What is the pH of the solution?

Question

An aqueous solution of base has a concentration of 0.234 M (@ 25 ^oC).

The conjugate acid of the base is known to have a K_a value of 3.82 x 10^-7.

Answer 1

Let the base be B

B + H₂O ==> BH⁺ + OH^-

KaKb = Kw = 1x10^-14

Kb = 1x10^-14 / Ka = 1x10^-14 / 3.82x10^-7

Kb = 2.62x10^-8

Kb = 2.62x10^-8 = [BH⁺][OH^-] / [B]

2.62x10^-8 = (x)(x) / 0.234

x² = 6.13x10^-9

x = 7.83x10^-5 M = [OH^-]

pOH = -log 7.83x10^-5 = 4.11

pH = 14 - pOH = 14 - 4.11

pH = 9.89