The solubility product for Zn(OH)2 is 3.0x10^-16. The formation constant for the hydroxo complex,Zn(OH)4^2- , is 4.6x10^17. What is the minimum concentration of OH- required to dissolve 1.6×10−2 mol of Zn(OH)2 in a liter of solution?

The minimum concentration of OH- required to dissolve 1.6×10−2 mol of Zn(OH)2 in a liter of solution is 4.6x10^-14 M.

To solve this problem, we can use the concept of solubility product, Ksp. The solubility product expression for Zn(OH)2 is:

Ksp = [Zn^2+][OH-]^2

Given that the solubility product for Zn(OH)2 is 3.0x10^-16, we can assume that [Zn^2+] is very small compared to [OH-]^2. Therefore, we can approximate the expression to:

Ksp = [OH-]^2

Now, we can solve for [OH-] by taking the square root of the solubility product:

[OH-] = sqrt(Ksp)
= sqrt(3.0x10^-16)
= 1.7x10^-8

The minimum concentration of OH- required to dissolve 1.6×10−2 mol of Zn(OH)2 in a liter of solution is 1.7x10^-8 M.

To find the minimum concentration of OH- required to dissolve 1.6×10^-2 mol of Zn(OH)2 in a liter of solution, we need to consider the solubility equilibrium of Zn(OH)2.

The balanced equation for the dissolving of Zn(OH)2 in water is:
Zn(OH)2(s) ⇌ Zn^2+(aq) + 2OH^-(aq)

From the solubility product constant (Ksp), we know that:

Ksp = [Zn^2+][OH^-]^2

Given that the solubility product constant for Zn(OH)2 is 3.0x10^-16, we can write the expression for [OH^-] as:

[OH^-] = √(Ksp / [Zn^2+])

Now, let's calculate the concentration of [OH^-]:

[Zn^2+] = (1.6×10^-2 mol) / (1 L) = 1.6×10^-2 M

Substituting the values into the equation for [OH^-]:

[OH^-] = √((3.0x10^-16) / (1.6×10^-2))

Simplifying the expression:

[OH^-] = √(1.875x10^-14)

[OH^-] ≈ 4.33x10^-8 M

Therefore, the minimum concentration of OH- required to dissolve 1.6×10^-2 mol of Zn(OH)2 in a liter of solution is approximately 4.33x10^-8 M.