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The nature of the interaction of electrolyte anions with the anode surface during the electrochemical dissolution of metals is an important problem. In many cases, complex ions of dissolving metal with anions of electrolyte form the primary product, which is involved in the elementary act of ionization of metal atoms. The anodic dissolution of tungsten, molybdenum, rhenium and other refractory metals in the alkaline solutions proceeds according this mechanism. It forms the basis for electrochemical polishing and electrochemical machining of metals, electrochemical sharpening of a wire for fabrication of scanning probe microscope tips and tools for electrochemical micro/nanomachining. In [1, 2] the rate of mass transfer in the anodic dissolution of metal with the formation of stable cationic and anionic complexes were calculated within the approximation of Nernst diffusion layer. In these works, the conditions for the absence of the limiting current associated with slow delivery of solution anions were determined, and approximate analytical equations for the limiting current were obtained. These equations give a semi-quantitative estimate of the mass transfer rate, because they ignore the presence of ions of other types in the solution and do not take into account the presence of several diffusion layers, which are associated with different diffusion coefficients of ions. This work is devoted to the theoretical analysis of mass transfer during anodic dissolution of metal with the formation of a stable complex with the anion of solution without using the approximation of Nernst diffusion layer and taking into account the presence of background electrolyte. The Nernst-Planck equations and the electroneutrality condition, which take into account the electro-diffusive and convective transfer of ions, are used as the mathematical model. The numerical solution is performed using the finite element method. The results of modeling anodic dissolution of rotating disk electrode with the formation of stable cationic and anionic complexes are presented. The dependences of the limiting current on the composition and concentration of solution and the transport properties of ions are obtained.