Solubility from ksp and molarity

Question

What is the solubility of La(IO₃)₃ in a solution that contains 0.150 M La³⁺ ions? (Ksp of La(IO₃)₃ is 7.5 × 10⁻¹²)

Answer 1

Balanced Chemical Reaction:

La³⁺ (aq) + 3IO₃^- (aq) ⇔ La(IO₃)₃ (s) K_sp = 7.5 x 10^-12

This question illustrates the common ion effect where La³⁺ is the common ion. Write the K_sp expression as:

K_sp = [La³⁺] [IO₃^-]³

[La³⁺] is given as 0.150 M. Since K_sp is a very small #, the additional La³⁺ concentration provided by the La(IO₃)₃ solution is insignificant.

Enter the values of K_sp and [La³⁺] = 0.150 M in the above expression, and then solve for [IO₃^-].

7.5 x 10^-12 = (0.150) (3x)³

5.0 x 10^-11 = 27x³

x³ = 1.9 x 10^-12

x = 1.2 x 10^-4 M