What is the solubility of La(IO₃)₃ in a solution that contains 0.250 M La³⁺ ions? (Ksp of La(IO₃)₃ is 7.5 × 10⁻¹²)

Question

What is the solubility of La(IO₃)₃ in a solution that contains 0.250 M La³⁺ ions? (Ksp of La(IO₃)₃ is 7.5 × 10⁻¹²)

Answer 1

La(IO₃)₃(s) <==> La³⁺(aq) + 3IO₃^- .. dissolution process

Ksp = 7.5x10^-12 = [La³⁺][IO₃^-]³

This is a common ion problem because we already have La³⁺ present as the common ion. We assume that the amount of La³⁺ contributed by dissolution of La(IO₃)₃(s) is small compared to 0.250 M and ignore it.

7.5x10^-12 = (0.250)[IO₃^-]³

[IO₃^-]³ = 7.5x10^-12 / 0.250

[IO₃^-]³ = 3x10^-11

[IO₃^-]³ = 3.11x10^-4 M

Since there are 3 moles of [IO₃^-] per mole of La(IO₃)₃, the solubility of La(IO₃)₃ would be 1.04x10^-4 M