First, let A^– represent acetate, CH₃COO^–, which is the conjugate weak base to the parent weak acid, acetic acid.

For acetic acid, CH₃COOH
K_a = 1.80 × 10^-5

For acetate ion, CH₃COO^–
K_b = K_wK_a = 5.56 × 10^-10

\(\displaystyle K_{\rm b} = {x^2 \over 0.01 – x} \)

\(K_{\rm b}(0.01) - K_{\rm b}(x) = x^2 \)

\(0 = x^2 + K_{\rm b}(x) - K_{\rm b}(0.01) \)

\(\displaystyle x = {-K_{\rm b} + \sqrt{K_{\rm b}^2 + 4K_{\rm b}(0.01)}\over 2}\)

\(\displaystyle x = 2.3567 \times 10^{-6} \)

For 0.01 M conj BASE (A^–)
where K_b = 5.56 × 10^-10

[H⁺] = 4.24 × 10^-9 M

[OH^-] = 2.36 × 10^-6 M

pH = 8.37

pOH = 5.63