Sodium sulfate is slowly added to a solution containing 0.0500 M Ca2 (aq) and 0.0230 M Ag (aq). What will be the concentration of Ca2 (aq) when Ag2SO4(s) begins to precipitate?
What percentage of the Ca2 (aq) can be separated from the Ag (aq) by selective precipitation?
To determine the concentration of Ca2+ when Ag2SO4(s) begins to precipitate, we need to find the common ion concentration at which Ag2SO4(s) will start to form. This occurs when the concentration of SO42- (from sodium sulfate) equals the solubility product constant (Ksp) for Ag2SO4.
The balanced chemical equation for the precipitation reaction is:
Ag+(aq) + SO42-(aq) -> Ag2SO4(s)
The Ksp expression for this reaction is:
Ksp = [Ag+]^2 * [SO42-]
Given that the initial concentration of Ag+ is 0.0230 M, we can assume that [Ag+] is approximately equal to the initial concentration since it is a weak ligand.
Let x be the concentration of Ca2+ when Ag2SO4(s) begins to precipitate. At this point, the concentration of SO42- will also be x.
Using the Ksp expression, we have:
Ksp = (0.0230)^2 * x
Since Ksp is a constant for a given temperature, we can solve for x:
(0.0230)^2 * x = Ksp
x = Ksp / (0.0230)^2
Now, let's calculate x using the given solubility product constant for Ag2SO4. The Ksp for Ag2SO4 is 1.3 x 10^-5.
x = (1.3 x 10^-5) / (0.0230)^2
x ≈ 0.00215 M
Therefore, the concentration of Ca2+ when Ag2SO4(s) begins to precipitate is approximately 0.00215 M.
Now, let's determine the percentage of the Ca2+(aq) that can be separated from the Ag+(aq) by selective precipitation.
The selective precipitation of Ca2+ can be achieved by adding a reagent that will react with Ca2+ but not Ag+. One such reagent that can be used is sodium oxalate (Na2C2O4) which will form CaC2O4(s) precipitate. This can be represented by the balanced equation:
Ca2+(aq) + C2O42-(aq) -> CaC2O4(s)
For every 1 mole of Ca2+ that reacts, 1 mole of CaC2O4(s) is formed.
To calculate the percentage of Ca2+(aq) that can be separated, we need to determine the ratio of moles of Ca2+ to moles of Ag+ in the initial solution:
(0.0500 M Ca2+ / 0.0230 M Ag+) * (1 mole Ca2+ / 1 mole Ag+) = 2.1739 moles Ca2+ per mole Ag+
This means that for every mole of Ag+ in the solution, there are approximately 2.1739 moles of Ca2+.
Therefore, approximately 2.1739 moles of Ca2+ can be separated per mole of Ag+.
To express this as a percentage:
Percentage of Ca2+ that can be separated = (2.1739 moles Ca2+ / 3.1739 moles total) * 100%
Percentage of Ca2+ that can be separated = 68.5%
Therefore, approximately 68.5% of the Ca2+(aq) can be separated from the Ag+(aq) by selective precipitation.
To determine the concentration of Ca2+ when Ag2SO4(s) begins to precipitate, you need to determine the solubility product (Ksp) of Ag2SO4 and compare it with the ion product (IP) of Ag+ and SO4 2-.
The balanced chemical equation for the dissociation of Ag2SO4 is:
Ag2SO4(s) ⇌ 2Ag+(aq) + SO4 2-(aq)
The solubility product expression for Ag2SO4 is:
Ksp = [Ag+]^2 * [SO4 2-]
To find the concentration of Ag+ at saturation, calculate the ion product (IP):
IP = [Ag+]^2 * [SO4 2-]
Given the initial concentrations of Ca2+ and Ag+ in the solution, you can assume that all Ag+ comes from Ag2SO4 dissociation and use the initial concentration of Ag+ for the IP calculation.
1. Calculate the IP for Ag+ and SO4 2- using their initial concentrations:
IP = [Ag+] * [SO4 2-]
2. Set up the Ksp expression and the IP expression equal to each other:
Ksp = IP
3. Substitute the given concentrations for Ag+ and SO4 2- into the IP expression:
Ksp = [Ag+]^2 * [SO4 2-]
Ksp = (0.0230 M)^2 * [SO4 2-]
4. Solve for [SO4 2-]:
[SO4 2-] = Ksp / (0.0230 M)^2
5. Substitute the concentration of [SO4 2-] into the Ksp expression to find [Ag+] at saturation:
Ksp = [Ag+]^2 * (Ksp / (0.0230 M)^2)
[Ag+] = sqrt(Ksp / (Ksp / (0.0230 M)^2))
Now that you have the concentration of Ag+ at saturation, you can determine the concentration of Ca2+ when Ag2SO4(s) begins to precipitate.
The selective precipitation of Ag+ by adding sodium sulfate (Na2SO4) ensures that all Ag+ precipitates as Ag2SO4. Thus, the concentration of Ag+ will decrease to zero, allowing you to calculate the remaining concentration of Ca2+.
To find the percentage of Ca2+ that can be separated from Ag+ by selective precipitation:
1. Calculate the initial moles of Ca2+ in the solution:
moles of Ca2+ = initial concentration of Ca2+ * volume of the solution
2. Calculate the final moles of Ca2+ remaining after Ag2SO4(s) precipitates:
final moles of Ca2+ = (initial concentration of Ca2+ - concentration of Ca2+ when Ag2SO4(s) precipitates) * volume of the solution
3. Calculate the percentage of Ca2+ separated from Ag+:
percentage of Ca2+ separated = (final moles of Ca2+ / initial moles of Ca2+) * 100
By following these steps, you can determine the concentration of Ca2+ when Ag2SO4(s) begins to precipitate and the percentage of Ca2+ that can be separated from Ag+ by selective precipitation.