Problem 38 - Chemistry and Chemical Reactivity

Question

For each of the following insoluble salts, (1) write a balanced equation showing the equilibrium occurring when the salt is added to water, and (2) write the \(K_{\mathrm{sp}}\) expression. (a) \(\mathrm{PbSO}_{4}\) (b) \(\mathrm{BaF}_{2}\) (c) \(\mathrm{Ag}_{3} \mathrm{PO}_{4}\)

Step-by-Step Solution

Answer

For each salt: (a) \( K_{\mathrm{sp}} = [\mathrm{Pb}^{2+}][\mathrm{SO}_{4}^{2-}] \); (b) \( K_{\mathrm{sp}} = [\mathrm{Ba}^{2+}][\mathrm{F}^{-}]^2 \); (c) \( K_{\mathrm{sp}} = [\mathrm{Ag}^{+}]^3[\mathrm{PO}_{4}^{3-}] \).

Step 1: Write the Dissolution Equation for \( \mathrm{PbSO}_{4} \)

The dissolution of \( \mathrm{PbSO}_{4} \) in water can be represented by the following equilibrium equation: \[ \mathrm{PbSO}_{4} (s) \rightleftharpoons \mathrm{Pb}^{2+} (aq) + \mathrm{SO}_{4}^{2-} (aq) \]

Step 2: Write the \( K_{\mathrm{sp}} \) Expression for \( \mathrm{PbSO}_{4} \)

The \( K_{\mathrm{sp}} \) expression is the product of the concentrations of the ions at equilibrium: \[ K_{\mathrm{sp}} = [\mathrm{Pb}^{2+}][\mathrm{SO}_{4}^{2-}] \]

Step 3: Write the Dissolution Equation for \( \mathrm{BaF}_{2} \)

The dissolution of \( \mathrm{BaF}_{2} \) in water can be represented by the equilibrium equation: \[ \mathrm{BaF}_{2} (s) \rightleftharpoons \mathrm{Ba}^{2+} (aq) + 2 \mathrm{F}^{-} (aq) \]

Step 4: Write the \( K_{\mathrm{sp}} \) Expression for \( \mathrm{BaF}_{2} \)

The \( K_{\mathrm{sp}} \) expression is given as: \[ K_{\mathrm{sp}} = [\mathrm{Ba}^{2+}][\mathrm{F}^{-}]^2 \]

Step 5: Write the Dissolution Equation for \( \mathrm{Ag}_{3} \mathrm{PO}_{4} \)

The dissolution of \( \mathrm{Ag}_{3} \mathrm{PO}_{4} \) in water can be represented by: \[ \mathrm{Ag}_{3} \mathrm{PO}_{4} (s) \rightleftharpoons 3 \mathrm{Ag}^{+} (aq) + \mathrm{PO}_{4}^{3-} (aq) \]

Step 6: Write the \( K_{\mathrm{sp}} \) Expression for \( \mathrm{Ag}_{3} \mathrm{PO}_{4} \)

The \( K_{\mathrm{sp}} \) expression is given by: \[ K_{\mathrm{sp}} = [\mathrm{Ag}^{+}]^3[\mathrm{PO}_{4}^{3-}] \]

Key Concepts

Insoluble Salts

Insoluble salts are compounds that do not dissolve easily in water. This doesn't mean they are completely insolvable, but their solubility is very low compared to other salts. When placed in water, only a small quantity dissolves, establishing a dynamic equilibrium.

The limited solubility occurs because only a few molecules dissociate into ions. The remaining part stays in solid form. Some common examples include lead sulfate (\( \text{PbSO}_4 \)), barium fluoride (\( \text{BaF}_2 \)), and silver phosphate (\( \text{Ag}_3\text{PO}_4 \)). These salts form saturated solutions with ions equilibrating between the dissolved and undissolved states.

• This equilibrium is essential in predicting the extent of dissolution.
• Knowing the nature of insoluble salts helps in various chemical processes, including precipitate formation and analysis.

Ksp Expression

The solubility product constant, \( K_{\text{sp}} \), is a measure of the solubility of a compound, which is an essential aspect of understanding the extent to which insoluble salts dissolve. It is specific to each salt and is represented as the product of the concentrations of the ions each raised to the power of their coefficients from the dissolution equation.

For example:

• For \( \text{PbSO}_4 \), the \( K_{\text{sp}} \) expression is \( K_{\text{sp}} = [\text{Pb}^{2+}][\text{SO}_4^{2-}] \).
• For \( \text{BaF}_2 \), it is \( K_{\text{sp}} = [\text{Ba}^{2+}][\text{F}^-]^2 \) since two fluoride ions form.
• Similarly, for \( \text{Ag}_3\text{PO}_4 \), the equation is \( K_{\text{sp}} = [\text{Ag}^+]^3[\text{PO}_4^{3-}] \) due to three silver ions.

Thus, \( K_{\text{sp}} \) expressions help predict solubility and are crucial in experiments to calculate ion concentrations at equilibrium.

Dissolution Equations

Dissolution equations illustrate how salts dissociate into their respective ions in water, reaching an equilibrium state. They are vital for understanding how different ions populate a solution when a salt is added. Each equation is balanced to show the correct stoichiometry of reactants and products.

For example:

• The dissolution of \( \text{PbSO}_4 \) is shown by \( \text{PbSO}_4 (s) \rightleftharpoons \text{Pb}^{2+} (aq) + \text{SO}_4^{2-} (aq) \).
• \( \text{BaF}_2 \) dissolution results in \( \text{BaF}_2 (s) \rightleftharpoons \text{Ba}^{2+} (aq) + 2\text{F}^- (aq) \), producing two fluoride ions for balance.
• For \( \text{Ag}_3\text{PO}_4 \), the equation is \( \text{Ag}_3\text{PO}_4 (s) \rightleftharpoons 3\text{Ag}^+ (aq) + \text{PO}_4^{3-} (aq) \).

These dissolution equations are crucial as they provide the basis for writing \( K_{\text{sp}} \) expressions and for understanding the solubility and behavior of ions in a solution.