Two improvements of the adsorption theory are offered. The first improvement expands the area of applicability of a lattice-gas model for description of adsorption of symmetric particles on amorphous surfaces. The second improvement raises the accuracy of determination of a microporous system volume. A new approach to calculating the equilibrium characteristics of the adsorption of spherically symmetric molecules on heterogeneous surfaces of adsorbents was developed. The new method was applied to adsorption of Ar atoms on an amorphous TiO2 (rutile) surface. On amorphous surfaces, adsorption centers are located chaotically and the distances between neighboring local minima of potential energy vary over a wide range. At adsorption of inert gases on amorphous surfaces, situations are possible where there is blocking by adspecies of several nearest adsorption centers. Therefore in general, the problem of the calculation of adspecies adsorption on amorphous surfaces represents a problem of adsorption of multisite particles on heterogeneous surfaces. Intermolecular adsorbate-adsorbate interactions are taken into account for nearest atoms in a quasichemical approximation. The energies of the lattice parameters of the all interactions of model are defined from the Lennard-Jones potential (12-6). The offered method gives a satisfactory quantitative description of the isosteric heat of adsorption and isotherm of adsorption in the submonolayer region. It is shown that the standard procedure of an estimation of micropore volume with help from the Dubinin-Radushkevich equation results in overestimated sizes. It follows that the filling of micropore volume occurs at pressures considerably smaller than vapor saturated pressure. The last fact is caused by joint influence of potentials of the adsorbate-wall and adsorbate-adsorbate. A more exact finding of mircopore volume with estimation of the pressure of filling of the micropore volume is suggested.