Ostwald's dilution law for weak electrolytes

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⁺

K_a  =  [ 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   K_a = (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)

K_a= a²C / (1-a) is known as the Ostwalds dilution law. For weak bases,

K_b= a²C / (1-a) and a = rt(K_b/C) at a = small values.

K_b = dissociation constant for weak base.