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In modeling the regions of precipitation and formation of thin films, we used four conditions: 1. The rule of solubility product; 2. The rule of molecular solubility; 3. The rule of solubility by intermediate; 4. Condition of precipitate of priority. This technique was used to build mathematical models of equilibriums from the pH of solution, concentration of reactants, and temperature. Mathematical models were also developed on the basis of experimental data obtained by potentiometry, residual concentration, thermogravimetry, etc. This model considers fluctuations of the pH of solution and predicts the chemical composition of compounds. It has been demonstrated that in synthesizing target compounds, the possibility of processes of fluctuations must be taken into account. A systemic mathematical model has been designed to optimize the synthesis of thin films and target compounds.

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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.