Calculate the molar solubility of gallium hydroxide, Ga(OH); (K.p 7.28 x 10 36), in a solution that is buffered at pH = 3.59.

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**Problem Statement:**

Calculate the molar solubility of gallium hydroxide, Ga(OH)₃ (Kₛₚ = 7.28 x 10⁻³⁶), in a solution that is buffered at pH = 3.59.

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**Detailed Explanation:**

In this problem, we are asked to find the molar solubility of gallium hydroxide, Ga(OH)₃, in a solution with a specific pH value. The provided data includes the solubility product constant (Kₛₚ) for Ga(OH)₃, which is 7.28 x 10⁻³⁶. Additionally, the pH of the solution is given as 3.59.

To solve this problem, we will use the concept of solubility product constant and the relationship between pH and hydroxide ion concentration to determine the molar solubility. 

**Steps:**

1. **Determine the hydrogen ion concentration from the pH of the solution:**
   \[ \text{pH} = 3.59 \]
   \[ \text{[H⁺]} = 10^{-\text{pH}} \]
   \[ \text{[H⁺]} = 10^{-3.59} \]

2. **Calculate the hydroxide ion concentration using the water dissociation constant (K_w):**
   \[ K_w = [H⁺][OH⁻] = 1 \times 10^{-14} \]
   \[ \text{[OH⁻]} = \frac{K_w}{[H⁺]} \]

3. **Set up the expression for the solubility product constant of Ga(OH)₃:**
   \[ \text{Ga(OH)₃ (s)} \rightleftharpoons \text{Ga³⁺ (aq)} + 3\text{OH⁻ (aq)} \]
   \[ Kₛₚ = [\text{Ga³⁺}][\text{OH⁻}]³ \]

4. **Express the molar solubility (s) in terms of [Ga³⁺] and [OH⁻]:**
   Given: \( [\text{Ga³⁺}] = s \) and \( [\text{OH
Transcribed Image Text:**Problem Statement:** Calculate the molar solubility of gallium hydroxide, Ga(OH)₃ (Kₛₚ = 7.28 x 10⁻³⁶), in a solution that is buffered at pH = 3.59. --- **Detailed Explanation:** In this problem, we are asked to find the molar solubility of gallium hydroxide, Ga(OH)₃, in a solution with a specific pH value. The provided data includes the solubility product constant (Kₛₚ) for Ga(OH)₃, which is 7.28 x 10⁻³⁶. Additionally, the pH of the solution is given as 3.59. To solve this problem, we will use the concept of solubility product constant and the relationship between pH and hydroxide ion concentration to determine the molar solubility. **Steps:** 1. **Determine the hydrogen ion concentration from the pH of the solution:** \[ \text{pH} = 3.59 \] \[ \text{[H⁺]} = 10^{-\text{pH}} \] \[ \text{[H⁺]} = 10^{-3.59} \] 2. **Calculate the hydroxide ion concentration using the water dissociation constant (K_w):** \[ K_w = [H⁺][OH⁻] = 1 \times 10^{-14} \] \[ \text{[OH⁻]} = \frac{K_w}{[H⁺]} \] 3. **Set up the expression for the solubility product constant of Ga(OH)₃:** \[ \text{Ga(OH)₃ (s)} \rightleftharpoons \text{Ga³⁺ (aq)} + 3\text{OH⁻ (aq)} \] \[ Kₛₚ = [\text{Ga³⁺}][\text{OH⁻}]³ \] 4. **Express the molar solubility (s) in terms of [Ga³⁺] and [OH⁻]:** Given: \( [\text{Ga³⁺}] = s \) and \( [\text{OH
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