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

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To answer these questions, we need to consider the equilibria in the system and determine the species that are relevant for expressing the solubility of zinc hydroxide (Zn(OH)2).

a) To express the solubility of Zn(OH)2, we need to consider the species involved in its dissolution. From the given equilibria, we see that Zn(OH)2 dissociates into Zn2+ and 2OH- ions. Therefore, we would need to use the concentration of Zn2+ ions and the concentration of OH- ions to express the solubility (S) of Zn(OH)2.

b) To write the expression for the Zn2+ concentration in terms of the prevailing OH- concentration, we need to consider the equilibrium reaction Zn2+ + OH- -> Zn(OH)+, which has equilibrium constant K1. The expression would be:

[Zn2+] = K1 * [OH-]

c) To write the expression describing the solubility of Zn(OH)2 in solution in terms of equilibrium constants and prevailing OH- only, we need to consider the equilibria involving the formation of Zn(OH)2. From the given equilibria, we see that Zn(OH)2 is formed from Zn(OH)- and OH- ions with the equilibrium constant K2, and Zn(OH)2 reacts with OH- ions to form Zn(OH)3- with equilibrium constant K3. The expression would be:

[S of Zn(OH)2] = K2 * K3 * [OH-]^3

Note that in this expression, we have multiplied the equilibrium constants because the overall formation of Zn(OH)2 involves multiple steps.

In summary:
a) The species relevant for expressing the solubility of Zn(OH)2 are Zn2+ and OH- ions.
b) The expression for the Zn2+ concentration in terms of prevailing OH- concentration is [Zn2+] = K1 * [OH-].
c) The expression describing the solubility of Zn(OH)2 in solution in terms of equilibrium constants and prevailing OH- only is [S of Zn(OH)2] = K2 * K3 * [OH-]^3.