Above what Fe2 concentration will Fe(OH)2 precipitate from a buffer solution that has a pH of 8.03?
The Ksp of Fe(OH)2 is 4.87×10-17 M3.
Convert pH to OH-, substitute into Ksp expression and solve for Fe.
To determine the concentration of Fe2+ at which Fe(OH)2 will precipitate from the buffer solution, we need to compare the solubility product constant (Ksp) of Fe(OH)2 with the concentrations of Fe2+ and OH- in the solution.
The balanced equation for the dissolution of Fe(OH)2 is:
Fe(OH)2(s) ↔ Fe2+(aq) + 2 OH-(aq)
We know the Ksp value for Fe(OH)2 is 4.87×10^-17 M^3, which represents the equilibrium constant for the reaction. The expression for Ksp is given by:
Ksp = [Fe2+][OH-]^2
Since Fe(OH)2 is a base, it will react with water to produce hydroxide ions (OH-) according to:
Fe(OH)2(s) + 2 H2O(l) ↔ Fe(OH)4^2-(aq) + 2 H+(aq)
Given that the pH of the buffer solution is 8.03, we can determine the concentration of hydroxide ions (OH-) using the relationship between pH and pOH, where pOH = 14 - pH:
pOH = 14 - 8.03 = 5.97
To convert pOH to OH- concentration, we use the following formula:
[OH-] = 10^(-pOH) = 10^(-5.97)
Now, we have the concentration of OH-. However, we need to find the concentration of Fe2+. Since Fe2+ and OH- have a stoichiometric ratio of 1:2, the concentration of Fe2+ is half the concentration of OH- in the buffer solution.
[Fe2+] = 0.5 × [OH-] = 0.5 × 10^(-5.97)
To determine the concentration of Fe2+ at which Fe(OH)2 precipitates, we need to compare [Fe2+] with the solubility product constant (Ksp) for Fe(OH)2.
So, the critical concentration above which Fe(OH)2 will precipitate is given by:
[Fe2+] > Ksp / [OH-]^2
Substituting the values, we get:
0.5 × 10^(-5.97) > 4.87×10^-17 M^3 / (10^(-5.97))^2
Simplifying the expression, we find:
0.5 × 10^(-5.97) > 4.87×10^-17 M^3 / 10^(-11.94)
Multiplying both sides by 10^11.94, we get:
0.5 × 10^(5.97 + 11.94) > 4.87×10^(-17 + 11.94) M^3
Simplifying further yields:
0.5 × 10^17.91 > 4.87 × 10^-5.06 M^3
Calculating this expression, we find:
5.65 × 10^17 > 4.87 × 10^-5.06 M^3
Therefore, the concentration of Fe2+ needs to be greater than 5.65 × 10^17 M for Fe(OH)2 to precipitate from the buffer solution with a pH of 8.03.