The systematic scheme exploits differences in solubility products (Ksp) of cation salts:

Group 0: NH4+ detected first by heating with NaOH → NH3 gas (smell, turns moist red litmus blue).

Group I (HCl group): Add dilute HCl. Only Pb2+, Ag+, $Hg2^{2+}$ form insoluble chlorides. PbCl2 dissolves in hot water (unlike AgCl, Hg2Cl2).

Group II (H2S in acid): Pass H2S through acidic solution (low S2- concentration). Only very insoluble sulfides precipitate: CuS, PbS, CdS, HgS, As2S3, Sb2S3, SnS. Divided into IIA (insoluble in yellow ammonium sulfide) and IIB (soluble — Arsenic subgroup).

Group III (NH4OH group): Add NH4Cl + NH4OH. Precipitates Fe(OH)3 (brown), Al(OH)3 (white gelatinous), Cr(OH)3 (green). NH4Cl is essential — without it, Mg(OH)2 would also precipitate (common ion effect controls OH- concentration).

Group IV (H2S in base): Pass H2S through basic solution (high S2- concentration). Precipitates: CoS (black), NiS (black), MnS $\frac{pink}{flesh}$, ZnS (white).

Group V ((NH4)2CO3): Add ammonium carbonate. Precipitates: BaCO3, SrCO3, CaCO3 (all white). Distinguished by flame test: Ba (apple green), Sr (crimson red), Ca (brick red).

Group VI: Remaining ions (Mg2+, Na+, K+) detected individually. Mg: magneson reagent (blue lake). Na: yellow flame. K: violet flame (through cobalt blue glass).