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:
$$K_a \times K_b = \frac{[A^-][H_3O^+]}{[HA]}\frac{[HA][OH^-]}{[A^-]}$$
$$K_a \times K_b = [H_3O^+][OH^-] = K_w$$
$$K_a \times K_b = K_w$$
