There are two main distinctions which we can make about bases. The base is either a strong base or a weak base. One can determine whether a base is weak or strong by looking at the extent to which the base will dissociate in water. Strong base will fully dissociate and a weak base will only partially dissociate, acids follow this same pattern, in that strong acids fully dissociate and weak acids only partially dissociate.
H2O + H2O = H3O+ + OH-
This reaction also illustrates the amphoteric properties of water. As one water molecule acts as a base and one acts as an acid.
[H3O+] = [OH-] = 10-7 mol dm-3
The product of these two concentrations = ionisation of water
Kw = [H3O+] [HO-] = 10-14 mol dm-3
We can derive the pH of a base on the premise that a base is strong.
Because bases and acids are related via the ionisation of water we are able to derive the pH for strong acids and bases. Looking back at the definition of a strong acid or base, we know that strong acids fully dissociate in solution to produce hydronium ions, the concentration of which will be equal to that of the acid. Strong bases also fully dissociate to produce hydroxide ions, therefore the pH can be determined, as pH is dependant on the concentration of hydronium ions.
pH = -log [H3O+]
And from the ionisation of water, we can determine the concentration of H3O+ from the OH- concentration, as we know that Kw is equal to 10-14
[H3O+] = 10-14 / [H-]
The next page discusses the acidity constant and its relationship with basicity