# The Ionization Constant of Water and Its Ionic Product

The conductivity measurements of water indicate that water is a weak electrolyte. Even in pure state water is weakly ionized to give H+(aq) and OH-(aq) ions as shown below: The ionization constant of water may be written as

K a(H2O) = [H+] [OH ] / [H2O]

Since concentration of water is very high(=  55.55 mol L – 1) and only a very small fraction of it undergoes ionization, therefore, [H2O] may be taken as constant and may be combined with K a(H2O) to have another constant Ka

Ka(H2O)[H2O] = [H+] [OH ]

Kw = [H+] [ OH ]

The constant Kw is called ionic product constant of water. The concentration of H+ in pure water is found out experimentally to be 1.0 x 10-7 mol dm-3 at 298 K. Moreover, in pure water concentration of H+ is equal to the concentration of OH- ions because dissociation of water produces equal number of H+ ions. Therefore,

[H+] = [OH]= 1 x 10 -7 mol -3

Kw  = [H3O+] [OH ]

Kw = (1 x 10 -7 mol dm -3) ( 1 x 10 -7 mol dm -3)

= 1 x 10 -14 mol2 dm -6

The degree of dissociation of water

= 10 -7 mol dm -3 / 55.55 mol dm -3 = 1.8 x 10 -9

Since with increase in temperature dissociation of water increases, therefore, value of Kw increases as the temperature is increased. However, at all temperatures [H+] remains equal to [OH-] in pure water. The values of Kw at different temperatures have been given in Table 25.3.

Table 25.3. Ionic Product of Water at Different Temperatures

Temperature (K)                               Ionic Product, Kw(mol2dm-<i)

273                                                      0.113 x 10-14

283                                                      0.292 x 10-14

293                                                      0.687 x 10-14

298                                                      1.008 x 10-14

313                                                      2.917 x 10-14

323                                                      5.474 x 10-14

373                                                      (56) x 10-14

Concentration ofH3O+ and OH-Ions in Aqueous Solutions of acids and bases

We have already seen that [H30 +] is equal to [OH-] in pure water. But, on addition of some acid or base to water these concentrations no longer remain equal. However, the value of ionic product of water (Kw) at a particular temperature always remains constant irrespective of the fact whether water is pure or some acid or base has been added to it. For example, if an acid (say HCl) is added to water, the concentration of hydronium ion becomes quite high. Consequently, the dissociation equilibrium of water shifts in the reverse direction (according to the Le-Chatelier’s principle), i.e., H3O + ions would combine with OH- ions to form undissociated water molecule, so that the value of Kw in the solution may remain the same as that in pure water. Thus, addition of an acid in water decreases the [OH-] according to the relation,

[OH ] = KW / [H3O+]

Similarly, the addition of a base such as NaOH increases the [OH] and decreases the [H3O+] according to the relation,

[H2O+] = Kw / [OH]

From the above discussion, it is clear that H3O+ ions and OH- ions are always present in the aqueous solution whether it is acidic or basic. However, the relative concentrations of these ions vary in different solutions. In general,

in neutral solutions [H3O+] = [OH]

in acidic solutions [H3O+] > [QH]

in basic solutions [H3O+] < [QH]

The concentrations of H3O+ ions and OH-ions in different types of acidic and basic solutions have been calculated in the following examples: