Calculating solubility of Al(OH)3

Question

Calculate the solubility of Al(OH)₃ in 0.001 M NaOH. (K_sp = 3.0 x 10^-34)

Answer 1

This is a problem dealing with the common ion effect. In this case, the common ion is OH^-.

Al(OH)₃(s) <==> Al³⁺(aq) + 3OH^-(aq)

K_sp = 3.0x10^-34 = [Al³⁺][OH^-]³

We can assume that the contribution of OH^- from Al(OH)₃ is negligible compared to 0.001 M from NaOH.

Thus, we can write...

3.0x10^-34 = [Al³⁺][0.001]³

[Al³⁺] = 3.0x10^-34 / [0.001]³

[Al³⁺] = 3.0x10^-31 = solubility of Al(OH)₃ in 0.001 M NaOH