Problem 42 - 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 \(K_{\text {sp }}\) expression. (a) \(\mathrm{PbSO}_{4}\) (b) \(\mathrm{BaF}_{2}\) (c) \(\mathrm{Ag}_{3} \mathrm{PO}_{4}\)

Step-by-Step Solution

Answer

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

Step 1

Write the dissociation equation for \( \mathrm{PbSO}_{4} \). When \( \mathrm{PbSO}_{4} \) is added to water, it dissociates into \( \mathrm{Pb}^{2+} \) and \( \mathrm{SO}_{4}^{2-} \) ions. The balanced dissociation equation is:\[ \mathrm{PbSO}_{4 (s)} \rightleftharpoons \mathrm{Pb}^{2+}_{(aq)} + \mathrm{SO}_{4}^{2-}_{(aq)} \]

Step 2

Write the \( K_{sp} \) expression for \( \mathrm{PbSO}_{4} \). The \( K_{sp} \) is the solubility product constant and is defined based on the concentrations of the dissolved ions:\[ K_{sp} = [\mathrm{Pb}^{2+}][\mathrm{SO}_{4}^{2-}] \]

Step 3

Write the dissociation equation for \( \mathrm{BaF}_{2} \). When \( \mathrm{BaF}_{2} \) is added to water, it dissociates into \( \mathrm{Ba}^{2+} \) and \( \mathrm{F}^{-} \) ions. The balanced dissociation equation is:\[ \mathrm{BaF}_{2 (s)} \rightleftharpoons \mathrm{Ba}^{2+}_{(aq)} + 2\mathrm{F}^{-}_{(aq)} \]

Step 4

Write the \( K_{sp} \) expression for \( \mathrm{BaF}_{2} \). The \( K_{sp} \) expression is defined based on the concentration of the dissolved ions:\[ K_{sp} = [\mathrm{Ba}^{2+}][\mathrm{F}^{-}]^{2} \]

Step 5

Write the dissociation equation for \( \mathrm{Ag}_{3} \mathrm{PO}_{4} \). When \( \mathrm{Ag}_{3} \mathrm{PO}_{4} \) is added to water, it dissociates into \( \mathrm{Ag}^{+} \) and \( \mathrm{PO}_{4}^{3-} \) ions. The balanced dissociation equation is:\[ \mathrm{Ag}_{3} \mathrm{PO}_{4 (s)} \rightleftharpoons 3 \mathrm{Ag}^{+}_{(aq)} + \mathrm{PO}_{4}^{3-}_{(aq)} \]

Step 6

Write the \( K_{sp} \) expression for \( \mathrm{Ag}_{3} \mathrm{PO}_{4} \). The \( K_{sp} \) expression is defined based on the concentrations of the dissolved ions:\[ K_{sp} = [\mathrm{Ag}^{+}]^{3}[\mathrm{PO}_{4}^{3-}] \]

Key Concepts

Insoluble Salts

Insoluble salts are compounds that do not readily dissolve in water. When these salts are added to water, they generally dissolve only slightly, reaching a state of chemical equilibrium between the solid and the ions in solution.
The concept of insolubility is not absolute. It means that the salt dissolves to a very small extent, but not entirely. This limited dissolution is crucial for understanding their solubility product constant, or Ksp, which measures the extent of an insoluble salt's solubility.

• Characteristics of Insoluble Salts: Insoluble salts have low solubility, meaning that although a small amount might dissolve, most of the salt remains undissolved. Examples include lead(II) sulfate (\(\mathrm{PbSO}_4\)) and barium fluoride (\(\mathrm{BaF}_2\)).
• Role of Water: Water acts as a medium facilitating the dissolution of these salts by breaking down the crystal lattice to release ions into the solution.

Recognizing insoluble salts and calculating their solubility helps in predicting precipitation and understanding reactions in aqueous solutions such as in qualitative analysis.

Chemical Equilibrium

Chemical equilibrium describes the state in which both reactants and products are present at concentrations that have no further tendency to change over time. When dealing with insoluble salts, the focus is on the equilibrium between the undissolved solid and the ions in solution.
For the salts discussed, such as \(\mathrm{PbSO}_4\), \(\mathrm{BaF}_2\), and \(\mathrm{Ag}_3\mathrm{PO}_4\), this equilibrium is represented by the equation showing the salt dissociating into its respective ions.

• Dynamic Balance: At equilibrium, the rate of dissolution of the salt equals the rate at which the ions recombine to form the solid. This dynamic process ensures a constant concentration of ions in the solution.
• Equilibrium Expressions: The expressions for \(K_{sp}\) are derived from these balances. For instance, \(\mathrm{K}_{sp}\) for \(\mathrm{PbSO}_4\) is \(\mathrm{K}_{sp} = [\mathrm{Pb}^{2+}][\mathrm{SO}_4^{2-}]\).

Understanding chemical equilibrium for insoluble salts provides insights into how various factors like temperature, concentration of ions, and the presence of other chemicals can affect solubility.

Dissociation Equations

Dissociation equations depict the process in which a solid ionic compound separates into its constituent ions when added to water. These equations are pivotal in understanding the dissolution process and the formation of a saturated solution, where no more solid can dissolve.
Writing dissociation equations allows us to visualize and compute necessary chemical equilibrium expressions like the solubility product constant.

• Example Equation: For \(\mathrm{BaF}_2\), the dissociation equation is \(\mathrm{BaF}_2(s) \rightleftharpoons \mathrm{Ba}^{2+}_{(aq)} + 2\mathrm{F}^-_{(aq)}\).
• Stoichiometry in Equations: Proper stoichiometry in dissociation equations, like the coefficients of the ions, directly influences the \(K_{sp}\) expression. For \(\mathrm{BaF}_2\), \(K_{sp} = [\mathrm{Ba}^{2+}][\mathrm{F}^-]^2\).

Accurately writing dissociation equations aids in predicting how much of a salt can dissolve under specific conditions and is essential for performing solubility calculations.