JEE Main & Advanced Chemistry Equilibrium / साम्यावस्था Dissociation Constants Of Acids And Bases

(1) Dissociation constant for weak acid : Consider an acid \[HA\] which, when dissolved in water ionizes as,

\[HA\]  \[\rightleftharpoons \]  \[{{H}^{+}}+{{A}^{-}}\]

Applying the law of mass action, \[{{K}_{a}}=\frac{[{{H}^{+}}][{{A}^{-}}]}{[HA]}\]

Where, \[{{K}_{a}}\] is the dissociation constant of the acid, \[HA\]. It has constant value at definite temperature and does not change with the change of concentration.

Dissociation Constant for polybasic acid : Polybasic acids ionise stepwise as, for example, orthophosphoric acid ionises in three steps and each step has its own ionisation constant.

\[{{H}_{3}}P{{O}_{4}}\]  \[\rightleftharpoons \] \[{{H}^{+}}+{{H}_{2}}PO_{4}^{-}\]              (I step)

\[{{H}_{2}}PO_{4}^{-}\]  \[\rightleftharpoons \]  \[{{H}^{+}}+HPO_{4}^{-2}\]                      (II step)

\[HPO_{4}^{-2}\]  \[\rightleftharpoons \] \[{{H}^{+}}+PO_{4}^{-3}\]                                   (III step)

Let \[{{K}_{1}},\ {{K}_{2}}\] and \[{{K}_{3}}\] be the ionization constants of first, second and third steps respectively. Thus,

        \[{{K}_{1}}=\frac{[{{H}^{+}}][{{H}_{2}}PO_{4}^{-}]}{[{{H}_{3}}P{{O}_{4}}]}\];\[{{K}_{2}}=\frac{[{{H}^{+}}][HPO_{4}^{-2}]}{[{{H}_{2}}PO_{4}^{-}]}\];\[{{K}_{3}}=\frac{[{{H}^{+}}][PO_{4}^{-3}]}{[HPO_{4}^{-2}]}\]

In general, \[{{K}_{1}}>{{K}_{2}}>{{K}_{3}}\]

The overall dissociation constant\[(K)\] is given by the relation,

\[K={{K}_{1}}\times {{K}_{2}}\times {{K}_{3}}\]

(2) Dissociation constant for weak base : The equilibrium of \[N{{H}_{4}}OH\] (a weak base) can be represented as,

\[N{{H}_{4}}OH\]  \[\rightleftharpoons \] \[NH_{4}^{+}+O{{H}^{-}}\]

Applying the law of mass action, \[{{K}_{b}}=\frac{[NH_{4}^{+}][O{{H}^{-}}]}{[N{{H}_{4}}OH]}\]

\[{{K}_{b}}\] is constant at a definite temperature and does not change with the change of concentration.