The novel competitive complexation/solvation theory of solvent extraction is modified for description of metal extraction by acidic extractants. According to the theory, the molecules of an extracting mixture compete for metal ion by the extent of their affinity for association and concentration. The metal is partitioned among the solvent components (extractant, diluent, water, adduct). As a consequence, a given measured property in mixed solvents can be calculated from its values measured in pure solvent components. The theory establishes a relationship between complexation and solvation. Four possible stages of extraction behavior and interacting mechanisms, depending on the extracting metal ion-solvent affinity constant ratios, metal ion concentration, and acidity of the aqueous solution are discussed. Extractants are considered amphoteric and may behave as acids (electron acceptors) or bases (electron donors) depending on the structure of their functional groups and composition of the organic phase and on the structure of the composition in the aqueous phase. Acidic extractant interacts as a conjugate acid with metal ions dissolved in water and coordinated by water molecules (hydrated). The same acidic extractant behaves as a conjugate base to metal ions dissolved in strong acid and coordinated by acid molecules (solvated). The theory introduces an active solvent (including water) and temperature as quantitative parameters. Mathematical descriptions and experimental techniques are developed and verified. A good agreement was obtained when the experimental and theoretically calculated data were compared for some metal extraction systems. The theory overcomes some limitations of the stoichiometric ion-exchange models. It presents novel theoretical insights, explains some problems in a clear-cut manner, which required ad hoc arguments using classical theories. But the main advantage of the presented approach lies in the mathematical description that provides a key for quantitative analysis and preliminary prediction of suitable extraction systems for different metals' separation.