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The model that describes the interaction of hydrated ions in uni-univalent electrolytes at various concentrations and temperatures was proposed. We show that, based on fundamental laws of physics, such as the Coulomb law and the Boltzmann distribution, using well-known published data, it is possible to calculate main physical factors that determine the interaction of ions in the solution, for example, the distribution of electric field and the change of hydrated shells of ions when they approach. On this basis, it is possible to explain the nonmonotonic character of curves that describe the activity coefficients and calculate the coefficients in the range of concentration from zero to several mol/l and the range of temperature from zero to several tens degrees, using minimal experimental information. For example, for the calculation of the activity coefficients of an electrolyte in the whole range of concentrations and temperature, it suffices to know the values of the coefficient only for one concentration at three temperature points. The limits of applicability and consistency of the model were analyzed. The conditions under which ions of distinct sign occupy a stable position relative to each other, i.e., the electrolyte is in the quasi-crystalline state were clarified. The approach proposed is verified by comparing simulation results with a considerable amount of published data.