologarithm. The logarithmic form of the equilibrium constant equation is pK = pH + pOH.