What is the pH of 0.22 M trimethylammonium chloride

Question

What is the pH of 0.22 M trimethylammonium chloride, (CH₃)₃NHCl? Enter your answer with two decimal places.

The K_b of trimethylamine, (CH₃)₃N, is 6.3 x 10^-5.

Answer is 5.23

Answer 1

Trimethylammonium ion is the conjugate acid of trimethylamine.

(CH₃)₃NH⁺ ==> H⁺ + (CH₃)₃N

Ka = 1x10^-14/6.3x10^-5 = 1.59x10^-10 = [H+][(CH)3N]/[(CH₃)₃NH]

1.59x10^-10 = (x)(x)/0.22 - x and assuming x is small...

x² = 3.5x10^-11

x 5.92x10^-6 = [H⁺]

pH = - log 5.92x10^-5

pH = 5.23