Question

(a) Explain the difference between solubility and solubility-product constant. (b) Write the expression for the solubility-product constant for each of the following ionic compounds: \(\mathrm{MnCO}_{3}, \mathrm{Hg}(\mathrm{OH})_{2}\), and \(\mathrm{Cu}_{3}\left(\mathrm{PO}_{4}\right)_{2}\).

Short answer

Solubility is the maximum amount of solute that can dissolve in a solvent, while the solubility-product constant (Ksp) is an equilibrium constant representing the extent of dissolution of a sparingly soluble ionic compound. For the given compounds: \(\mathrm{MnCO}_{3}\): \(K_{sp} = [\mathrm{Mn^{2+}}][\mathrm{CO}_3^{\mathrm{2}-}]\) \(\mathrm{Hg(OH)}_{2}\): \(K_{sp} = [\mathrm{Hg^{2+}}][\mathrm{OH}^-]^2\) \(\mathrm{Cu}_{3}(\mathrm{PO}_{4})_{2}\): \(K_{sp} = [\mathrm{Cu}^{2+}]^3[\mathrm{PO}_{4}^{\mathrm{3}-}]^2\)

Step-by-step solution

A. Explaining the difference between solubility and solubility-product constant

Solubility is the maximum amount of solute that can dissolve in a given amount of solvent at a specific temperature, expressed in units such as grams per liter (g/L) or molarity (M). It is a measure of how well a solute dissolves in a solvent and depends on factors such as temperature, pressure, and the nature of both solute and solvent. The solubility-product constant (Ksp) is an equilibrium constant that represents the extent of dissolution of a sparingly soluble ionic compound in a solution. It is defined as the product of the equilibrium concentrations of the ions in the saturated solution, each raised to the power of their coefficients in the balanced chemical equation. The Ksp value does not have a unit and depends only on temperature.

B. Determining the solubility-product constant expression for \(\mathrm{MnCO}_{3}\)

First, we need to write the dissolution equilibrium expression for the ionic compound. The balanced chemical equation for \(\mathrm{MnCO}_{3}\): \[\mathrm{MnCO}_{3} \rightleftharpoons \mathrm{Mn^{2+}} + \mathrm{CO}_3^{\mathrm{2}-}\] The expression for solubility-product constant (Ksp) is: \[K_{sp} = [\mathrm{Mn^{2+}}][\mathrm{CO}_3^{\mathrm{2}-}]\]

C. Determining the solubility-product constant expression for \(\mathrm{Hg(OH)}_{2}\)

The balanced chemical equation for \(\mathrm{Hg(OH)}_{2}\) is: \[\mathrm{Hg(OH)}_{2} \rightleftharpoons \mathrm{Hg^{2+}} + 2\mathrm{OH}^-\] The expression for solubility-product constant (Ksp) is: \[K_{sp} = [\mathrm{Hg^{2+}}][\mathrm{OH}^-]^2\]

D. Determining the solubility-product constant expression for \(\mathrm{Cu}_{3}(\mathrm{PO}_{4})_{2}\)

The balanced chemical equation for \(\mathrm{Cu}_{3}(\mathrm{PO}_{4})_{2}\) is: \[\mathrm{Cu}_{3}\left(\mathrm{PO}_{4}\right)_{2} \rightleftharpoons 3\mathrm{Cu}^{2+} + 2\mathrm{PO}_{4}^{\mathrm{3}-}\] The expression for solubility-product constant (Ksp) is: \[K_{sp} = [\mathrm{Cu}^{2+}]^3[\mathrm{PO}_{4}^{\mathrm{3}-}]^2\]