What is the minimum pH at which cobalt(II) hydroxide [Ksp = 2.0 × 10^-16] will precipitate from a solution 0.020 M in CO₃²⁺?

Question

Quizplus · Accepted Answer

The solubility product expression for cobalt(II) hydroxide is:

Ksp = [Co2+][OH-]^2

Initially, the solution is at a pH of 13, so the concentration of hydroxide ions is 10^-1^3 mol/L. We can use this information to calculate the initial concentration of cobalt(II) ions:

Ksp = [Co2+][OH-]^2
2.0 × 10^-16 = [Co2+](10^-13)^2
[Co2+] = 2.0 × 10^-6 mol/L

We can use an ICE table to determine the concentration of cobalt(II) ions that will remain in solution at a lower pH. Let x be the concentration of hydroxide ions, then the new concentration of cobalt(II) ions will be:

[Co2+] = 2.0 × 10^-6 - x

At the minimum pH for precipitation, the concentration of hydroxide ions will be equal to the solubility of cobalt(II) hydroxide:

x = [OH-] = √(Ksp/[Co2+]) = √(2.0 × 10^-16/2.0 × 10^-6) = 1.4 × 10^-5 mol/L

Taking the negative logarithm of this concentration gives a pH of 7.0:

pH = -log([OH-]) = -log(1.4 × 10^-5) = 7.0

Therefore, the minimum pH at which cobalt(II) hydroxide will precipitate from the solution is 7.0, which corresponds to choice C.

What Is the Minimum PH at Which Cobalt(II) Hydroxide [Ksp