The solubility of `Mg(OH)_(2)` is increased by the addition of `overset(o+)NH_(4)` ion. Calculate
a. `Kc` for the reaction:
`Mg(OH)_(2) +2overset(o+)NH_(4) hArr 2NH_(3) +2H_(2)O + Mg^(+2)`
`K_(sp) of Mg(OH)_(2) = 6 xx 10^(-12), K_(b) of NH_(3) = 1.8 xx 10^(-5)`.
b. Find the solubility of `Mg(OH)_(2)` in a solution containing `0.5M NH_(4)C1` before addition of `Mg(OH)_(2)`.b

Explanation

To solve the problem, we will break it down into two parts as stated in the question.

### Part A: Calculate \( K_c \) for the reaction

The reaction given is:
\[ \text{Mg(OH)}_2 + 2 \text{NH}_4^+ \rightleftharpoons 2 \text{NH}_3 + 2 \text{H}_2O + \text{Mg}^{2+} \]

1. **Identify the relevant equilibrium constants**:
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