Arrange the following salts in order of increasing molar solubility in 0.0010 M

Question

Arrange the following salts in order of increasing molar solubility in 0.0010 M AgNO3

A.) Ag2CO3

B.) AgI

C.) Ag2S

D.) AgCl

E.) AgBr

I know the answer is C<B<E<D<A, but I'm not sure as to why. I know the common ion effect plays a role in that my intial concentration of silver will be = 0.0010 in my ICE tables. Is there a quicker way to look at a problem like this and understand which is more soluble without making ICE tables for each salt? Also, the Ksp values are in a table in my book but not included in the question.

Explanation / Answer

For solubility comparisson:

AgCl, AgBr; AgI ---- > AB <-> A+ + B-; Ksp = [A+][B-] = (0.001)*S

Ag2CO3; Ag2S ---> A2B <--> 2A+ + B-2 Ksp = [(0.001^2)[B-2] = 0.000001* S

Compare S:

AgCl --> S= (1.77*10^-10)/(0.001) = 1.77*10^-7

AgBr --> S= (5.35*10^-13)/(0.001) = 5.35*10^-10

AgI --> S = (8.52*10^-17)/(0.001) = 8.52*10^-14

Ag2CO3 --> S= (8.46*10^-12)/(0.000001) = 8.46*10^-6

Ag2S --> S= (3.3*10^-50)/(0.000001) = 3.3*10^-44

clearly:

Ag2CO3 > AgCl > AgBr > AgI> Ag2S

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