To determine the concentration of Co3+ in different solutions, we need to consider the solubility product constant (Ksp) and the balanced chemical equation for the dissolution of Co(OH)3.
The balanced chemical equation for the dissolution of Co(OH)3 is:
Co(OH)3(s) ⇌ Co3+(aq) + 3OH-(aq)
Given: Ksp of Co(OH)3 = 3.00×10^(-45)
(a) Pure Water:
In pure water, there is no common ion present that can influence the equilibrium of Co(OH)3 dissolution. Therefore, we assume that the concentration of OH- is very low and negligible.
Let's assume the concentration of Co3+ in pure water is 'x'. The concentration of OH- can be assumed to be very small compared to 'x'.
Co(OH)3(s) ⇌ Co3+(aq) + 3OH-(aq)
Using the Ksp expression, we have:
Ksp = [Co3+][OH-]^3
Since the concentration of OH- can be considered negligible, we can approximate the Ksp expression as:
Ksp = [Co3+][OH-]^3 ≈ [Co3+]
Substituting the given value of Ksp, we have:
3.00×10^(-45) = [Co3+]
Therefore, the concentration of Co3+ in pure water is approximately 3.00×10^(-45) M.
(b) 0.0100 M NaOH:
When we add 0.0100 M NaOH to the solution, it provides a common ion (OH-) that can affect the equilibrium of Co(OH)3 dissolution.
Since NaOH is a strong base, it fully dissociates in water to form OH- ions. Therefore, the concentration of OH- is equal to the concentration of NaOH, which is 0.0100 M.
Using the Ksp expression, we have:
Ksp = [Co3+][OH-]^3
Substituting the given value of Ksp and the concentration of OH-, we have:
3.00×10^(-45) = [Co3+](0.0100)^3
Solving for [Co3+], we find:
[Co3+] = 3.00×10^(-45) / (0.0100)^3
Calculating this expression gives:
[Co3+] ≈ 3.00×10^(-45) / 1.00×10^(-6)
[Co3+] ≈ 3.00×10^(-39) M
Therefore, the concentration of Co3+ in a 0.0100 M NaOH solution is approximately 3.00×10^(-39) M.