Question

A 1.00-g sample of piperazine hexahydrate is dissolved in enough water to produce 100.0 mL of solution and is titrated with 0.500 M HCl.
What is the initial of the solution, before any titrant is added?

Piperazine,HN(C4H8)NH, is a diprotic weak base used as a corrosion inhibitor and an insecticide and has the following properties:
pkb1=4.22
pkb2=8.67
For writing the reactions of this base in water, it can be helpful to abbreviate the formula as Pip:
Pip+H2O<--->PipH2^2+ +OH-
PipH+ +H2O<-->PipH2^2+ +OH-

The piperazine used commercially is a hexahydrate with the formula C4H10N2*6H2O

Answer 1

pip + H2O ==> PIPH^+ + OH^- (I think you made a typo in this equation).
I would ignore Kb2.
Convert pKb1 to Kb1.
Kb1 = (pipH^+)(OH^-)/(pip.6H2O)
Let x = (pipH^+) = (OH^-) and (pip.6H2O) = moles/L soln where moles = grams/molar mass.