# Introduction to Equilibrium Constant of Water

Even the purest sample of water is found to conduct electricity to a small extent. Specific conductance of pure water is found to be 5.53 x 10-6Sm-1 at 25ºc.  This indicates the presence of charged particles in pure water.

In a self-ionization reaction of water (auto ionization) two water molecules react to produce a hydronium ion (H3O+) and a hydroxide ion(OH).

2 H2O (l)  H3O+ (aq) + OH (aq)

## Equilibrium Constant of Water

Water has a chemical composition of H2O, but it does not exist as such in practice. This prevail equilibrium between the undissociated water molecule and the ions obtained by its dissociation. But this tendency of water to dissociate into its ions is also not too large. It has been found that the concentration of H+ ion (must be equal to the concentration of OH ion) is only 10-7 mol/dm3

The expression for the equilibrium constant of water can be obtained by using the law of mass action,

2 H2O (l)  H3O+ (aq) + OH (aq)

If k1 is the rate constant for the forward reaction, i.e., the dissociation reaction of water molecule and k2 is the rate constant for the backward reaction, i.e., the association of the proton (hydronium ion) and the hydroxide ion, then the equilibrium constant for the above reaction gives the equilibrium constant of water, which can be given by,

K = k1 / k2  or

Keq = [H3O+] [OH-] / [H2O]

Keq = [H+] [OH-] / [H2O]

But, [H2O] virtually remains constant ( 1 dm3 of water = 1000g = 1000 / 18 =55.55moles. Out of which, only 10-7 mole of it ionizes. Hence, [H2O] is virtually 55.55 mol/dm3 itself.)

Therefore, Keq . [H2O] = [H+] [OH-]

Kw = Keq . [H2O] = [H+] [OH-]

Kw = [H+] [OH-] a constant.

Where,

Keq is the equilibrium constant of water dissociation reaction,

Kw is the ionic product of water.

Variation of Kw with temperature:

In water or any other aqueous solution, the product of H+ ion concentration and OH- ion concentration remains constant at a given temperature. It is called Ionic product of water. Its value at 25ºc is 10-14.  With temperature, the ionic product of the solution also changes, since the dissociation of the water molecule becomes easier at higher temperature. But, the concentration of hydroxide and hydronium ion remains same always, at any temperature.

## Significance of Equilibrium Constant of Water

The pH of water is taken as a reference value to relate the acidity or basicity of other solutions. The pH of water is 7, which is neutral. For an acidic solution pH remains less than 7 and for a basic solution it is greater than 7.

pH = -log10 [H+]                                              pOH = -log10 [OH-]

pH = -log10 10-7                                             pOH = -log10 10-7

pH = 7                                                               pOH = 7