The availability of polymetallic ores is getting leaner in grade and is larger but inferior in volumes than in the past, making the extraction of copper, nickel and other non-ferrous metals metallurgically more difficult to produce. The standard technologies, including enrichment and concentration, do not provide methods for obtaining monometallic concentrates and high extraction of metals into the commercial product. Pyrometallurgical processing of large volumes of poor raw materials is not economical and is complicated from the technological point of view. Conditions of chemical enrichment of poor natural materials have been studied with the use of technology of salt exchange leaching. The main impurity in sulfide ores of nonferrous metals is iron present in the forms of pyrite and pyrrhotite and the properties of chemical enrichment for nickel in pyrite concentrates has been investigated in this work. On the basis of thermodynamic analysis carried out with the use of Potential-pH Pourbaix’s Diagrams, it has been established that, with the use of nickel salt, it is possible to leach iron sulfides from ores. Based on the study of the mechanism and kinetics of the process of dissolution of iron sulfides with nickel salts, it was established that during the dissolution, the chemical composition and thermodynamic characteristics of the dissolved iron sulfides change—the residues from leaching are enriched with iron sulfides that are rich in sulfur and also result with elemental sulfur formation. Enrichment of leaching residues with sulfide iron with increased sulfur content and formation on the surface of nickel sulfide leads to increase of diffusional resistances and the process is limited by the velocity of mass transfer. To increase the velocity of the process and completeness of the reaction, it is necessary to activate the process, in particular, by grinding the solid phase.