What is the solubility of La(IO₃)₃ in a solution that contains 0.100 M IO₃⁻ 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 0.100 M IO₃⁻ ions? (Ksp of La(IO₃)₃ is 7.5 × 10⁻¹²)

Answer 1

This is a "common ion effect" problem.

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

Ksp = [La³⁺][IO₃^-]³ .. Ksp expression

Because the Ksp is so low, we can ignore any contribution from La(IO₃)₃(s) to the [IO₃^-] and assume that all of the IO₃^- comes from that added to the solution, i.e [IO₃^-] = 0.100 M

7.5x10^-12 = [La³⁺][0.100]³

[La³⁺] = 7.5x10^-9 M

Solubility of La(IO₃)₃ in a solution containing 0.100 M IO₃^- = 7.5x10^-9 M