Problem 82 - Chemistry Matter and Change

Question

Describe the process by which adding potassium hydroxide to a saturated aluminum hydroxide solution reduces the concentration of aluminum ions. Write the solubility equilibrium equation and solubility product constant expression for a saturated aqueous solution of aluminum hydroxide.

Step-by-Step Solution

Answer

When potassium hydroxide (KOH) is added to a saturated aluminum hydroxide (Al(OH)₃) solution, it increases the concentration of hydroxide ions (OH⁻) in the solution, shifting the solubility equilibrium (Al(OH)₃(s) ⇌ Al³⁺(aq) + 3OH⁻(aq)) to the left due to the common ion effect and Le Chatelier's principle. This results in a decrease in the concentration of dissolved aluminum ions (Al³⁺) as they combine with the hydroxide ions to form aluminum hydroxide. The solubility product constant expression for aluminum hydroxide is Kₛp = [Al³⁺][OH⁻]³.

Step 1: Write the chemical formula for aluminum hydroxide

First, we need to write down the chemical formula for aluminum hydroxide, which is Al(OH)₃. This will help us in understanding the dissolution process and forming the required equations.

Step 2: Write the solubility equilibrium equation

When aluminum hydroxide dissolves in water, it forms an equilibrium with its ions. The solubility equilibrium equation for aluminum hydroxide can be written as: Al(OH)₃(s) ⇌ Al³⁺(aq) + 3OH⁻(aq) This equation shows that solid aluminum hydroxide dissociates into aluminum ions (Al³⁺) and hydroxide ions (OH⁻) in water.

Step 3: Write the solubility product constant expression for aluminum hydroxide

By using the solubility equilibrium equation, we can write the expression for the solubility product constant (Kₛp) of aluminum hydroxide. Kₛp is the equilibrium constant for the dissolution of a sparingly soluble compound in water. For the given equation: Kₛp = [Al³⁺][OH⁻]³ where [Al³⁺] and [OH⁻] represent the equilibrium concentrations of the aluminum ions and hydroxide ions, respectively.

Step 4: Describe the addition of potassium hydroxide to the saturated solution

When potassium hydroxide (KOH) is added to the saturated aluminum hydroxide solution, a common ion effect occurs. The reaction can be written as: KOH(aq) → K⁺(aq) + OH⁻(aq) Potassium ions (K⁺) will not affect the equilibrium, but the increase in hydroxide ions (OH⁻) will shift the equilibrium of aluminum hydroxide solubility to the left, as per Le Chatelier’s principle.

Step 5: Explain the reduction in concentration of aluminum ions

As the equilibrium shifts to the left due to the increased concentration of hydroxide ions from the addition of potassium hydroxide, more solid aluminum hydroxide will be formed. This results in a decrease in the concentration of dissolved aluminum ions (Al³⁺) in the solution as they combine with hydroxide ions to form aluminum hydroxide. In conclusion, the addition of potassium hydroxide to a saturated aluminum hydroxide solution reduces the concentration of aluminum ions due to the common ion effect and Le Chatelier's principle. The solubility equilibrium equation is given by Al(OH)₃(s) ⇌ Al³⁺(aq) + 3OH⁻(aq), and the solubility product constant expression is Kₛp = [Al³⁺][OH⁻]³.

Key Concepts

Aluminum Hydroxide

Aluminum hydroxide is a chemical compound with the formula \( \text{Al(OH)}_3 \). It is amphoteric, meaning it can react with both acids and bases. In water, it dissolves slightly to form aluminum ions \( \text{Al}^{3+} \) and hydroxide ions \( \text{OH}^- \). The reaction is represented by:

• \( \text{Al(OH)}_3(s) \leftrightarrow \text{Al}^{3+}(aq) + 3\text{OH}^-(aq) \)

This equilibrium reaction is crucial for understanding its solubility. Because it's sparingly soluble, it doesn't dissolve completely in water. Instead, it reaches a balance between dissolved ions and undissolved solid, which can be affected by changes in solution conditions.

Common Ion Effect

The common ion effect occurs when a compound's solubility is reduced due to the presence of a common ion in the solution. For aluminum hydroxide, adding a compound like potassium hydroxide (KOH) introduces additional hydroxide ions \( \text{OH}^- \) into the solution. This increase in \( \text{OH}^- \) concentration pushes the equilibrium:

• \( \text{Al(OH)}_3(s) \leftrightarrow \text{Al}^{3+}(aq) + 3\text{OH}^-(aq) \)

to the left, resulting in more solid \( \text{Al(OH)}_3 \) forming and decreasing the solubility of aluminum ions \( \text{Al}^{3+} \). This is a classic example of the common ion effect.

Solubility Product Constant (Ksp)

The solubility product constant \( K_{sp} \) is a special equilibrium constant for sparingly soluble salts. For aluminum hydroxide, \( K_{sp} \) can be expressed using the concentrations of aluminum and hydroxide ions:

• \( K_{sp} = [\text{Al}^{3+}][\text{OH}^-]^3 \)

This expression helps predict whether a precipitate will form under certain conditions. A higher concentration of \( \text{OH}^- \) shifts equilibrium, affecting \( K_{sp} \). By calculating \( K_{sp} \), chemists can determine how much \( \text{Al(OH)}_3 \) will dissolve in water at equilibrium.

Le Chatelier's Principle

Le Chatelier’s Principle predicts how an equilibrium reacts to external changes. When potassium hydroxide is added, it adds \( \text{OH}^- \) ions:

• \( \text{KOH}(aq) \rightarrow \text{K}^+(aq) + \text{OH}^-(aq) \)

The increase in \( \text{OH}^- \) causes the equilibrium:

• \( \text{Al(OH)}_3(s) \leftrightarrow \text{Al}^{3+}(aq) + 3\text{OH}^-(aq) \)

to shift left, according to Le Chatelier's Principle, to counter the change. This results in more solid \( \text{Al(OH)}_3 \) forming, reducing \( \text{Al}^{3+} \) concentration. Understanding this principle helps predict chemical reactions' behavior under various conditions.