What fraction of piperazine (perhydro-1,4-diazine) is in each of its three forms (H2A, HA–, A2–) at pH 7.22?

Answer 1

I totally screwed up when I tried to answer this question for someone else, but here is the work from Dr.Matthews:

aH2A = [H+]^2/([H+]^2 + [H+]K1 + K1K2)

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

aA2- = K1K2/([H+]^2 + [H+]K1 + K1K2)

Ka1 = 4.65×10–6 and Ka2 = 1.86×10–10