Use Ksp to find the concentration of an ion in a saturated solution. Consider a 2.50E-3 M solution of Al2(SO4)3.
(a) What [OH^-] is required to initiate precipitation of Al^3+ from the solution?
(b) What [OH^-] is required to lower the [Al^3+] to 2.00E-7 M ?
2.5E-3M Al2(SO4)3 ==> 2Al^3+ + 3SO4^=
Look up Ksp for Al(OH)3.
Ksp = (Al^3+)(OH^-)^3
Substitute Ksp and 2.5E-3 and solve for OH^- for part A.
b. I assume this is a different problem and the Al is as quoted in part b and has nothing to do with part a.
Substitute for Ksp ad 2E-7 and solve for OH^-
To find the concentration of an ion in a saturated solution, we can use the solubility product constant (Ksp) and the stoichiometric coefficients of the balanced chemical equation for the dissolution of the compound.
In this case, we want to find the concentration of the Al^3+ ion in a saturated solution of Al2(SO4)3.
The balanced chemical equation for the dissolution of Al2(SO4)3 is:
2 Al2(SO4)3 -> 6 Al^3+ + 3 SO4^2-
The solubility product constant expression for this reaction is:
Ksp = [Al^3+]^6 * [SO4^2-]^3
For part (a) of the question, we want to determine the [OH^-] required to initiate precipitation of Al^3+ from the solution. This means we need to find the concentration of OH^- at which the [Al^3+] reaches its maximum solubility (i.e., when it is equal to the solubility product constant).
Step 1: Calculate the [Al^3+] from the given concentration of Al2(SO4)3.
The concentration of Al^3+ in the 2.50E-3 M Al2(SO4)3 solution is 6 times the concentration of Al2(SO4)3 because of the stoichiometric coefficient in the balanced equation.
[Al^3+] = 6 * 2.50E-3 M = 1.50E-2 M
Step 2: Set up the solubility product constant expression with the [Al^3+] unknown.
Ksp = [Al^3+]^6 * [SO4^2-]^3
Step 3: Substitute the known values into the equation and solve for [OH^-].
Ksp = (1.50E-2)^6 * [OH^-]^3
We can rearrange the equation to solve for [OH^-]:
[OH^-] = (Ksp / (1.50E-2)^6)^(1/3)
Using the given value of the solubility product constant (Ksp) for Al2(SO4)3, substitute it into the equation to calculate the [OH^-] required to initiate precipitation of Al^3+.
For part (b) of the question, we want to determine the [OH^-] required to lower the [Al^3+] to 2.00E-7 M. This means we need to find the concentration of OH^- at which the [Al^3+] reaches the desired value.
Step 1: Calculate the [Al^3+] from the given desired concentration.
The desired [Al^3+] is 2.00E-7 M.
Step 2: Set up the solubility product constant expression with the [Al^3+] unknown.
Ksp = [Al^3+]^6 * [SO4^2-]^3
Step 3: Substitute the known values into the equation and solve for [OH^-].
Ksp = (2.00E-7)^6 * [OH^-]^3
We can rearrange the equation to solve for [OH^-]:
[OH^-] = (Ksp / (2.00E-7)^6)^(1/3)
Using the given value of the solubility product constant (Ksp) for Al2(SO4)3, substitute it into the equation to calculate the [OH^-] required to lower the [Al^3+] to 2.00E-7 M.