Silver sols that contain mainly small silver nanoparticles (up to 10 nm) have been synthesized by a method of electrolysis using silver electrodes under conditions of altered current polarity in the sodium polyacrylate (NaPA) solutions. It is shown that the values of the current of the anode dissolution of silver increase with increasing of NaPA concentration and the dependence of іanode—E is linear. Its proposed multistage scheme of formation stabilized by polyacrylate anion (PA−) silver nanoparticles that includes (1) ionization of silver and the complexation of produced Ag+ ions with polyacrylate, (2) cathode reduction of silver ions from the complex, (3) formation of PA− stabilized nanoclusters, and (4) aggregation of nanoclusters and formation of nanoparticles is proposed. Using UV-vis spectroscopy, observable rate constants of the nucleation and the growth of silver nanoparticles depending on temperature and sodium polyacrylate concentration have been estimated. It was found that the formation of silver nanoparticles is carried out in electrode space and is limited by diffusion. The correlations of the size of silver nanoparticles with observable rates of the nucleation and growth were shown. Graphical abstract"."