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Ka and Kb Relationship - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:35 AM | #JEE Main

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Relation Between Ka, Kb and Kw for Conjugate Pair

The relation between Ka,Kb and Kw can be understand by the following reaction.
\mathrm{NH_{3}\: +\: H_{2}O\: \rightleftharpoons \: NH_{4}^{+}\: +\: OH^{-}}
Base                      Conjugate acid

The equilibrium constant Kb for base NH3 is given as:
\mathrm{K_{b}\: =\: \frac{[NH_{4}^{+}][OH^{-}]}{NH_{3}}}
Again, the reaction is:
\mathrm{NH_{4}^{+}\: +\: H_{2}O\: \rightleftharpoons \: NH_{3}\: +\: H_{3}O^{+}}

The equilibrium constant Ka for conjugate acid NH4+ is given as:
\mathrm{K_{a}\: =\: \frac{[NH_{3}][H_{3}O^{+}]}{NH_{4}^{+}}}

Thus, \mathrm{K}_{\mathrm{a}} \times \mathrm{K}_{\mathrm{b}}=\left[\mathrm{H}_3 \mathrm{O}^{+}\right]\left[\mathrm{OH}^{-}\right]=\mathrm{K}_{\mathrm{w}}
Thus, \mathrm{K}_{\mathrm{a}} \propto 1 / \mathrm{K}_{\mathrm{b}} at a given temperature

Therefore, if Ka of acid increases, then Kb of the conjugate base decreases. In other words, the conjugate base of strong acid is a weak base and vice-versa.

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Relation Between Ka, Kb and Kw for Conjugate Pair

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Ka and Kb Relationship

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Relation Between Ka, Kb and Kw for Conjugate Pair

Chemistry Part I Textbook for Class XI

Page No. : 222

Line : 22

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