Question 8.3: A Weak-Base Problem. Find the pH of 0.10 M ammonia.

When ammonia is dissolved in water, its reaction is

\underset{\begin{matrix} Ammonia \\ F − x \end{matrix} }{NH_{3}} + H_{2}O \xrightleftharpoons[]{K_{b}} \underset{\begin{matrix} Ammonium  ion \\ x \end{matrix} }{NH_{4}^{+}} +  \underset{\begin{matrix} \\ x \end{matrix} }{OH^{−}}

In Appendix G, we find ammonium ion, NH_{4}^{+} , listed next to ammonia. pK_{a} for ammonium ion is 9.245. Therefore, K_{b} for NH_{3} is

K_{b} = \frac{K_{w}}{K_{a}} = \frac{10^{−14.00}}{10^{−9.245}} = 1.76 × 10^{−5}

To find the pH of 0.10 M NH_{3}, we set up and solve the equation

\frac{[NH_{4}^{+}][OH^{−}]}{[NH_{3}]} = \frac{x²}{0.10  −  x} = K_{b} = 1.76 × 10^{−5}

x = [OH^{−}] = 1.3_{2} × 10^{−3} M

[H^{+}] = \frac{K_{w}}{[OH^{−}]} = 7.6 × 10^{−12} M ⇒ pH = − \log [H^{+}] = 11.12

Test Yourself     Find the pH of 0.10 M methylamine. (Answer: 11.80)