JEE Main & Advanced Chemistry Equilibrium / साम्यावस्था Ostwald's Dilution Law

The strength of an acid or a bas is experimentally measured by determining its dissociation or ionisation constant. 

When acetic acid (a weak electrolyte) is dissolved in water, it dissociates partially into \[{{H}^{+}}\] or \[{{H}_{3}}{{O}^{+}}\] and \[C{{H}_{3}}CO{{O}^{-}}\] ions and the following equilibrium is obtained,

\[C{{H}_{3}}COOH+{{H}_{2}}O\]  \[\rightleftharpoons \]  \[C{{H}_{3}}CO{{O}^{-}}+{{H}_{3}}{{O}^{+}}\]

Applying law of chemical equilibrium, 

\[K=\frac{[C{{H}_{3}}CO{{O}^{-}}]\times [{{H}_{3}}{{O}^{+}}]}{[C{{H}_{3}}COOH]\times [{{H}_{2}}O]}\]

In dilute solution, \[[{{H}_{2}}O]\] is constant. The product of \[K\] and constant \[[{{H}_{2}}O]\] is denoted as \[{{K}_{a}}\], the ionization constant or dissociation constant of the acid is,

\[{{K}_{a}}=\frac{[C{{H}_{3}}CO{{O}^{-}}]\times [{{H}_{3}}{{O}^{+}}]}{[C{{H}_{3}}COOH]}\]                                                                                              …..(i)

The fraction of total number of molecules of an electrolyte which ionise into ions is known as degree of dissociation/ionisation \[\alpha \].

If \['C'\] represents the initial concentration of the acid in moles \[{{L}^{-1}}\] and \[\alpha \] the degree of dissociation, then equilibrium concentration of the ions \[(C{{H}_{3}}CO{{O}^{-}}\] and \[{{H}_{3}}{{O}^{+}})\] is equal to \[C\alpha \] and that of the undissociated acetic acid \[=C(1-\alpha )\] i.e., we have

                \[C{{H}_{3}}COOH+{{H}_{2}}O\] \[\rightleftharpoons \]  \[C{{H}_{3}}CO{{O}^{-}}+{{H}_{3}}{{O}^{+}}\]

Initial conc      \[C\]                                           0              0

Conc. at eqb. \[C(1-\alpha )\]                    \[C\alpha \]       \[C\alpha \]

Substituting the values of the equilibrium concentrations in equation (i), we get

\[{{K}_{a}}=\frac{C\alpha .C\alpha }{C(1-\alpha )}=\frac{{{C}^{2}}{{\alpha }^{2}}}{C(1-\alpha )}=\frac{C{{\alpha }^{2}}}{1-\alpha }\]                          …..(ii)

In case of weak electrolytes, the value of \[\alpha \] is very small and can be neglected in comparison to 1 i.e., \[1-\alpha =1\].

Hence, we get

\[{{K}_{a}}=C{{\alpha }^{2}}\] or \[\alpha =\sqrt{\frac{{{K}_{a}}}{C}}\]                                                                                                                   …..(iii)

The degree of dissociation, \[\alpha \] can therefore be calcualted at a given concentration, \[C\] if \[{{K}_{a}}\] is known. Furher, if \[V\] is the volume of the solution in litres containing 1 mole of the electrolyte, \[C=1/V\]. Hence we have

     \[\alpha =\sqrt{{{K}_{a}}V}\]                                                                                                                                                                                 …..(iv)

Similarly, for a weak base like \[N{{H}_{4}}OH\], we have

\[\alpha =\sqrt{{{K}_{b}}/C}=\sqrt{{{K}_{b}}V}\]                                                                                                                                                       …..(v)

The above equations lead to the following result

“For a weak electrolyte, the degree of ionisation is inversely proportional to the square root of molar concentration or directly proportional to the square root of volume containing one mole of the solute.”

This is called Ostwald’s dilution law.