Find Kb from given pH

Question

The pH of a 5.18E-1 M solution of a weak base if 9.54. Calculate K_b for this base.

Answer 1

Let the base be represented by B

B + H₂O ==> BH⁺ + OH^-

Kb = [BH⁺][OH^-]/[B]

From the pH = 9.54, we can find the [H⁺] and from that we can find the [OH^-]. Since [OH^-] = [BH⁺], and we are given the initial [B], we have all we need to calculate the Kb.

[H⁺] = 1x10^-9.54 = 2.88x10^-10

[H⁺][OH^-] = Kw = 1x10^-14

[OH^-] = 1x10^-14 / 2.88x10^-10

[OH^-] = 3.47x10^-5 M = [BH⁺]

Kb = (3.47x10^-5][3.47x10^-5] / 5.18x10^-1

Kb = 2.32x10^-9