what is the molar solubility of Fe(OH)3 in a buffered solution with pH=8.2 at 25 degrees Celsius given ksp =4.0*10^-38.
........Fe(OH)3 ==> Fe^3+ + 3OH^-
I........solid.......0.......0
C........solid.......x.......3x
E........solid.......x.......3x
Ksp = (Fe^3+)(OH^-)^3
You know Ksp, OH can be calculated from pH, solve for x which is the solubility.
Student
Step by step
To find the molar solubility of Fe(OH)3 in a buffered solution with pH=8.2, we need to first determine the concentration of hydroxide ions (OH-) in the solution, as the solubility of Fe(OH)3 depends on the concentration of OH- ions.
To calculate the concentration of OH- ions, we can use the pH of the solution.
In a solution with a pH of 8.2, the concentration of H+ ions is given by the equation: [H+] = 10^(-pH).
Since the solution is buffered, we need to consider the dissociation of water as well. In pure water, the concentration of H+ ions equals the concentration of OH- ions (10^(-7) M). In a buffered solution, however, the concentration of H+ ions will be different from 10^(-7) M.
To calculate the concentration of OH- ions, we can use the fact that in a balanced chemical equation, the concentration of OH- ions is equal to the concentration of the product (Fe(OH)3) when it reaches equilibrium.
Fe(OH)3(s) ⇌ Fe^3+(aq) + 3OH^-(aq)
From the balanced equation, we can see that for every Fe(OH)3 molecule that dissolves, three OH- ions are formed. Therefore, the concentration of OH- ions is three times the molar solubility of Fe(OH)3.
Next, we need to calculate the molar solubility of Fe(OH)3. The solubility product constant (Ksp) for Fe(OH)3 is given as 4.0 * 10^(-38).
The formula for Ksp expression is: Ksp = [Fe^3+] * [OH-]^3.
Since the concentration of Fe^3+ ions can be assumed to be negligible compared to the concentration of OH- ions, we can simplify the equation to: Ksp = [OH-]^3.
Substituting the given value of Ksp into the equation, we get:
4.0 * 10^(-38) = [OH-]^3.
Now, solve for [OH-]:
[OH-] = (4.0 * 10^(-38))^(1/3).
Calculating this expression, we find the concentration of OH- ions to be approximately 2.51 * 10^(-13) M.
Since the concentration of OH- ions is three times the molar solubility of Fe(OH)3, we divide this value by 3 to get the molar solubility:
Molar solubility of Fe(OH)3 ≈ 2.51 * 10^(-13) M / 3 ≈ 8.37 * 10^(-14) M.
Therefore, the molar solubility of Fe(OH)3 in a buffered solution with pH=8.2 at 25 degrees Celsius is approximately 8.37 * 10^(-14) M.