In this paper, we have presented experimental data and the theoretical basis for the extraction of silver ions from aqueous solutions, using metal sulfides (PbS, ZnS, MnS, CuS, FeS) in the form of thin films, nanocrystals in gel matrices, and precipitates. A mathematical model, taking into account the sorption of Ag(I) due to a three-stage ion exchange in the occurence of solid-liquid phase contact, containing complexing entities (Na 2 S 2 O 3 , N 2 H 4 CS, N 3 H 5 CS, NH 3 , EDTA, TEA). This model was applied in the technology of equipment design.