Question

Not every job at your secret government agency is glorious – especially for a grunt like yourself. But hey, at least you get paid. By analyzing the molar solubilities of the following K_sps, rank them in order of least soluble to most soluble:

Compound:         K_sp:

Cu(OH)₂                  2.2 x 10^-19

AlPO₄                       9.8 x 10^-21

CoS                            4 x 10^-21

Ba₃(PO4)₂              3 x 10^-22

Answer 1

Cu(OH)2(s) <--> Cu2+ (aq) + 2OH- (aq)

Ksp = S(2S)^2 = 4S^3 = 2.2 x 10^-19 ,

S = 3.8 x 10^-7 M

AlPO4 (s) <---> Al3+ (aq) + PO4^3- (aq)

Ksp = S^2 = 9.8 x 10^-21 ,

S = solubility = 9.9 x 10^-11 M

CoS (s) <---> Co2+ (aq) + S^2- (aq)

Ksp = S^2 = 4 x 10^-21. ,

S = 6.3 x 10^-11

Ba3(PO4)2 (s) <---> 3Ba2+ (aq) + 2 PO4^3- (aq)

Ksp = [Ba2+]^3 [PO43-]^2 = (3S) ^3 ( 2S)^2 = 108S^5 = 3 x 10^-22

S = 1.94 x 10^-5 M

Now based on solubilities order from least to most is

CoS < ALPO4 < Cu(OH)2 < Ba3(PO4)2