General Chemistry: Principles and Modern Applications (10th Edition)

Published by Pearson Prentice Hal
ISBN 10: 0132064529
ISBN 13: 978-0-13206-452-1

Chapter 16 - Acids and Bases - Example 16-12 - Evaluating Ionization Constants for Hydrolysis Reactions - Page 726: Practice Example B


Since the $K_b$ for $CN^-$ is greater than the $K_a$ for $N{H_4}^+$, the solution of this salt is basic.

Work Step by Step

$$K_a(NH_4^+) = \frac{K_w}{K_b(NH_3)}= \frac{1.0 \times 10^{-14}}{1.8 \times 10^{-5}} = 5.6 \times 10^{-10}$$ $$K_b (CN^-) = \frac{K_w}{K_a(HCN)} = \frac{1.0 \times 10^{-14}}{6.2 \times 10^{-10}} = 1.6 \times 10^{-5}$$ $$K_b \gt K_a$$ Therefore, the solution of $NH_4CN$ is basic.
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