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How is pKa related to pKb?

How can I find a relationship to pKa and pKb using pK = - log K ?
Alex Baskin baskin@scruznet.com

Imagine you have an acid dissociation

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

[HA]

followed by hydrolysis of the A- ion,

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

[A-]

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-]

[HA]
× [OH-][HA]

[A-]
= [H+][OH-] = Kw

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

Back to Just Ask Antoine!

Author: Fred Senese senese@antoine.frostburg.edu



General Chemistry Online! How is pK_a_ related to pK_b_?

Copyright © 1997-2010 by Fred Senese
Comments & questions to fsenese@frostburg.edu
Last Revised 02/23/18.URL: http://antoine.frostburg.edu/chem/senese/101/acidbase/faq/pKa-and-pKb.shtml