Sodium sulfate is slowly added to a solution containing 0.0500 M Ca2 (aq) and 0.0210 M Ag (aq). What will be the concentration of Ca2 (aq) when Ag2SO4(s) begins to precipitate?

Ksp=1.20×10^–5 silver sulfate
ksp=4.93x 10 ^-5 calcium sulfate

1 answer

Ksp Ag2SO4 = 1.2E-5 = (Ag^+)^2(SO4^2-)
Ksp CaSO4 = 4.93E-5 = (Ca^2+)(SO4^2-)

So CaSO4 ppts first. How do you know that. Calculate the (SO4^2-) when each bgins to ppt.
Ag2SO4. (SO4^2-) = Ksp/(Ag^+)^2
(SO4^2-) = you do it. I get approx 2.7E-2M
CaSO4. (SO4^2-) = Ksp/(Ca^2+) = you do it but I have approx 1E-3. So if you are adding Na2SO4 slowly to the mix, the 1E-3 level will be reached before the 3E-2.

Visualize what is happening. Na2SO4 is being added slowly to a mix of Ag^+ and Ca^2+. As soon as the Ksp for CaSO4 is exceeded it starts to ppt and it will continue to ppt until (even after) the Ksp for Ag2SO4 is exceeded. When will that be. With a (Ag^+) = 0.021, Ksp will be exceeded when SO4^2- = that 2.7E-2 we calculated above. So slip 2.7E-2 (that's an aprox remember so go through the work to get a good number). Then calculate (Ca^2+).