Zn(OH)2 was saturated in a solution of sodium hydroxide. The following equilibra exist under these conditions

Zn(OH)2 -> Zn2+ +2OH- Ksp
Zn2+ +OH- -> Zn(OH)+ K1
Zn(OH)- + OH- -> Zn(OH)2 K2
Zn(OH)2 + OH- -> Zn(OH)3- K3
Zn(OH)3- +OH- -> Zn(OH)42- K4
a) Sum of which species would you use to express the solubility S of zinc hydroxide in the above system
b)Write the expression for the Zn2+ concentration in terms of prevailing OH- concentration
c) Write the expression describing the solubility of zinc hydroxide in solution in term of equilibrium constants and prevailing OH- only

a) To express the solubility S of zinc hydroxide in the given system, we need to consider all the species that contribute to the dissolution of zinc hydroxide. In this case, the species that participate in the dissolution are Zn(OH)2, Zn2+, OH-, Zn(OH)-, Zn(OH)3-, and Zn(OH)42-. Therefore, the sum of these species is used to express the solubility of zinc hydroxide in the system.

b) We can write the expression for the concentration of Zn2+ in terms of the prevailing OH- concentration using the equilibrium constant.

The following equilibrium equation is relevant: Zn(OH)2 ⇌ Zn2+ + 2OH-

Since the equation shows that 1 Zn(OH)2 dissociates to form 1 Zn2+ and 2 OH-, the stoichiometric coefficient of Zn2+ is 1. So, the expression for Zn2+ concentration ([Zn2+]) can be written as:

[Zn2+] = Ksp x [OH-]^2

Where [OH-] is the prevailing concentration of hydroxide ions.

c) To write the expression describing the solubility of zinc hydroxide in terms of equilibrium constants and prevailing OH- only, we need to consider all relevant equilibria.

The relevant equilibria are:
Zn(OH)2 ⇌ Zn2+ + 2OH- (Ksp)
Zn2+ + OH- ⇌ Zn(OH)+ (K1)
Zn(OH)- + OH- ⇌ Zn(OH)2 (K2)
Zn(OH)2 + OH- ⇌ Zn(OH)3- (K3)
Zn(OH)3- + OH- ⇌ Zn(OH)42- (K4)

To express the solubility of zinc hydroxide, we combine the species from the equilibria that contribute to the dissolution of zinc hydroxide. In this case, we have:

Zn(OH)2 ⇌ Zn2+ + 2OH- (Ksp)
Zn2+ + OH- ⇌ Zn(OH)+ (K1)
Zn(OH)- + OH- ⇌ Zn(OH)2 (K2)

Taking into account the stoichiometry, we can write the expression for the solubility of zinc hydroxide ([Zn(OH)2]) as:

[Zn(OH)2] = ([Zn2+] + [Zn(OH)-]) = (Ksp x K2) / K1

Note that this expression includes the equilibrium constants (Ksp, K1, and K2) and the prevailing concentration of hydroxide ions ([OH-]).