Ostwald's dilution law for weak electrolytes
According to Arrhenius theory, weak electrolytes partially dissociate into ions in water which are in equilibrium with the undissociated electrolyte molecules. Ostwald's dilution law relates the dissociation constant of the weak electrolyte with the degree of dissociation and the concentration of the weak electrolyte. Consider the dissociation equilibrium of CH3COOH which is a weak electrolyte in water.
CH3COOH <-- -- > CH3COO- + H+
Ka = [ H + ][CH 3COO - ] / [CH3COOH]
a is the degree of dissociation which represents the fraction of total concentration of CH3COOH that exists in the completely ionised state. Hence (1 - a) is the fraction of the total concentration of CH3COOH, that exists in the unionised state. If 'C' is the total concentration of CH 3COOH initially, then at equilibrium Ca, Ca and C (1 - a) represent the concentration of H+, CH3COO- and CH3COOH respectively.
Then Ka = (Ca .C a) / C (1-a ) / a2 C / (1-a)
If a is too small, then Ka = a2C
a = root(Ka/C) also [H+] = [CH3COO-] = Ca
[H+] = root(Ka.C)
Ka= a2C / (1-a) is known as the Ostwalds dilution law. For weak bases,
Kb= a2C / (1-a) and a = rt(Kb/C) at a = small values.
Kb = dissociation constant for weak base.This law fails for strong electrolytes. For strong electrolytes, a tends to 1.0 and therefore Ka increases tremendously.