Sodium sulfate is slowly added to a solution containing 0.0500 M Ca2 (aq) and 0.0290 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?
Do you have the corresponding Ksp values?
Ag2SO4 will begin to ppt when
Ksp = (Ag^+)^2(SO4^2-) is exceeded.
(SO4^2-) = Ksp/(Ag^+)^2
(SO4^2-) = Ksp/(0.290)^2
Solve for SO4^2- and substitute into Ksp for CaSO4. Solve for Ca^2+
To determine the concentration of Ca2+ when Ag2SO4(s) begins to precipitate, we need to find the solubility product constant (Ksp) of Ag2SO4 and compare it to the ion concentrations present in the solution.
First, let's write the balanced chemical equation for the precipitation reaction:
Ag2SO4 (s) ⇌ 2 Ag+ (aq) + SO4^2- (aq)
The Ksp expression for Ag2SO4 is:
Ksp = [Ag+]²[SO4^2-]
We know the concentration of Ag+ in the solution is 0.0290 M, so we can substitute it into the Ksp expression:
Ksp = (0.0290 M)²[SO4^2-]
Now, let's determine the molar solubility of Ag2SO4 (s) by assuming x M of Ag2SO4 dissolves in the solution:
Ksp = (0.0290 M + 2x)²(SO4^2-)
Since Ag2SO4 is a 1:1 electrolyte, the concentration of SO4^2- is also equal to 0.0290 M + 2x.
Next, calculate the concentration of Ca2+ when Ag2SO4(s) begins to precipitate. This occurs when the concentration of Ag+ matches the solubility product constant (Ksp) for Ag2SO4. So, set the concentration of Ag+ to its limiting value:
0.0290 M + 2x = Ksp
Now, plug in the calculated value for Ksp:
0.0290 M + 2x = (0.0290 M + 2x)²(0.0290 M + 2x)
Solve this equation to find the value of x, which represents the molar solubility of Ag2SO4 in the solution.
Once you have the value of x, you can calculate the concentration of Ca2+ when Ag2SO4(s) begins to precipitate. Since Ca2+ does not participate in the precipitation reaction, its concentration will remain the same at 0.0500 M.
To find the percentage of Ca2+(aq) that can be separated from Ag+(aq) by selective precipitation, we need to compare the solubility product constants (Ksp) of the respective precipitates.
For CaSO4, the Ksp expression is:
Ksp(CaSO4) = [Ca2+][SO4^2-]
We know the concentration of Ca2+ is 0.0500 M, so we can substitute it into the Ksp expression:
Ksp(CaSO4) = (0.0500 M)(0.0290 M + 2x)
Now, we can compare the two Ksp expressions for Ag2SO4 and CaSO4. Since the precipitate with the lower Ksp value will form first, we can determine the percentage of Ca2+(aq) that can be separated from Ag+(aq) by selective precipitation.
By comparing the Ksp expressions for Ag2SO4 and CaSO4, you can determine which precipitate will form first and calculate the percentage of Ca2+ that can be separated from Ag+.
Please note that the calculations involved may be complex and require numerical iterations to solve the equations accurately.
CaSO4 Ksp= 4.93E^-5
Ag2SO4 Ksp= 1.20E^-5