The reaction between adsorbed CO molecules and O atoms on epitaxially grown RuO2(110) was investigated by scanning tunneling microscopy. Two types of titration experiments were performed at 300 K, in which either CO was dosed on the stoichiometric oxide surface, or O-2 on the CO saturated surface. In both cases, reaction steps could be atomically resolved, and the surface mobility of adsorbed CO molecules and O atoms could be studied. CO molecules adsorbing on the stoichiometric surface react with bridge bonded O atoms at largely random positions. O-2 molecules adsorbing on the CO saturated surface react with cus-bonded CO molecules first at CO vacancies, and then also in a mainly random fashion. The statistical nature of the reaction is explained by the relatively high surface diffusion barriers, which are of the same size as the activation energies for the reactions.