Hydrazine is a weak base, kb=3.0x10^-6. find the ph of an aqueous 2.0 m solution of its conjugate acid

Answer is: pH of hydrazine conjugate acid is 4.088.

Chemical reaction: N₂H₅⁺ + H₂O ⇄ N₂H₄ + H₃O⁺.

[N₂H₅⁺] = 2.0 M.

[N₂H₄] = [H₃O⁺] = x.

Kb (N₂H₄) = 3.0·10⁻⁶.

Kb·Ka = 1.00·10⁻¹⁴.

Ka (N₂H₅⁺) = 1.00·10⁻¹⁴ : 3.0·10⁻⁶.

Ka = 3.33·10⁻⁹.

Ka = [N₂H₄]·[H₃O⁺] / [N₂H₅⁺].

3.33·10⁻⁹ = x² / 2.0 M.

x = [H₃O⁺] = √3.33·10⁻⁹ · 2.0 M.

[H₃O⁺] = 8.1·10⁻⁵ M.

pH = - log[H₃O⁺].

pH = - log (8.1·10⁻⁵ M).

pH = 4.088.