Application of solubility product and common ion effect

Qualitative analysis of cations is largely based on the principle of solubility product and common ion effect. Cations are separated in to six groups depending on the solubility of their salts.
Group-1 as insoluble chlorides
Only Ag⁺, Hg²⁺ and Pb²⁺ form insoluble chlorides since they have low values of K_sp.
Group-2 as insoluble sulphide in acidic medium
H₂S <========> H⁺ + HS^- ;
K₁ - first ionization constant
HS^- <========> H⁺ + S^2-;
K₂ – second ionization constant
[S^2-] = K₁K₂ [H₂S]/[H⁺]²
K_sp values of second group sulphides (PbS, CuS, SnS, HgS, As₂S₃, Bi₂S₃, Sb₂S₃) are very low. In acidic buffer, [S^2-] is decreased due to common ion effect and this results in the precipitation of Pb²⁺, Cu²⁺ etc of second group as their sulphides. Third and fourth group sulphides have high value of K_sp, hence they remain soluble.
Group- 3 as insoluble hydroxide in basic buffer of NH₄OH and NH₄Cl
The concentration of OH^- in ammoniacal solution decreases when NH₄Cl is added to it, because of the common ion effect. Thus only for least soluble hydroxide of Fe³⁺, Al³⁺, Cr³⁺ etc. ionic product exceeds the corresponding solubility products, hence only these ions are precipitated. Hydroxides of successive remain soluble due to high K_sp values.