The paper deals with a special interacting particle system on a finite set. This system models in particular the process of adsorption-desorption of ions on the surface of an electrode, assumed to be a lattice. The model was proposed in [6],[7] for the study of the dynamics of the process, especially the phenomenon known in chemistry as the underpotcntial deposition. In the model considered, a vacant site of a lattice becomes occupied (adsorption) at a constant rate and conversely an occupied site becomes vacant (desorption) at a rate which depends on the current configuration of occupied and vacant sites. The latter expresses the effect of interactions between adsorbed ions. The paper studies the dynamics of some characteristics of the process important in applications, namely, the coverage of the lattice by occupied sites and the formation of clusters. Continuing the research originated in [2], a sufficient condition for the mathematical expectation of the coverage to be a, concave function in time is established. This condition appears to be identical to a classical sufficient condition of crgodicity of the same process on an infinite lattice. Also the expression For the mean length of the border of clusters is derived. Special attention is paid to the dependence of the behavior of the process on the geometry of the underlying lattice.