## Chemistry (4th Edition)

For a saturated zinc hydroxide solution: $pH = 9.53$
1. Write the $K_{sp}$ expression: $Zn(OH)_2(s) \lt -- \gt 1Zn^{2+}(aq) + 2OH^{-}(aq)$ $1.8 \times 10^{-14} = [Zn^{2+}]^ 1[OH^{-}]^ 2$ 2. Considering a pure solution: $[Zn^{2+}] = 1S$ and $[OH^{-}] = 2S$ $1.8 \times 10^{-14}= ( 1S)^ 1 \times ( 2S)^ 2$ $1.8 \times 10^{-14} = 4S^ 3$ $4.5 \times 10^{-15} = S^ 3$ $\sqrt [ 3] {4.5 \times 10^{-15}} = S$ $1.7 \times 10^{-5} = S$ - This is the molar solubility value for this salt. Since each molecule has 2 hydroxide ions: $[OH^-] = 2 * 1.7 \times 10^{-5} = 3.4 \times 10^{-5}$ 3. Calculate the pOH: $pOH = -log[OH^-]$ $pOH = -log( 3.4 \times 10^{- 5})$ $pOH = 4.47$ 4. Find the pH: $pH + pOH = 14$ $pH + 4.47 = 14$ $pH = 9.53$