Help with chem: solubility?

Question

which compound has the greatest molar solubility in water? why, explain

CdCO3 AgI Cd(OH)2 ZnCO3 CaF2

Answer 1

we look up the two categories of Ksp  's

those with two ions:

CdCO3...  K = 1.8e-14

AgI .....K = 18.3e-17

ZnCO3.... K= 1.0e-10

the largest K comes from the one with the largest solubility , that's ZnCO3

then we look at those with 3 ions:

Cd(OH)2 ... K = 2.5e-14

CaF2 ... K = 3.9 e -11

the largest solubility one of these is CaF2

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when yoiu are used to it , educated guessing works, but we should calculate the solubility instead, whenever there are different amounts of ions in the molecules.  we have narrowed it down to two CaF2 & ZnCO3:

ZnCO3 --> Zn+2  &  (CO3)-2

K = [Zn+2]  [(CO3)-2]

1.0e-10 = K = [x]  [x]

x = 1e-5 Molar Zn+2 is in solution because the same amount of ZnCO3 is soluble

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the multitude of ions gives false impressions of insolubility , because with multiple ions , you get exponents that super inflate the K into smallness

CaF2 --> Ca+2  & 2F-

K = [Ca+2] [F-]^2

3.9e-11 = [x] [2x]^2

4x3 = 3.9e-11

x3 =  9.75e-12

x = 2.1e-4 Molar

CaF2 is your answer

(having to square the {F-} gives its K that false impression of insolubility)