what will the new solubility of the solid be?

Question

At a particular temperature, the solubility of In₂(SO₄)₃ in water is 0.0090 M. You have found Ksp to be 6.4 × 10⁻⁹. If solid In₂(SO₄)₃ is added to a solution that already contains 0.150 M In(NO₃)₃, what will the new solubility of the solid be?

Answer 1

This is a common ion problem:

Here, the common ion is In³⁺

In₂(SO₄)₃(s) <==> 2In³⁺(aq) + 3SO₄^2-(aq) ... Ksp = 6.4x10^-9

Ksp = 6.4x10^-9 = [In³⁺]²[SO₄^2-]³

Since the solution already contains 0.150 M In³⁺ which comes from the In(NO₃)₃, we can use that as [In³⁺].

6.4x10^-9 = [0.150]²[SO₄^2-]³ = 0.0225 x³

x3 = 284x10^-9

x = 6.58x10^-3 M = [SO₄^2-]

New solubility of the salt In2(SO4)3 will thus be 2.19x10^-3 M since 1 mol of salt produces 3 moles SO₄^2-.