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

I do not know where to start.

To solve this question, we need to analyze each part and understand the given equilibria. Let's break down the problem step by step:

a) The solubility of zinc hydroxide, Zn(OH)2, can be expressed in terms of its constituent ions, Zn2+ and OH-. From the given equilibria, we can see that Zn(OH)2 dissociates into Zn2+ and 2OH-. So, the sum of these species, Zn2+ + 2OH-, would be used to express the solubility, S, of zinc hydroxide.

b) Now, let's determine the expression for the Zn2+ concentration in terms of the prevailing OH- concentration. From the equilibria given, we can see that Zn2+ is formed from Zn(OH)2 and OH-. The equation for this reaction is: Zn(OH)2 + OH- -> Zn2+ + 2OH-.

Since we are looking for the expression of Zn2+ in terms of the OH- concentration, we can consider the reaction as a simple forward reaction, neglecting the reverse reaction. In this case, the concentration of Zn2+ would be proportional to the concentration of OH-. Thus, the expression for Zn2+ concentration, [Zn2+], would be [OH-].

c) To write the expression describing the solubility of zinc hydroxide in solution in terms of the equilibrium constants and the prevailing OH- concentration only, we can use the principle of mass action and the given equilibria. The solubility product constant, Ksp, for Zn(OH)2 is given as Zn(OH)2 -> Zn2+ + 2OH-.

Using the equilibrium expression, we have: [Zn2+][OH-]^2 = Ksp.

However, we need to express the solubility in terms of the prevailing OH- concentration only. From the previous answer, we found that the concentration of Zn2+ is proportional to the OH- concentration. So, we can substitute [Zn2+] with [OH-] in the equilibrium expression:

[OH-][OH-]^2 = Ksp.

Simplifying the expression, we get: [OH-]^3 = Ksp.

This expression describes the solubility of zinc hydroxide in solution in terms of equilibrium constant (Ksp) and the prevailing OH- concentration only.

Remember to always double-check the calculations and ensure that the equilibrium constants and species are correctly written to avoid any errors in your answer.