Question

± Solubility of Zinc Hydroxide in Basic Solution

The solubility-product constant for Zn(OH)2 is Ksp=3.00×10−16.

The formation constant for the hydroxo complex, Zn(OH)42−, is Kf=4.60×1017.

A solubility-product constant, Ksp, corresponds to a reaction with the following general format:

salt(s)⇌cation(aq)+anion(aq)

A formation constant, Kf, corresponds to a reaction with the following general format:

metal ion(aq)+Lewis base(aq)⇌complex ion(aq)

Part A

When Zn(OH)2(s) was added to 1.00 L of a basic solution, 1.01×10⁻² mol of the solid dissolved. What is the concentration of OH− in the final solution?

Express your answer with the appropriate units.

Hints

[OH−] =

Answer 1

Solubility product constant
3.00 e-16 = [Zn+2] [OH-]^2
so
[Zn+2] = 3.00 e-16 / [OH-]^2

the formation constant for comlpex ion
4.6 e17 = [Zn(OH)4^2-] / [Zn+2] [OH-]^4
so
[Zn+2] = [Zn(OH)4^2-] / [OH-]^4 (4.6 e17)
Both concentration of Zn+2 must be equal
[Zn+2] = [Zn+2]
then
(3.00 e-16) / [OH-]^2 = [Zn(OH)4^2-] / [OH-]^4 (4.6 e17)

(3.00 e-10) (4.6 e+17) = [Zn(OH)4^2-] [OH-]^2 / [OH-]^4

1380= [Zn(OH)4^2-] / [OH-]^2

[OH-]^2 = [Zn(OH)4^2-] / 1380

[OH-]^2 = [1.01×10^−2 ] / 1380

[OH-]^2 = 7.3188 e-6

[OH] = 0.0027