Question

What fraction of piperazine (perhydro-1,4-diazine) is in each of its three forms (H2A, HA-, A2−) at pH 6.50? The acid dissociation constant values for piperazine are ?a1=4.65×10−6 and ?a2=1.86×10−10.

Answer 1

pKa1 + pKa2 = 14

Ka1 = 4.65 x 10^-6

Ka2 = 1.86 x 10^-10

pH = 6.50

[H+] = 3.16 x 10^-7 M

[H+]^2 = 1.0 x10^-13

Ka1 Ka2 = 8.65 x 10^-16

Ka1 [H+] = 1.47 x 10^-12

[H+]^2 + Ka1 Ka2 + Ka1 [H+]   = 1.571 x 10^-12

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

_H2A = 0.0636

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

_HA- = 0.936

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

_A2- = 5.51 x 10^-4