What is the basis for classifications of cations into various groups in qualitative analysis

The qualitative analysis the cations are classified into different groups they are
(NH4+) ammonium ion ------------- Zero Group
(Pb+2) Lead ions --------------------  First group
(Pb+2, Cu+2, Hg+2, As+3) --------- Second group
(Al+3, Fe+3) -------------------------- Third group
(Ni+2,Zn+2, Co+3, Mn+2) --------- Fourth group
( Ca+2, Sr+2, Ba+2) ----------------- Fifth group
( Na+, K+, Mg+2 )-------------------- Sixth group
The basis of classification of these elements in various groups is 

 

For precipitation the most important condition is  

 

 For first group the group reagent is Dilute HCl. When the acid is added to the O.S. (Original Solution) the acid dissociates into

under highly acidic conditions (HCl being strong electrolyte more H+ ions are available in the solution) Pb+2 ions get precipitated as chlorides thus white ppt's of PbCl2 are formed.

For second group the group reagent is Dil. HCl + H2S gas . H2S is a weak electrolyte thus the dissociation is

 According to Le Chatelier's principle or common ion effect the dissociation of H2S is suppressed as equilibrium shifts towards backward direction in reaction

Thus under low sulphide ion concentration and not very strong acidic medium ion of Pb+2, Cu+2, Hg+2, As+3 are precipitated as sulphides

This logic can be extended to all the groups as per their group reagent(s)