## Chemistry: Molecular Approach (4th Edition)

Published by Pearson

# Chapter 16 - Exercises - Page 771: 23

#### Answer

For a conjugate acid-base pair, the acid ionization constant and the base ionization constant relate to each other by the equation: $$K_a \times K_b = K_w$$ At 25 $^oC$: $K_a \times K_b = 1.0 \times 10^{-14}$

#### Work Step by Step

1. Write the generic $K_a$ and $K_b$ equations for a conjugate acid-base pair: $$K_a = \frac{[A^-][H_3O^+]}{[HA]}$$ $$K_b = \frac{[HA][OH^-]}{[A^-]}$$ 2. Multiplying the equations: $$K_a \times K_b = \frac{[A^-][H_3O^+]}{[HA]}\frac{[HA][OH^-]}{[A^-]}$$ $$K_a \times K_b = [H_3O^+][OH^-] = K_w$$ $$K_a \times K_b = K_w$$

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