To determine the solubility product constant [tex]\((K_{\text{sp}})\)[/tex] for the dissociation of [tex]\( \text{Fe(OH)}_3 \)[/tex] in water, let’s consider the balanced chemical equation:
[tex]\[ \text{Fe(OH)}_3 (s) \leftrightarrow \text{Fe}^{3+} (aq) + 3 \text{OH}^- (aq) \][/tex]
In this equilibrium, the solubility product constant [tex]\( K_{\text{sp}} \)[/tex] is a measure of the solubility of the compound in water. It is the product of the ion concentrations of the products, each raised to the power of its coefficient in the balanced dissociation equation.
For the dissociation of [tex]\( \text{Fe(OH)}_3 \)[/tex]:
- The concentration of [tex]\( \text{Fe}^{3+} \)[/tex] is [tex]\( [\text{Fe}^{3+}] \)[/tex].
- The concentration of [tex]\( \text{OH}^- \)[/tex] is [tex]\( [\text{OH}^-] \)[/tex], and since there are three hydroxide ions produced for every formula unit of [tex]\( \text{Fe(OH)}_3 \)[/tex] that dissociates, it is raised to the third power.
Thus, the solubility product constant [tex]\( K_{\text{sp}} \)[/tex] is given by:
[tex]\[ K_{\text{sp}} = [\text{Fe}^{3+}][\text{OH}^-]^3 \][/tex]
Therefore, the correct formula for [tex]\( K_{\text{sp}} \)[/tex] of [tex]\( \text{Fe(OH)}_3 \)[/tex] is:
[tex]\[ K_{\text{sp}} = [\text{Fe}^{3+}][\text{OH}^-]^3 \][/tex]
