Rank the following sulfides in order of decreasing solubility: Cu 2 S, ZnS, Ag 2

Question

Rank the following sulfides in order of decreasing solubility: Cu2S, ZnS, Ag2S, CuS. (Use the appropriate <, =, or > symbol to separate substances in the list.

I am not sure if I have to look at the Ksp or the Molar Solubility constant (x) values to compare these.

The correct answer is ZnS > Cu2S > Ag2S > CuS but I am not sure how to get that. Help?

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

We have to compare the molar solubility values for each compound

Cu2S --------> 2Cu+ + S^2-

let solubility of Cu+ and S^2- be s

Ksp of Cu2S = (2s)^2 * s = 4s^3

Ksp of Cu2S = 4s^3

s = cube root ( 1.6 x 10^-48 / 4)

s = 7.37 x 10^-17 M

ZnS ---------> Zn2+ + S^2-

Let solubility of Zn2+ and S^2- be s

Ksp of Zns = s * s = s^2

So,

s = square root ( 1.1 x 10^-21)

s = 3.32 x 10^-11 M

Ag2S ----------> 2Ag+ + S^2-

Let solubility of Ag+ and S^2- be s

Ksp of Ag2S = (2s)^2 * s = 4s^3

s = cube root ( 6.3 x 10^-50 / 4)

s = 2.51 x 10^-17 M

CuS --------> Cu2+ + S^2-

Ksp of CuS = s * s = s^2

s = square root ( Ksp)

s = square root ( 6.3 x 10^-36)

s = 2.51 x 10^-18 M

So, the order of solubility in decreasing order is

ZnS > Cu2S > Ag2S > CuS     where ZnS is most soluble because it's molar solubility is highest and CuS is least soluble because it's molar solubility is lowest

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