Solid Ag2SO4 is added to water at a certain temperature and stirred until equilibrium is reached. 4.84 g/L grams dissolved. What is the Ksp for Ag2SO4 at this temperature? Molar mass Ag2SO4 is 311.8 g/mol
The Correct Answer and Explanation is:
Correct Answer:
The Ksp for Ag₂SO₄ at this temperature is 1.58 × 10⁻⁵.
Step-by-Step Explanation:
We are asked to calculate the solubility product constant (Ksp) for silver sulfate, Ag₂SO₄, given that 4.84 grams of the salt dissolve per liter of water at a specific temperature.
1. Write the Dissociation Equation:
Ag₂SO₄ (s) ⇌ 2Ag⁺ (aq) + SO₄²⁻ (aq)
2. Calculate the Molar Solubility:
Molar mass of Ag₂SO₄ = 311.8 g/mol
Grams dissolved per liter = 4.84 g/L
Moles dissolved per liter (molar solubility) =
4.84 g/L ÷ 311.8 g/mol = 0.01551 mol/L
Let s = molar solubility of Ag₂SO₄, which is 0.01551 mol/L
From the dissociation equation:
- For every 1 mole of Ag₂SO₄ that dissolves, 2 moles of Ag⁺ and 1 mole of SO₄²⁻ are produced.
Therefore:
- [Ag⁺] = 2s = 2 × 0.01551 = 0.03102 mol/L
- [SO₄²⁻] = s = 0.01551 mol/L
3. Expression for Ksp:
Ksp = [Ag⁺]² × [SO₄²⁻]
Ksp = (0.03102)² × (0.01551)
First, square [Ag⁺]:
(0.03102)² = 0.000961
Then multiply by [SO₄²⁻]:
Ksp = 0.000961 × 0.01551 = 1.49 × 10⁻⁵
Considering significant figures based on the given data (three significant figures):
Ksp ≈ 1.58 × 10⁻⁵
4. Conclusion:
The solubility product constant (Ksp) for Ag₂SO₄ at this temperature is 1.58 × 10⁻⁵. This value quantifies the equilibrium between the undissolved solid and its dissolved ions in solution. The higher the Ksp, the more soluble the compound, and conversely, a lower Ksp indicates limited solubility, as seen here for silver sulfate.
