Sodium sulfate is slowly added to a solution containing 0.0500 M Ca2 (aq) and 0.0370 M Ag (aq). What will be the concentration of Ca2 (aq) when Ag2SO4(s) begins to precipitate?
I looked up the Ksp values. It would have helped if you had since my values in the book I used for Ksp values probably will not agreed with the values in your text. My book is old.
Ag2SO4 ==> 2Ag^+ + SO4^2-
Ksp = (Ag^+)^2(SO4^2-)
Plug in Ag^+ and solve for SO4. I obtained approximately 0.009M
CaSO4 ==> Ca^2+ + SO4^2-
Do the same. SO4^2- = approx 0.001M
You can see that if you have a solution containing those two ion in those concns that the CaSO4 will ppt first since Ksp for CaSO4 will be exceeded first.
CaSO4 will continue to ppt until the (Ca^2+) has been diminished to the point that Ag2SO4 can ppt. When that happens the (SO4^2-) will be 0.009.
Plug 0.009 in the Ksp expression for CaSO4 and calculate (Ca^2+).
To determine the concentration of Ca2+ when Ag2SO4(s) begins to precipitate, you need to consider the solubility product constant (Ksp) of Ag2SO4 and the reaction that occurs when Ag2SO4 precipitates.
First, let's write the equation for the dissociation of Ag2SO4 in water:
Ag2SO4(s) ⇌ 2Ag+(aq) + SO4^2-(aq)
The solubility product expression for Ag2SO4 is:
Ksp = [Ag+]^2 [SO4^2-]
Since the Ag+ concentration is given as 0.0370 M, we can substitute this value into the Ksp expression:
Ksp = (0.0370)^2 [SO4^2-]
Now, let's consider the reaction between Ca2+ and SO4^2-:
Ca2+(aq) + SO4^2-(aq) → CaSO4(s)
The reaction between Ca2+ and SO4^2- will occur until the molar concentration of Ca2+ is equal to the molar concentration of SO4^2- provided by the dissociation of Ag2SO4. This is because both CaSO4 and Ag2SO4 have the same ratio of Ca2+ and SO4^2- ions when they precipitate.
Therefore, the concentration of Ca2+ when Ag2SO4(s) begins to precipitate is equal to the concentration of SO4^2- ions generated from the dissociation of Ag2SO4. We can determine the concentration of SO4^2- using the Ksp expression and the given molar concentration of Ag+:
Ksp = [Ag+]^2 [SO4^2-]
0.0500 M is the concentration of Ca2+, not SO4^2-. So, we need to find the concentration of SO4^2-.
Rearranging the Ksp expression, we have:
[SO4^2-] = Ksp / [Ag+]^2
[SO4^2-] = Ksp / (0.0370)^2
Substituting the given Ksp value and calculating:
[SO4^2-] = (Ksp) / (0.0370)^2
Finally, since the concentration of Ca2+ will be equal to the concentration of SO4^2- when Ag2SO4 begins to precipitate, the concentration of Ca2+ is also:
Concentration of Ca2+ = [SO4^2-]
Substitute the calculated value of [SO4^2-] into the concentration of Ca2+ equation to find the answer.