How is pK_a related to pK_b?

How can I find a relationship to pK_a and pK_b 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 K_a and K_b is K_w:

Ka Kb =

[H+][A-] [HA]

×

[OH-][HA] [A-]

=

[H+][OH-] = Kw

Take minus the log of both sides of this equation and you get pK_a + pK_b = pK_w.

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Author: Fred Senese senese@antoine.frostburg.edu