In the present work, we study the structures and molecular geometries of $CH_{4}$, $SO_{2}$ and $O_{2}$ adsorbed on $Cr_{2}O_{3}(0001)$. Using computational calculations based on the density functional theory (DFT), we analyze the most suitable sites to carry out the adsorption of each of the molecules mentioned, and the influence of each species on the adsorption and dissociation of the others. The results allow us to understand the activation of the $Cr_{2}O_{3}(0001)$ surface, which leads to the presence of $SO_{2}$ during the oxidation of $CH_{4}$, as was experimentally verified.