Ksp Question?

Question

A solution is 0.10 M AgNO3 and 0.10 M Ba(NO3)2. If solid Na2SO4 is added to the solution, what is [Ba2+] when Ag2SO4 begins to precipitate? (Ksp BaSO4 = 1.1 x 10^-10, Ag2SO4 = 1.1 x 10^-5)

The answer is: 1.0 x 10^-7 but I don't know how they got that. Please show how you would find that answer. Thanks!! :)

Answer 1

If you follow the process in "slow motion" the BaSO4 starts precipitating out first. Ag2SO4 will start ppt. out when
[Ag+]2 [SO4=] = 1.1x10-5.
At that point, Ag+ is still 0.1 M. Then, at that point, [SO4=] = 1.1x10-3 M. Since the Ba+2 level is limited by the Ksp, at this SO4= conc, Ba+2 = 1x10-7.