Discuss the presence of cations belonging to groups

Question

1). An aqueous solution was tested for the presence of cations belonging to Groups I-V. The first group reagent was added to 1 mLof the aqueous solution and any precipitate was separated from the supernatant liquid. The second group reagent was added to the supernatant liquid and any precipitate was separated, etc. In thisway, the four group reagents were sequentially added to the supernatant liquid obtained from the previous separation step. The experimental results are:

1. dilute HCL ---> precipitated
2. H2S in 0.3 M HCl ---> no precipitate
3. H2S in NH3/NH4Cl ---> no precipitate
4. (NH4)2CO3 in NH3/NH4Cl ---> precipitate

Cations from which groups are or maybe present in this solution?Explain.

2. To prove the statement, PbCl2 is more soluble than AgCl and Hg2Cl2 calculate the molar solubilities of AgCl, Hg2Cl2, and PbCl2in pure water.
Equilibria are:

AgCl (s) <--> Ag⁺ (aq) + Cl^- (aq)     Ksp = 1.8 x 10^^-10
Hg2Cl2(s) <--> Hg2 ⁺² (aq) + 2 Cl^- (aq)    Ksp = 1.2 x 10^^-18
PbCl2 (s)<--> Pb ⁺²(aq) + 2Cl^-(aq)          Ksp =1.7 x 10^^-5