The salt `Zn (OH)_(2)` is involved in the following two equilibria:
`Zn(OH)_(2)(s) hArr Zn^(3+)(aq) +2 overset(Theta)OH(aq) K_(sp) = 1.2 xx 10^(-17)`
`Zn(OH)_(2)(s)+2 overset(Theta)OH hArr Zn(OH)_(4)^(2-)(aq)K_(f) = 0.12`
Calculate `|overset(Theta)OH|` at which solubility of `Zn(OH)_(2)` be a minimum. Also find the solubility of `Zn(OH)_(2)` at this `pH`.

Explanation

To solve the problem, we need to determine the concentration of hydroxide ions \([OH^-]\) at which the solubility of \(Zn(OH)_2\) is minimized, and then find the solubility of \(Zn(OH)_2\) at that concentration.

### Step-by-Step Solution:

1. **Write the Equilibria**:
The two equilibria given are:
\[
Zn(OH)_2(s) \rightleftharpoons Zn^{2+}(aq) + 2OH^-(aq) \quad (K_{sp} = 1.2 \times 10^{-17})
...