Question

Write the balanced chemical equation describing the dissolving of each of the following sparingly soluble salts in water. Write the expression for \(K_{\mathrm{sp}}\) for each process. a. \(\mathrm{NiS}(s)\) b. \(\mathrm{CuCO}_{3}(s)\) c. \(\mathrm{BaCrO}_{4}(s)\) d. \(\mathrm{Ag}_{3} \mathrm{PO}_{4}(s)\)

Short answer

The balanced chemical equations and \(K_{sp}\) expressions for the given sparingly soluble salts are: a. NiS(s): $\mathrm{NiS}(s) \rightleftharpoons \mathrm{Ni^{2+}}(aq) + \mathrm{S^{2-}}(aq)$, \(K_{\mathrm{sp}} = [\mathrm{Ni^{2+}}][\mathrm{S^{2-}}]\) b. CuCO3(s): $\mathrm{CuCO}_{3}(s) \rightleftharpoons \mathrm{Cu^{2+}}(aq) + \mathrm{CO}_{3}^{(2-)}(aq)$, \(K_{\mathrm{sp}} = [\mathrm{Cu^{2+}}][\mathrm{CO}_{3}^{2-}]\) c. BaCrO4(s): $\mathrm{BaCrO}_{4}(s) \rightleftharpoons \mathrm{Ba^{2+}}(aq) + \mathrm{CrO}_{4}^{(2-)}(aq)$, \(K_{\mathrm{sp}} = [\mathrm{Ba^{2+}}][\mathrm{CrO}_{4}^{2-}]\) d. Ag₃PO₄(s): $\mathrm{Ag}_{3}\mathrm{PO}_{4}(s) \rightleftharpoons 3 \mathrm{Ag^{+}}(aq) + \mathrm{PO}_{4}^{3-}(aq)$, \(K_{\mathrm{sp}} = [\mathrm{Ag^{+}}]^3[\mathrm{PO}_{4}^{3-}]\)

Step-by-step solution

a. Balancing the chemical equation for NiS

When NiS(s) dissolves in water, it dissociates into its constituent ions: $$\mathrm{NiS}(s) \rightleftharpoons \mathrm{Ni^{2+}}(aq) + \mathrm{S^{2-}}(aq)$$ The given reaction is already balanced.

a. \(K_{\mathrm{sp}}\) expression for NiS

The solubility product constant expression for NiS is the equilibrium constant for the dissolution process, given by the product of the equilibrium concentrations of the dissociated ions: \(K_{\mathrm{sp}} = [\mathrm{Ni^{2+}}][\mathrm{S^{2-}}]\)

b. Balancing the chemical equation for CuCO3

When CuCO3(s) dissolves in water, it dissociates into its constituent ions: $$\mathrm{CuCO}_{3}(s) \rightleftharpoons \mathrm{Cu^{2+}}(aq) + \mathrm{CO}_{3}^{(2-)}(aq)$$ The given reaction is already balanced.

b. \(K_{\mathrm{sp}}\) expression for CuCO3

The solubility product constant expression for CuCO3 is the equilibrium constant for the dissolution process, given by the product of the equilibrium concentrations of the dissociated ions: \(K_{\mathrm{sp}} = [\mathrm{Cu^{2+}}][\mathrm{CO}_{3}^{2-}]\)

c. Balancing the chemical equation for BaCrO4

When BaCrO4(s) dissolves in water, it dissociates into its constituent ions: $$\mathrm{BaCrO}_{4}(s) \rightleftharpoons \mathrm{Ba^{2+}}(aq) + \mathrm{CrO}_{4}^{(2-)}(aq)$$ The given reaction is already balanced.

c. \(K_{\mathrm{sp}}\) expression for BaCrO4

The solubility product constant expression for BaCrO4 is the equilibrium constant for the dissolution process, given by the product of the equilibrium concentrations of the dissociated ions: \(K_{\mathrm{sp}} = [\mathrm{Ba^{2+}}][\mathrm{CrO}_{4}^{2-}]\)

d. Balancing the chemical equation for Ag₃PO₄

When Ag₃PO₄(s) dissolves in water, it dissociates into its constituent ions: $$\mathrm{Ag}_{3}\mathrm{PO}_{4}(s) \rightleftharpoons 3 \mathrm{Ag^{+}}(aq) + \mathrm{PO}_{4}^{3-}(aq)$$ The given reaction is now balanced.

d. \(K_{\mathrm{sp}}\) expression for Ag₃PO₄

The solubility product constant expression for Ag₃PO₄ is the equilibrium constant for the dissolution process, given by the product of the equilibrium concentrations of the dissociated ions: \(K_{\mathrm{sp}} = [\mathrm{Ag^{+}}]^3[\mathrm{PO}_{4}^{3-}]\) For each of the given sparingly soluble salts, we have determined their dissolution chemical equations and \(K_{sp}\) expressions.

Key concepts

Sparingly Soluble Salts

Sparingly soluble salts are ionic compounds that do not dissolve well in water. This means that only a small amount of the salt will actually dissolve to form ions in solution. In this context, terms like 'soluble' and 'insoluble' are relative. While most salts dissolve to some degree, sparingly soluble salts usually do so minimally, leading to saturated solutions where undissolved solid remains. Examples of sparingly soluble salts include Nickel Sulfide (NiS), Copper Carbonate (CuCO₃), Barium Chromate (BaCrO₄), and Silver Phosphate (Ag₃PO₄).
Understanding sparingly soluble salts is crucial in predicting the behavior of salts in various chemical reactions and environmental contexts. Remember that the saturation point is achieved once the maximum amount of salt has dissolved, forming an equilibrium between the solid and its dissolved ions.

Chemical Equation Balancing

Balancing chemical equations is a fundamental skill in chemistry that ensures the conservation of mass and charge. In a balanced chemical equation, the number of atoms for each element is the same on both sides of the equation, and the total charge is balanced. For sparingly soluble salts dissolving in water, the dissolution process is represented by an equilibrium equation.
For instance, when Nickel Sulfide (NiS) dissolves, the balanced equation is \(\mathrm{NiS}(s) \rightleftharpoons \mathrm{Ni^{2+}}(aq) + \mathrm{S^{2-}}(aq)\). Similarly, for Silver Phosphate (Ag₃PO₄), the equation is adjusted to account for the stoichiometry: \(\mathrm{Ag}_{3}\mathrm{PO}_{4}(s) \rightleftharpoons 3\mathrm{Ag^{+}}(aq) + \mathrm{PO}_{4}^{3-}(aq)\).
Ensuring equations are balanced is essential for accuracy in calculations and predictions in chemical reactions.

Solubility Product Constant (Ksp)

The Solubility Product Constant, denoted as \(K_{sp}\), is an equilibrium constant specific to sparingly soluble salts. It quantifies the extent to which a compound will dissolve in water, providing insight into the solubility of the salt. The \(K_{sp}\) expression is derived from the equilibrium concentrations of ions that the salt dissociates into when it dissolves.
For example, the \(K_{sp}\) for NiS is expressed as \(K_{sp} = [\mathrm{Ni^{2+}}][\mathrm{S^{2-}}]\), indicating how NiS dissolves into nickel and sulfide ions. Unique expressions exist for each compound, like \(K_{sp} = [\mathrm{Ag^{+}}]^3[\mathrm{PO}_{4}^{3-}]\) for Ag₃PO₄.
Understanding and calculating \(K_{sp}\) helps predict precipitation reactions and the extent of dissolution in various solvents.

Dissolution Process

The dissolution process is the interaction of a solid with a liquid solvent to form a solution, essentially converting solid compounds into ions. In the case of sparingly soluble salts, this process reaches a dynamic equilibrium: some of the solid dissolves, releasing ions until a saturation point is reached, where the rate of dissolution equals the rate of precipitation.
During dissolution, the solid salt dissociates into its component ions, such as \(\mathrm{CuCO}_{3}(s) \rightleftharpoons \mathrm{Cu^{2+}}(aq) + \mathrm{CO}_{3}^{(2-)}(aq)\). The specific ions and their stoichiometric coefficients depend on the particular salt being dissolved.
Understanding this process is vital for applications in chemical manufacturing, environmental science, and pharmaceuticals, as it influences the availability and concentration of ions.