The pain killer morphine is a weak base when added to water. The Kb is 1.6 × 10–6. What is the pH of a 4.44 × 10–3 M solution of morphine?

Question

The pain killer morphine is a weak base when added to water. The K_b is 1.6 × 10^–6. What is the pH of a 4.44 × 10^–3 M solution of morphine?

Answer 1

Let B represent the weak base morphine.

B + H2O ==> BH⁺ + OH^-

Kb = [BH⁺][OH^-] / [B]

1.6x10^-6 = (x)(x)/4.44x10^-3 - x (assuming x is small)...

x² = 7.1x10^-9

x = 8.4x10^-5 = [OH^-]

pOH = -log 8.4x10^-5 = 4.07

pH = 14 - pOH = 14 - 4.07

pH = 9.93