Problem 50 - Chemistry The Molecular Science

Question

Write a balanced chemical equation for the equilibrium occurring when each of these solutes is added to water, then write the \(K_{\mathrm{sp}}\) expression. (a) \(\mathrm{Ag}_{3} \mathrm{AsO}_{4}\) (b) Silver sulfate (c) Calcium phosphate (d) Manganese(III) hydroxide (e) Iron(II) carbonate

Step-by-Step Solution

Answer

Balanced equations and Ksp expressions were derived for all solutes.

Step 1: Identify the Dissociation of Silver Arsenate

Silver arsenate, represented as \(\text{Ag}_3\text{AsO}_4\), dissociates in water into its constituent ions. The balanced chemical equation for this dissociation is:\[ \text{Ag}_3\text{AsO}_4 (s) \rightleftharpoons 3\text{Ag}^+ (aq) + \text{AsO}_4^{3-} (aq) \]

Step 2: Write the Solubility Product Expression for Silver Arsenate

The solubility product (\(K_{\text{sp}}\)) for silver arsenate is expressed based on the concentration of its ions at equilibrium:\[ K_{\text{sp}} = [\text{Ag}^+]^3 [\text{AsO}_4^{3-}] \]

Step 3: Identify the Dissociation of Silver Sulfate

Silver sulfate, represented as \(\text{Ag}_2\text{SO}_4\), dissociates in water as follows:\[ \text{Ag}_2\text{SO}_4 (s) \rightleftharpoons 2\text{Ag}^+ (aq) + \text{SO}_4^{2-} (aq) \]

Step 4: Write the Solubility Product Expression for Silver Sulfate

The \(K_{\text{sp}}\) expression for silver sulfate is:\[ K_{\text{sp}} = [\text{Ag}^+]^2 [\text{SO}_4^{2-}] \]

Step 5: Identify the Dissociation of Calcium Phosphate

Calcium phosphate, \(\text{Ca}_3(\text{PO}_4)_2\), dissociates as follows:\[ \text{Ca}_3(\text{PO}_4)_2 (s) \rightleftharpoons 3\text{Ca}^{2+} (aq) + 2\text{PO}_4^{3-} (aq) \]

Step 6: Write the Solubility Product Expression for Calcium Phosphate

For calcium phosphate, the \(K_{\text{sp}}\) expression is:\[ K_{\text{sp}} = [\text{Ca}^{2+}]^3 [\text{PO}_4^{3-}]^2 \]

Step 7: Identify the Dissociation of Manganese(III) Hydroxide

Manganese(III) hydroxide, \(\text{Mn(OH)}_3\), dissociates as:\[ \text{Mn(OH)}_3 (s) \rightleftharpoons \text{Mn}^{3+} (aq) + 3\text{OH}^- (aq) \]

Step 8: Write the Solubility Product Expression for Manganese(III) Hydroxide

The \(K_{\text{sp}}\) for manganese(III) hydroxide is expressed as:\[ K_{\text{sp}} = [\text{Mn}^{3+}] [\text{OH}^-]^3 \]

Step 9: Identify the Dissociation of Iron(II) Carbonate

Iron(II) carbonate, \(\text{FeCO}_3\), dissociates in water:\[ \text{FeCO}_3 (s) \rightleftharpoons \text{Fe}^{2+} (aq) + \text{CO}_3^{2-} (aq) \]

Step 10: Write the Solubility Product Expression for Iron(II) Carbonate

The solubility product expression is:\[ K_{\text{sp}} = [\text{Fe}^{2+}] [\text{CO}_3^{2-}] \]

Key Concepts

Chemical Equilibrium

Understanding chemical equilibrium is essential when studying reactions like the dissolution of slightly soluble salts in water. It refers to the state in a chemical reaction where the rate of the forward reaction is equal to the rate of the reverse reaction. At this point, the concentration of reactants and products remains constant over time. Simultaneously, it does not mean that the amounts are equal, but that their ratios remain constant. In the context of solubility, equilibrium is achieved when the solid salt dissolves and produces its ions in solution to the point where no more can dissolve. This balance allows us to calculate the solubility product constant, or \(K_{sp}\), which gives insight into the solubility of a substance in a solvent.

Dissociation Equation

A dissociation equation shows how a compound breaks down into its ions when dissolved in water. For instance, when a solid salt such as silver arsenate \(\text{Ag}_3\text{AsO}_4\) is added to water, it dissociates into its ionic components: \(3 \text{Ag}^+\) and \(\text{AsO}_4^{3-}\). The equation illustrating this process would be:

• \(\text{Ag}_3\text{AsO}_4 (s) \rightleftharpoons 3\text{Ag}^+ (aq) + \text{AsO}_4^{3-} (aq)\)

These dissociation reactions help in calculating the concentrations of ions in solution. Knowing these can lead us to understand the extent of solubility and determine the saturation point of the solution, crucial for calculating \(K_{sp}\).

Solubility Product Expression

The solubility product expression is an equation that relates the concentrations of ionic constituents of a dissolved solid in a saturated solution at equilibrium. The \(K_{sp}\) value forms the basis of this expression, primarily used for sparingly soluble salts. For example, in the case of silver arsenate \(\text{Ag}_3\text{AsO}_4\), the solubility product expression is:

• \(K_{sp} = [\text{Ag}^+]^3 [\text{AsO}_4^{3-}]\)

This expression is derived from the dissociation equation and highlights the stoichiometry of the reaction. The exponents correspond to the coefficients of the ions appearing in the dissociation equation and indicate the molar relation required to maintain equilibrium.

Aqueous Ion Concentration

Aqueous ion concentration refers to the amounts of individual ions present in a solution when a solute dissolves. It is the cornerstone of understanding the processes involved in solubility. When a compound like calcium phosphate \(\text{Ca}_3(\text{PO}_4)_2\) dissolves in water, it dissociates into ions \(3\text{Ca}^{2+}\) and \(2\text{PO}_4^{3-}\). The concentrations of these ions in water would reach a point of equilibrium, where their ratio matches the \(K_{sp}\) expression:

• \(K_{sp} = [\text{Ca}^{2+}]^3 [\text{PO}_4^{3-}]^2\)

Understanding aqueous ion concentration allows us to predict the solubility of substances, calculate ion concentrations in saturated solutions, and estimate the effects of various factors such as temperature and pH on solubility. By mastering these concepts, students can solve complex chemical equilibrium problems effectively.