How is pKa related to pKb?

How can I find a relationship to pKa and pKb using pK = - log K ?
Alex Baskin

Imagine you have an acid dissociation

HA H+ + A- Ka = [H+][A-]


followed by hydrolysis of the A- ion,

A- + H2O HA + OH- Kb = [OH-][HA]


If you add the two reactions together, the net reaction is the hydrolysis of water,

H2O H+ + OH- Kw = [H+][OH-] = 1.01×10-14

Looking at the equilibrium expressions, you can see that the product of Ka and Kb is Kw:

Ka Kb = [H+][A-]

× [OH-][HA]

= [H+][OH-] = Kw

Take minus the log of both sides of this equation and you get pKa + pKb = pKw.

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Author: Fred Senese

General Chemistry Online! How is pK_a_ related to pK_b_?

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