Answer
$K = 8.037 \times 10^{-13}$
Work Step by Step
1. We can calculate the K by using this formula:
$K = K_b * K_{ps}$
2. Find the $K_b$ of $CO_3^{2-}$, using the $K_a$ of $H{CO_3}^-$:
$Ka * Kb = Kw$
$Kb = \frac{10^{-14}}{5.6 \times 10^{-11}}$
$Kb = 1.786 \times 10^{-4}$
3. Calculate K:
$K = 1.786 \times 10^{-4} * 4.5\times 10^{-9}$
$K = 8.037 \times 10^{-13}$
