Posted by molar solubility on Saturday, July 30, 2011 at 7:44pm.
The 0.15M has a lot to do with it. You have Ag^+ from two sources.
Ag2CO3 ==> 2Ag^+ + CO3^2- AND
AgNO3 ==> Ag^+ + NO3^-
Ksp = (Ag^+)^2(CO3^2-) = 8.1E-12
If you want to go through it rigorously, then Ag^+ from Ag2CO3 is 2x and CO3^2- is x and Ag^+ from AgNO3 (it is soluble and 100% ionized) is 0.15. Substituting we get
(2x+0.15)^2(x) = 8.1E-12.
The easy way to solve this is to recognize that the solubility of Ag2CO3 is small so 2x+0.15 is essentially equal to 0.15. The equation then becomes
(0.15)^2(x)=8.1E-12 and solve for x. That gives you the CO3^2- which ALSO is Ag2CO3.
For your second question, note the formula is Hg2Cl2 and NOT HgCl2.(mercury(I) chloride is a dimer.) so
Hg2Cl2(s) ==> Hg22+ + 2Cl^-
Ksp = (Hg22+)(Cl^-)^2
So Hg22+ = x and Cl^- is 2x. Substituting gives 4s^3
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