What [I ? ] is needed to start precipitation of AgI from a saturated solution of

Question

What [I ? ] is needed to start precipitation of AgI from a saturated solution of AgCl? (See the appendix.)
M

Substance Ksp at 25 oC Aluminum Al(OH)3 1.9 x 10-33 Barium Ba(OH)2 5.0 x 10-3 BaCO3 8.1 x 10-9 BaSO4 1.1 x 10-10 Ba3(PO4)2 3.4 x 10-23 Cadmium Cd(OH)2 2.5 x 10-14 CdCO3 5.2 x 10-12 CdS 8.0 x 10-27 Calcium Ca(OH)2 5.5 x 10-6 CaCO3 4.8 x 10-9 Ca3(PO4)2 1.0 x 10-26 CaF2 3.9 x 10-11 Chromium Cr(OH)3 6.3 x 10-31 Cobalt Co(OH)2 1.6 x 10-15 CoS 4.0 x 10-21 Copper Cu(OH)2 2.2 x 10-20 Cu2S 1.6 x 10-48 CuCO3 1.4 x 10-10 CuS 6.3 x 10-36 Iron Fe(OH)2 8.0 x 10-16 FeS 6.3 x 10-18 Fe(OH)3 2.5 x 10-39 FePO4 9.9 x 10-29 Lead Pb(OH)2 2.8 x 10-16 PbF2 3.7 x 10-8 PbCl2 1.7 x 10-5 PbBr2 6.3 x 10-6 PbI2 6.5 x 10-9 PbCrO4 1.8 x 10-14 PbSO4 1.7 x 10-8 PbS 8.4 x 10-28 Magnesium Mg(OH)2 1.8 x 10-11 Manganese Mn(OH)2 1.9 x 10-13 MnCO3 8.8 x 10-11 MnS 5.6 x 10-16 Nickel Ni(OH)2 1.6 x 10-14 Silver AgCl 1.8 x 10-10 AgBr 5.0 x 10-13 AgI 8.3 x 10-17 AgCN 1.2 x 10-16 Ag2S 6.3 x 10-50 Ag2CrO4 1.1 x 10-12 Ag3PO4 2.6 x 10-18 Tin Sn(OH)2 1.4 x 10-28 SnS 1.3 x 10-23 Zinc ZnCO3 1.0 x 10-10 Zn(OH)2 4.5 x 10-17 ZnS 1.1 x 10-21

Explanation / Answer

Given Ksp for AgCl = 1.8x10-10

For a saturated solution of AgCl, ionic product must be equal to the solubility product(Ksp)

Hence for AgCl,  ionic product = solubility product(Ksp)

=> [Ag+]x[Cl-] = 1.8x10-10

For AgCl,  [Ag+] = [Cl-]

=>  [Ag+]x[Cl-] = [Ag+]2 = 1.8x10-10

=> [Ag+] = square root(1.8x10-10 ) = 1.34x10-5 M

Ksp for AgI = 8.3x10-17

Now for the precipitation of AgI, the ionic product of Ag+  and I- must be greater than solubility product(Ksp) of AgI

=>  [Ag+]x[I-] > 8.3x10-17

For AgI,  [Ag+] = [I-]

=>  [Ag+]x[I-] = [I-]2 >  8.3x10-17

=> [I-] > square root(8.3x10-17 ) = 9.1x10-9 M

Hence the minimum concentration required to start the precipitation of AgI is  9.1x10-9 M

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