A) Since the [SO₄²⁻] required to precipitate CaSO₄ is smaller, CaSO₄ will precipitate first.
B) 1.2 * 10⁻⁶ L of Na₂SO₄ is required to initiate the precipitation of CaSO₄
From the data provided:
To determine which salt will precipitate first, the concentration of SO₄²⁻ in each salt is determined from the Ksp values of the salts:
Dissociation equations of CaSO₄ and Ag₂SO₄ is given below:
For CaSO₄; Ksp = [Ca²⁺][SO₄²⁻]
[SO₄²⁻] = Ksp/[Ca²⁺]
[SO₄²⁻] = 2.4 x 10⁻⁵/ 0.2
[SO₄²⁻] = 1.2 * 10⁻⁴ M
For Ag₂SO₄; Ksp = [Ag⁺]²[SO₄²⁻]
[SO₄²⁻] = Ksp/[Ag⁺]
[SO₄²⁻] = 2.4 x 10⁻⁵/ [0.3]²
[SO₄²⁻] = 1.67 * 10⁻⁴ M
Therefore, since the [SO₄²⁻] required to precipitate CaSO₄ is smaller, CaSO₄ will precipitate first.
B) Volume of Na₂SO₄ required to initiate the precipitation is calculated using the formula:
Number of moles SO₄²⁻ = concentration * volume
volume of initial solution = 0.01 L; concentration of SO₄²⁻ = 1.67 * 10⁻⁴ M
number of moles SO₄²⁻ = 1.2 * 10⁻⁴ M * 0.01 L = 1.2 * 10⁻⁶ moles
Volume of Na₂SO₄ required = 1.2 * 10⁻⁶ moles * 1.0 M
Volume of Na₂SO₄ required = 1.2 * 10⁻⁶ L
Therefore, 1.2 * 10⁻⁶ L of Na₂SO₄ is required to initiate the precipitation of CaSO₄
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