🤓 Based on our data, we think this question is relevant for Professor Carlon's class at UCB.
Consider an amphoteric hydroxide, M(OH)2(s), where M is a generic metal.
M(OH)2 (s) ⇌ M2+ (aq) + 2OH- (aq) Ksp = 2 x 10-16
M(OH)2 (s) + 2OH- (aq) ⇌ M(OH)42- (aq) Kf = 0.060
Estimate the solubility of M(OH)2 in a solution buffered at pH = 7.0, 10.0, and 14.0.
M(OH)2 (s) ⇌ M2+ (aq) + 2OH- (aq)
From this balanced equation we can see that equilibrium expression for Ksp:
Ksp= [M2][OH-]22 = 2 x 10-16
This is so because we have 1 mole of M(OH)2 producing 1 mole of M2+ and 2 moles of OH-.
We are looking for Molar solubility, or x. In our equation, [M2] = x, so we need to solve for [M2].