A metals finishing facility needs to treat spent plating baths that contain high
ID: 982701 • Letter: A
Question
A metals finishing facility needs to treat spent plating baths that contain high concentrations of nickel and chromium. Engineers at the facility have installed a precipitation system that uses a pH meter to control the feed of hydroxide solution to the mixing tank. They set the controller to a pH of 10. What concentrations of Ni^2+ and Cr^3+will remain in solution at this pH? Give your answer calculations. Will the effiluent stream (the water after the precipitated solids are removed) meet the EPA monthly average concentration guidelines for nickel and chromium of 2.38 and 1.71 mg/L, respectively? Answer yes or no, but support your answer with calculations.Explanation / Answer
(a) Given pH = 10
=> pOH = 14 - pH = 14 - 10 = 4
=> pOH = - log[OH-] = 4
=> [OH-] = 10-4 M
For the dissociation of Ni(OH)2(s), let 'S1' be the solubility
--------------------Ni(OH)2(s) + H2O ---- > Ni2+(aq) + 2OH-, Ksp = 2.0x10-15
Conc.at eqm: Na--------------Na----------- S1 --------- 2S1
Ksp = 2.0x10-15 = [Ni2+(aq)] x [OH-]2
=> 2.0x10-15 = S1 x (2S1)2 = 4(S1)2
=> S1 = 2.236x10-8 M (or mol/L)
Hence concentration of Ni2+ , [Ni2+(aq)] = S1 = 2.236x10-8 mol/L or 2.24x10-8 mol/L (answer)
For the dissociation of Cr(OH)3(s), let 'S2' be the solubility
--------------------Cr(OH)3(s) + H2O ---- > Cr3+(aq) + 3OH-, Ksp = 6.3x10-31
Conc.at eqm: Na--------------Na----------- S2 --------- 3S2
Ksp = 6.3x10-31 = [Cr3+(aq)] x [OH-]3
=> 6.3x10-31 = S2 x (3S2)2 = 9(S2)2
=> S2 = 2.646x10-16 M (or mol/L)
Hence concentration of Cr3+ , [Cr3+(aq)] = S2 = 2.646x10-16 mol/L or 2.65x10-16 mol/L (answer)
(b) concentration of Ni2+ , [Ni2+(aq)] = S1 = 2.236x10-8 mol/L
molecular mass of Ni = 58.7 g.mol-1 = 58700 mg.mol-1
=> [Ni2+(aq)] = 2.236x10-8 mol/L = 2.236x10-8 mol x(58700 mg.mol-1)/L = 1.31x10-3 mg/L
concentration of Cr3+ , [Cr3+(aq)] = S2 = 2.646x10-16 mol/L
molecular mass of Cr = 52.0 g.mol-1 = 52000 mg.mol-1
=> [Ni2+(aq)] = 2.646x10-16 mol/L = 2.646x10-16 mol x(52000 mg.mol-1)/L = 1.38x10-11 mg/L
Hence the concetration of Ni2+ and Cr3+ after precipitation is respectively 1.31x10-3 mg/L and 1.38x10-11 mg/L.
These are less than the EPA monthly average concentration of 2.38 and 1.71 mg/L. Hence the answer should be Yes.