SBA-2 and STAC-1 are periodic mesoporous silicas with slightly different structures whose pore networks consist of spherical cavities interconnected by windows. This feature makes them attractive for adsorptive separation processes where the selectivity originates from molecular sieving. Recently, we were able to obtain realistic atomistic models for these materials by means of a kinetic Monte Carlo (kMC) method. In this paper, we evaluate the ability of the model to predict adsorption of both nonpolar (methane and ethane) and polar (carbon dioxide) adsorptives. Predictions are in good agreement with experimental data, demonstrating the potential of these kMC-based models for use in the design of adsorption processes and the materials used in them. In particular, we show that surface roughness is a key feature for predicting adsorption in SBA-2 materials at low pressures; this is especially relevant in prospective applications such as carbon dioxide capture.