Question

What fraction of piperazine (perhydro-1,4-diazine) is in each of its three forms (H2A, HA–, A2–) at pH 6.67? The acid dissociation constant values for piperazine are Ka1 = 4.65×10–6 and Ka2 = 1.86×10–10.

Answer 1

pH = 6.67 = -log[H+]

[H+] = 2.14 x 10^-7 M

For diprotic acid we have equations as,

[H2A] = [H+]^2/([H+]^2 + [H+]K1 + K1K2)

Feed values,

[H2A] = (2.14 x 10^-7)^2/((2.14 x 10^-7)^2 + (2.14 x 10^-7)4.65 x 10^-6 + 4.65 x 10^-6 x 1.86 x 10^-10)

          = 4.58 x 10^-14/(4.58 x 10^-14 + 9.951 x 10^-13 + 8.649 x 10^-16)

          = 0.044 M

[HA-] = K1[H+]/([H+]^2 + [H+]K1 + K1K2)

Feed values,

[HA-] = 4.65 x 10^-6 x 2.14 x 10^-7/((2.14 x 10^-7)^2 + (2.14 x 10^-7)4.65 x 10^-6 + 4.65 x 10^-6 x 1.86 x 10^-10)

         = 9.951 x 10^-13/(4.58 x 10^-14 + 9.951 x 10^-13 + 8.649 x 10^-16)

         = 9.951 x 10^-13/1.042 x 10^-12

         = 0.960 M

[A2-] = K1K2/([H+]^2 + [H+]K1 + K1K2)

Feed values,

[A2-] = 4.65 x 10^-6 x 1.86 x 10^-10/1.042 x 10^-12

         = 8.30 x 10^-4 M