Question 8.2: A Weak-Acid Problem. Find the pH of 0.050 M trimethylammoniu...
A Weak-Acid Problem
Find the pH of 0.050 M trimethylammonium chloride.
We assume that ammonium halide salts are completely dissociated to give (CH_{3})_{3}NH^{+} and Cl^{−}.^{†} We then recognize that trimethylammonium ion is a weak acid, being the conjugate acid of trimethylamine, (CH_{3})_{3}N, a weak base. Cl^{−} has no basic or acidic properties and should be ignored. In Appendix G, we find trimethylammonium ion listed as trimethylamine but drawn as trimethylammonium ion, with pK_{a} = 9.799, at an ionic strength of μ = 0. So,
K_{a} = 10^{−pK_{a}} = 10^{−9.799} = 1.59 × 10^{−10}
From here, everything is downhill.
\underset{F – x}{(CH_{3})_{3}NH^{+}} \xrightleftharpoons[]{K_{a}} \underset{x}{(CH_{3})_{3}N} + \underset{x}{H^{+}}
\frac{x^{2}}{0.050 − x} = 1.59 × 10^{−10} (8-12)
x = 2.8 × 10^{−6} M ⇒ pH = 5.55
Test Yourself Find the pH of 0.050 M triethylammonium bromide. (Answer: 6.01)
Cl^{−} has no acidic or basic properties because it is the conjugate base of the strong acid, HCl. If Cl^{−} had appreciable basicity, HCl would not be completely dissociated.
