Consider a solution that is 0.022 M in Fe2+ and 0.014 M in Mg+2.
A). If potassium carbonate is used to selectively precipitate one of the cations while leaving the other on solution, which cation will precipitate first? What minimum concentration of K2CO3 will trigger the precipitate first?
B). What is the remAining concentration of the cation that precipitates first, when the other cation begins to precipatate?
The Fe^2+ will precipitate first.
and i'm also confused on second part...
First look up ksp for both FeCO3 and MgCO3.
FeCO3 ksp=3.07*10^-11
MgCO3 ksp=6.82*10^-6
Which is less soluble? FeCO3 so in a solution it would precipitate first.
How to find K2CO3 concentration?
Fe ksp=[Fe2+][K2CO3]
3.07*10^-11= 0.022*[K2CO3]
Solve for K2CO3
A). To determine which cation will precipitate first, we need to compare the solubility product constants (Ksp) of the corresponding precipitates. The precipitate with the lower Ksp value will form first.
The solubility product constant for the precipitation of Fe2+ as FeCO3 is given as:
Ksp (FeCO3) = [Fe2+][CO3^-2]
The solubility product constant for the precipitation of Mg+2 as MgCO3 is given as:
Ksp (MgCO3) = [Mg+2][CO3^-2]
Since both cations have carbonate, CO3^-2, as the anion that will precipitate with them, we can compare the solubility product constants based on the concentrations of the cations. Fe2+ has a concentration of 0.022 M, while Mg+2 has a concentration of 0.014 M.
The minimum concentration of K2CO3 that will trigger precipitation can be calculated using the common ion effect. The common ion effect predicts that the presence of a common ion reduces the solubility of a compound. In this case, the common ion is CO3^-2, which comes from K2CO3, so we can determine the concentration of CO3^-2 that will precipitate each cation.
For Fe2+ to precipitate, the concentration of CO3^-2 needs to exceed the solubility product constant, Ksp(FeCO3). Let's assume the minimum concentration of K2CO3 needed to exceed this Ksp value is x M.
Then, using the solubility product constant expression, we have:
Ksp (FeCO3) = (0.022 - x)(x)
For Mg+2 to precipitate, the concentration of CO3^-2 needs to exceed the solubility product constant, Ksp(MgCO3). Assuming the minimum concentration of K2CO3 needed to exceed this Ksp value is y M, we have:
Ksp (MgCO3) = (0.014 - y)(y)
Now we need to compare the solubility product constants to determine which cation precipitates first:
Ksp (FeCO3) < Ksp (MgCO3)
Substituting the given concentrations and solving for x and y:
(0.022 - x)(x) < (0.014 - y)(y)
We don't have enough information to solve for exact values of x and y, but based on the concentrations, we can infer that the cation with the lowest solubility product constant, Ksp, will precipitate first.
B). When one cation begins to precipitate, its concentration will decrease, while the other cation's concentration will remain the same. The remaining concentration of the cation that precipitates first can be calculated using the initial concentration minus the concentration that precipitates.
Let's assume the cation that precipitates first is Fe2+.
Using the given concentration of Fe2+ (0.022 M) and assuming x M of CO3^-2 precipitates:
Remaining concentration of Fe2+ = 0.022 - x
Similarly, for Mg+2, the remaining concentration would be:
Remaining concentration of Mg+2 = 0.014
Note that the exact value of x cannot be determined without additional information, but the remaining concentration of the cation that precipitates first will be the initial concentration minus the concentration that precipitates.
To determine which cation will precipitate first and the minimum concentration of K2CO3 required to trigger the precipitation, we need to make use of the solubility product constant (Ksp) values for the respective salts.
A). To determine which cation will precipitate first, we compare the solubility product constants of the possible precipitates. The reaction for the precipitation of Fe2+ can be represented as:
Fe2+(aq) + CO3^2-(aq) → FeCO3(s)
And the reaction for the precipitation of Mg2+ can be represented as:
Mg2+(aq) + CO3^2-(aq) → MgCO3(s)
The solubility product constant for FeCO3 is given by Ksp(FeCO3), and the solubility product constant for MgCO3 is given by Ksp(MgCO3).
If we compare the Ksp values, we find that Ksp(FeCO3) is smaller than Ksp(MgCO3). Therefore, FeCO3 will precipitate first.
To determine the minimum concentration of K2CO3 required to trigger the precipitation of FeCO3, we need to compare the ion product (Q) with the Ksp value. The ion product is calculated by multiplying the concentrations of the respective ions present in the solution.
For FeCO3:
Q(FeCO3) = [Fe2+][CO3^2-]
Since the concentration of Fe2+ is 0.022 M and the concentration of CO3^2- would be determined by the concentration of K2CO3, we can represent it as [CO3^2-] and obtain:
Q(FeCO3) = (0.022)[CO3^2-]
To trigger the precipitation of FeCO3, the ion product Q(FeCO3) must exceed the solubility product constant Ksp(FeCO3).
Q(FeCO3) > Ksp(FeCO3)
(0.022)[CO3^2-] > Ksp(FeCO3)
Now, we need to find the minimum concentration of [CO3^2-] (K2CO3) that satisfies this inequality.
B). To determine the remaining concentration of the cation that precipitates first when the other cation begins to precipitate, we need to apply the common ion effect. The common ion effect states that the presence of a common ion from another compound decreases the solubility of a salt.
In this case, when MgCO3 begins to precipitate, the concentration of CO3^2- in the solution will decrease due to the formation of MgCO3. This decrease in CO3^2- concentration will affect the solubility of FeCO3. However, since the problem does not specify the concentration of K2CO3 at which MgCO3 begins to precipitate, we cannot provide an exact concentration of the remaining Fe2+ ion.
To summarize:
A). Fe2+ will precipitate first, and the minimum concentration of K2CO3 to trigger its precipitation can be determined by solving the inequality (0.022)[CO3^2-] > Ksp(FeCO3).
B). The remaining concentration of Fe2+ when MgCO3 begins to precipitate cannot be determined without the specific concentration of K2CO3 at which MgCO3 precipitation occurs.