Ionization of Water
In the section on amphiprotic species, we saw that water can act as a very weak acidAn acid that ionizes only partially in a given solvent. and a very weak baseAn base that ionizes only partially in a given solvent., donating protons to itself to a limited extent:
Applying the equilibriumA state in which no net change is occurring, that is, in which the concentrations of reactants and products remain constant; chemical equilibrium is characterized by forward and reverse reactions occurring at the same rate. law to this reaction, we obtain
However, as can be seen in the section on the law of chemical equilibrium, the concentrationA measure of the ratio of the quantity of a substance to the quantity of solvent, solution, or ore. Also, the process of making something more concentrated. of water has a constant value of 55.5 mol dm–3, and so its square can be multiplied by Kc to give a new constant Kw, called the ion-productA substance produced by a chemical reaction. constant of water:
Measurements of the electrical conductivity of carefully purified water indicate that at 25°C [H3O+] = [OH–] = 1.00 × 10–7 mol dm–3, so that
(Since the equilibrium law is not obeyed exactly, even in dilute solutions, results of most equilibrium calculations are rounded to three significant figures. Hence the value of Kw = 1.00 × 10–14 mol2 dm–6 is sufficiently accurate for all such calculations.)
The equilibrium constantThe value of the equilibrium constant expression when equilibrium concentrations are substituted; a value greater than one indicates the position of equilibrium lies toward products (product-favored), and a value less than one indicates the position of equilibrium lies toward reactants (reactant-favored). Kw applies not only to pure water but to any aqueous solution at 25°C. Thus, for example, if we add 1.00 mol of the strong acidAn acid that ionizes completely in a particular solvent. HNO3 to H2O to make a total volume of 1 dm3, essentially all the HNO3 molecules donate their protons to H2O:
and a solution in which [H3O+] = 1.00 mol dm–3 is obtained. Although this solution is very acidic, there are still hydroxide ions present. We can calculate their concentration by rearranging Eq. (1):
The addition of the HNO3 to H2O not only increases the hydronium-ion concentration but also reduces the hydroxide-ion concentration from an initially minute 10–7 mol dm–3 to an even more minute 10–14 mol dm–3.
EXAMPLE Calculate the hydronium-ion concentration in a solution of 0.306 M Ba(OH)2.
Solution Since 1 mol Ba(OH)2 produces 2 mol OH– in solution, we have
[OH–] = 2 × 0.306 mol dm–3 = 0.612 mol dm–3
Note that since strong acids like HNO3 are completely converted to H3O+ in aqueous solution, it is a simple matterAnything that occupies space and has mass; contrasted with energy. to determine [H3O+], and from it, [OH–]. Similarly, when a strong baseA base that dissociates completely or ionizes completely in a particular solvent. dissolves in H2O it is entirely converted to OH–, so that [OH–], and from it [H3O+] are easily obtained.