Write the ion-product expressions for (a) iron(III) hydroxide; (b) barium phosphate; (c) magnesium fluoride.

The solubility product constant, denoted as \( K_{sp} \), is a type of equilibrium constant used in chemistry that helps us understand the solubility of sparingly soluble ionic compounds. It specifically applies to salts that dissolve in water.

When these salts dissolve, they break into their constituent ions. The \( K_{sp} \) expression reflects the concentration of these ions in a saturated solution. The general form is:

\[ K_{sp} = [A^m^+]^a [B^n^-]^b \]

Here, \( A \) and \( B \) represent the ions, and \( a \) and \( b \) are the stoichiometric coefficients from the balanced dissociation equation. Understanding \( K_{sp} \) helps predict whether a precipitate will form when two solutions are mixed and to what extent salts dissolve in water.

Dissociation in water refers to the process by which ionic compounds break into their ions when dissolved in water. For example, when iron(III) hydroxide, \( \text{Fe(OH)}_3 \), dissolves in water, it dissociates into \( \text{Fe}^{3+} \) and \( \text{OH}^- \) ions:

\[ \text{Fe(OH)}_3 (s) \rightleftharpoons \text{Fe}^{3+} (aq) + 3\text{OH}^- (aq) \]

This balanced equation tells us the ratio of ions produced. Understanding dissociation is crucial because it allows us to write ion-product expressions and predict the behavior of ions in solution.

Similarly, barium phosphate, \( \text{Ba}_3 (\text{PO}_4)_2 \), dissociates as:

\[ \text{Ba}_3 (\text{PO}_4)_2 (s) \rightleftharpoons 3\text{Ba}^{2+} (aq) + 2\text{PO}_4^{3-} (aq) \]

These reactions highlight how compounds break down when they dissolve in water, giving us insight into the ion concentrations at equilibrium.

A chemical formula represents the elements in a compound and their relative proportions. It's essential for understanding and predicting chemical reactions and the behavior of molecules. For example, iron(III) hydroxide has the chemical formula \( \text{Fe(OH)}_3 \). This notation tells us that one molecule of iron(III) hydroxide contains one iron (Fe) ion and three hydroxide (OH) ions.

Similarly, barium phosphate is written as \( \text{Ba}_3 (\text{PO}_4)_2 \), indicating three barium (Ba) ions and two phosphate (PO_4) groups per formula unit.

Lastly, magnesium fluoride's chemical formula is \( \text{MgF}_2 \), meaning each unit consists of one magnesium (Mg) ion and two fluoride (F) ions.

Understanding chemical formulas helps us write balanced chemical equations, calculate molecular weights, and derive ion-product expressions crucial for studying solubility and chemical reactions.