The equilibrium constant K for a base is usually defined as the association constant for protonation of the base, B, to form the conjugate acid, .
Using similar reasoning to that used before
K is related to K for the conjugate acid. In water, the concentration of the hydroxide ion, , is related to the concentration of the hydrogen ion by , therefore
Substitution of the expression for  into the expression for K gives
When K, K and K are determined under the same conditions of temperature and ionic strength, it follows, taking cologarithms, that pK = pK − pK. In aqueous solutions at 25 °C, pK is 13.9965, so
with sufficient accuracy for most practical purposes. In effect there is no need to define pK separately from pK, but it is done here as often only pK values can be found in the older literature.
For an hydrolyzed metal ion, K can also be defined as a stepwise dissociation constant
This is the reciprocal of an association constant for formation of the complex.