The Ksp of Al(OH)3 is 1.0 x 10-33. What is the solubility of Al(OH)3 in 0.00010 M NaOH?

Question

The K_sp of Al(OH)₃ is 1.0 x 10^-33. What is the solubility of Al(OH)₃ in 0.00010 M NaOH?

The answer id 1.0e-21

please show your steps

Answer 1

This is a common ion effect problem where the common ion is OH^-. Some comes from Al(OH)₃ and some comes from NaOH.

Al(OH)3(s) <===> Al3+ + 3OH-

Ksp = [Al³⁺][OH^-]³

We are given the [OH^-] as 0.00010 M from the NaOH, which will be the majority of the OH^- since the Ksp for Al(OH)₃ is so very small (10^-33). This tells you that very little OH^- comes from Al(OH)₃.

1.0x10^-33 = [Al³⁺][0.00010]³ = [Al³+][1x10-4]³

[Al³⁺] = 1.0x10^-33 / (1x10^-4)³

[Al³⁺] = 1.0x10^-21 M = solubility of Al(OH)₃ in 1x10-4 M NaOH