A solution containing a mixture of metal cations was treated with dilute HCl and a precipitate formed. The solution was filtered, and H2S was bubbled through the acidic solution. A precipitate again formed and was filtered off. Then, the pH was raised to about 8 and H2S was again bubbled through the solution. This time, no precipitate formed. Finally, the solution was treated with a sodium carbonate solution, which resulted in the formation of a precipitate.
Classify the metal ions based on whether they were definitely present, definitely absent, or whether it was possible they were present in the original mixture.

Cd²⁺, Sb³⁺, Hg²⁺, Pb²⁺, Ba²⁺, Zn²⁺, Fe²⁺, Cr³⁺, Sn⁴⁺, Li⁺, Mg²⁺, Hg₂²⁺, Ag⁺