Problem 37 - 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) AgCN (b) \(\mathrm{NiCO}_{3}\) (c) \(\mathrm{AuBr}_{3}\)

Step-by-Step Solution

Answer

AgCN: \(K_{sp} = [\text{Ag}^+][\text{CN}^-]\); NiCO₃: \(K_{sp} = [\text{Ni}^{2+}][\text{CO}_3^{2-}]\); AuBr₃: \(K_{sp} = [\text{Au}^{3+}][\text{Br}^-]^3\).

Step 1: Identify Salt and Write Dissociation Equation for AgCN

AgCN is silver cyanide. When AgCN is added to water, it barely dissolves, dissociating into its constituent ions: Ag⁺ and CN⁻. The equilibrium equation is: \[ \text{AgCN (s)} \rightleftharpoons \text{Ag}^+ (aq) + \text{CN}^- (aq) \] This represents the dissociation of solid AgCN into aqueous ions.

Step 2: Write the Solubility Product (Ksp) for AgCN

Based on the dissociation equation for AgCN, the solubility product expression (\(K_{sp}\)) is written as: \[ K_{sp} = [\text{Ag}^+] [\text{CN}^-] \] This expression shows that the \(K_{sp}\) is the product of the molar concentrations of the dissolved ions at equilibrium.

Step 3: Identify Salt and Write Dissociation Equation for NiCO3

NiCO₃ is nickel(II) carbonate. When NiCO₃ is added to water, it dissociates very slightly into nickel(II) ions (Ni²⁺) and carbonate ions (CO₃²⁻). The equilibrium equation is: \[ \text{NiCO}_3 (s) \rightleftharpoons \text{Ni}^{2+} (aq) + \text{CO}_3^{2-} (aq) \] This reflects the dissociation into its ionic components.

Step 4: Write the Solubility Product (Ksp) for NiCO3

For the dissociation of NiCO₃, the solubility product expression is: \[ K_{sp} = [\text{Ni}^{2+}] [\text{CO}_3^{2-}] \] This \(K_{sp}\) formula is derived from the equilibrium concentrations of the ions in solution.

Step 5: Identify Salt and Write Dissociation Equation for AuBr3

AuBr₃ is gold(III) bromide. In water, AuBr₃ dissociates into gold ions (Au³⁺) and bromide ions (Br⁻), but only slightly since it is an insoluble salt. The equation is: \[ \text{AuBr}_3 (s) \rightleftharpoons \text{Au}^{3+} (aq) + 3\text{Br}^- (aq) \] This equation represents the dissociation process of AuBr₃ in water.

Step 6: Write the Solubility Product (Ksp) for AuBr3

The solubility product (\(K_{sp}\)) for AuBr₃ based on its dissociation is: \[ K_{sp} = [\text{Au}^{3+}] [\text{Br}^-]^3 \] This \(K_{sp}\) expression includes the concentration of each type of ion raised to the power of its coefficient in the balanced equation.

Key Concepts

Insoluble Salts

In the realm of chemistry, some salts hardly dissolve in water and are termed insoluble salts. This might seem counterintuitive since we often think of salts as dissolving easily, like table salt. However, insoluble salts exhibit very low solubility, meaning they do not easily form ions in water.
Insoluble salts, such as silver cyanide (AgCN), nickel(II) carbonate (NiCO₃), and gold(III) bromide (AuBr₃), are characterized by their limited ability to dissolve.

- **AgCN**: This compound remains mostly undissolved in water, releasing just a few Ag⁺ and CN⁻ ions.
- **NiCO₃**: Similarly, this salt slightly breaks into Ni²⁺ and CO₃²⁻ ions when placed in water.
- **AuBr₃**: This too does not dissolve completely, releasing a minimal amount of Au³⁺ and Br⁻ ions.
These behaviors are explained by their low solubility product constants, denoted as \(K_{sp}\). Engaging with the topic of insoluble salts allows chemists to delve into detailed studies about equilibrium and solubility behaviors.

Chemical Equilibrium

Chemical equilibrium in the context of insoluble salts is a state where the rate of dissolution equals the rate of precipitation. This means the amount of solid salt dissolving into ions is balanced by the amount of ions recombining to form the solid.
For insoluble salts like AgCN, NiCO₃, and AuBr₃, the equilibrium is represented by a dissociation equation written with a double arrow (↔). This means that ions are continuously formed and reformed in a dynamic balance.

To visualize this, consider the dissociation of silver cyanide:
\[ \text{AgCN} (s) \rightleftharpoons \text{Ag}^+ (aq) + \text{CN}^- (aq) \]
At equilibrium, the concentrations of Ag⁺ ions and CN⁻ ions remain constant.

This state of balance is crucial in understanding the reactivity and formation of products in chemical solutions, particularly for reactions involving insoluble salts.
Understanding equilibrium helps in predicting how changes in conditions, like concentration or temperature, can shift this balance, according to Le Chatelier's principle.

Dissociation Equations

Dissociation equations are essential tools for understanding how salts dissolve in water to form their corresponding ions. They provide a snapshot of what happens at the microscopic level when a salt is added to water.
For insoluble salts such as AgCN, NiCO₃, and AuBr₃, although they do not fully dissolve, dissociation equations highlight the ionic species that are present in the solution.

For example, the dissociation equation for AgCN is:
\[ \text{AgCN} (s) \rightleftharpoons \text{Ag}^+ (aq) + \text{CN}^- (aq) \]
Here, the double arrow indicates that the reaction can proceed in both directions: forming ions and recombining to form the solid.

This is critical for determining the solubility product constant, \(K_{sp}\), which is derived from the concentrations of ions at equilibrium:
\[ K_{sp} = [\text{Ag}^+] [\text{CN}^-] \] Dissociation equations play a key role in calculating the extent of solubility and understanding the behavior of salts in different chemical environments.