Question

What fraction of piperazine (perhydro-1,4-diazine) is in each of its three forms (H2A, HA-, A2-) at pH 8.87? The acid dissociation constant values for piperazine are Ka1 = 4.65 x 10^-6 and Ka2 = 1.86 x 10^-10.

Answer 1

pKa1 + pKa2 = 14

Ka1 = 4.65 x 10^-6

Ka2 = 1.86 x 10^-10

pH = 8.87

[H+] = 1.35 x 10^-9

[H+]^2 = 1.82 x10^-18

Ka1 Ka2 = 8.70 x 10^-16

Ka1 [H+] = 6.27 x 10^-15

[H+]^2 + Ka1 Ka2 + Ka1 [H+]   = 7.14 x 10^-15

_H2A = [H+]^2 / [H+]^2 + Ka1 Ka2 + Ka1 [H+]

_H2A = 2.55 x 10^-4

_{HA- =} Ka1 [H+] / [H+]^2 + Ka1 Ka2 + Ka1 [H+]   

_HA- = 0.878

_A2- = Ka1 Ka2 / [H+]^2 + Ka1 Ka2 + Ka1 [H+]

_A2- = 0.122