Acids & Bases Chemistry Math Question 7

Question

Determine the pH of a 0.12 M aqueous solution of ammonia.

K_b(NH₃) = 1.8x10^-5.

Answer 1

Ammonium acting as a base:

NH₃ + H₂O ==> NH₄OH ==> NH₄⁺ + OH^-

Kb = [NH₄⁺][OH-]/[NH₃]

1.8x10^-5 = (x)(x)/0.12-x and if we assume x is small we can ignore it in the denominator

1.8x10^-5 = x²/0.12

x² = 2.16x10^-6

x = 4.7x10^-3 M = [OH-] (and this is small. i.e. < 5% compared to 0.12 so the assumption was valid)

From this, we can find pOH and then pH:

pOH = -log 4.7x10^-3 = 2.33

pH = 14 - pOH = 11.7