P.G. Kudryavtsev, O.L. Figovsky, Simulation of Hardening Processes, in Silicate Systems, Volume 44, International Letters of Chemistry, Physics and Astronomy (Volume 44) https://www.scipress.com/ILCPA.44.1 Abstract: In this paper we consider the Quasi-homogeneous Approximation to Describe the Properties of Disperse Systems. We have used the statistical polymer method is based on the consideration of averaged structures of all possible macromolecules of the same weight. One has derived equations allowing evaluation of all additive parameters of macromolecules and their systems. The statistical polymer method allows modeling of branched crosslinked macromolecules and their systems in equilibrium or non-equilibrium. The fractal consideration of statistical polymer allows modeling of all kinds of random fractal and other objects studied by fractal theory. The statistical polymer method is applicable not only to polymers but also to composites, gels, associates in polar liquids and other aggregates. In this paper Description of the state of colloidal solutions of silicon oxide from the viewpoint of statistical physics is based on the idea lies in the fact that a colloidal solution of silica - silica sol consists of a very large number of interacting with each other particles that are in continuous motion. It is devoted to the study of an idealized system of colliding, but non-interacting particles of sol. Analysis was conducted of the behavior of silica sol, in terms of Maxwell-Boltzmann distribution and was calculated the mean free path of the colloidal particles. Based on these data, it was calculated the number of particles capable to overcome the potential barrier in a collision. To modeling of the sol-gel transition kinetics had considered various approaches. Keywords: Colloidal Solutions, Crosslink Formation, Fractal Method, Mean Free Path, Quasi-Homogeneous Approximation, Silica Sol, Sol-Gel Transition, Statistical Polymer Method