At `25^@C`, will a precipitate of `Mg(OH)_2` form in a `1 xx 10^(–4)`M solution of `Mg(NO_3)_2` if pH of the solution is adjusted to 9.0. `[K_(sp) (Mg(OH))_2 = 8.9 xx 10^(–12) M^3]`. At which minimum pH will the precipitation start ?

Explanation

To determine whether a precipitate of \( \text{Mg(OH)}_2 \) will form in a \( 1 \times 10^{-4} \, \text{M} \) solution of \( \text{Mg(NO}_3)_2 \) when the pH is adjusted to 9.0, we need to follow these steps:

### Step 1: Calculate the concentration of \( \text{H}^+ \) ions at pH 9.0
The concentration of \( \text{H}^+ \) ions can be calculated using the formula:
\[ [\text{H}^+] = 10^{-\text{pH}} \]
Substituting \( \text{pH} = 9.0 \):
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