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.