The present paper presents a multiscale (DFT to mean-field) modeling approach for describing barium sulfate formation through the adsorption of sulfur oxides on BaO. Sulfur oxide emissions, a major environmental concern, also represent one of the technological issues for a large-scale implementation of alkaline-earth oxides as NOx abatement techniques for vehicle exhaust depollution. SOx adsorption was studied at the atomic level on various BaO sites (terraces, surface defects, and bulk) for a closer description of a real storage material. Ab initio data were used to conceive a kinetic model for SOx adsorption that allows us to follow species adsorption and desorption dynamics. Our results confirm that sulfur oxides interact strongly with the NOx trapping material to form thermodynamically favored sulfate species, consequently leading to the blockage of NOx sorption sites and altering the storage properties.