The results of a study of the dynamics of the excitation angle of a surface electromagnetic wave (SEW) at the interface between a silver/NaCl aqueous solution of concentrations 10−3, 10−4, 10−6 and 10−10 M are presented. It is shown that the rate of change in the excitation angle of SEW is proportional to the concentration of the solution up to a dilution of 10−10 M. The observed effect is explained by the formation of silver chloride on the surface of the silver film as a result of the interaction of solution ions with nanoscale clusters of the silver film. The proposed technique for measuring the dynamics of the excitation angle of SEW can be used for a comparative analysis of the concentrations of highly dilute solutions, as well as for studying the formation and dynamics of transition layers and physicochemical processes in the near-surface regions.