Zinc hydroxide is not very soluble in water, but in basic solution, it may dissolve as the tetrahydroxozinc complex ion: Zn(OH)₄^2-.
The solubility product constant of zinc hydroxide is K_sp = 2.1 x 10^-16.
The formation constant of Zn(OH)₄^2- is K_f = 2.8 x 10¹⁵.
a) If 150.0 mg of zinc hydroxide crystals are mixed with 250.0 mL of pure water, what mass of crystals will remain undissolved and what will be the pH of the resulting solution?  Justify your answer by showing your calculations.
b) If 150.0 mg of zinc hydroxide crystals are mixed with 250.0 mL of a 0.100 mol/L NaOH solution, what mass of crystals will remain undissolved?  Justify your answer by showing your calculations.

One of the students I'm tutoring came to me with this problem.  I got answers of 0.1499 g / pH 8.87 and 8.87 x 10^-13 g for questions a and b respectively when I tried it but since there was no answer provided with the problem, we have no way are checking these numbers.  Would anybody mind trying the problem and comparing answers?  Thanks!

The solubility product constant of zinc hydroxide is K_sp = 2.1 x 10^-16.

I'm assuming they mean in neutral pH

What does that mean? You mean Ksp values are not pH dependent?

I got answers of 0.1499 g / pH 8.87 and 8.87 x 10^-13 g for questions a and b respectively

a - OK

b - 4 mg

Assuming there is some solid left, maximum concentration of Zn²⁺ is given by solubility product - and is 2.1*10^-14M. Concentration of complex is given by K_f[Zn²⁺ ][OH^- ]⁴ = 5.88*10^-3 (assuming Zn²⁺ concentration as given by solubilty product). Thus there is 0.25*5.88*10^-3*99.4=0.146 g of Zn in solution (in form of complex, free ions can be neglected). This confirms our assumption that some solid was left and gives mass of the solid as 150-146=4mg (3.9 to use 2 sd).

A-ha!  It has been quite some time since I have done these kinds of questions.

Over 20 years in my case. No joking - I have spent some time last year on pH, but not on solubilities or complexes.

The amount of free ions from any particular compound allowed to remain in solution at equilibrium must always follow the K_sp expression for that compound;

Can't be greater than - but can be lower!

When dealing with ions that complex in solution, it is best to first calculate the amount of free ions that are allowed to exist in the solution from the given K_sp values, then calculate the amount of complex in solutions.  Nice  

But later you have to check if there is solid left. If not - K_sp is of no use.