Five carbonaceous materials exhibiting catalytic activity for hydrogen sulfide oxidation from moist air were used as H2S removal media from digester gas. The breakthrough capacity was measured at dynamic conditions with various amounts of water present in the system ( either on carbon or in the challenging digester gas). The initial and exhausted materials after the breakthrough tests were characterized using sorption of nitrogen, thermal analysis, XRF, and surface pH measurements. The results obtained demonstrate the complex dependence of the capacity on surface chemistry, porosity ( volume and sizes), and water content. In all cases, elemental sulfur is the predominant product of surface reactions. In the case of materials with potassium present in the ash, preadsorbed water enhances the adsorption capacity, likely contributing to dissociation of hydrogen sulfide, which is further oxidized to sulfur by oxygen chemisorbed on the carbon. When the inorganic phase contains alkaline earth oxides nonreactive with water, the moisture on carbons does not affect the removal process. On the other hand, water in the gas mixture impedes the adsorption capacity via deactivation of catalytic centers, which react with carbonic or sulfurous acids. When reactive adsorption takes place, for the efficient oxidation of hydrogen sulfide, the volume of small size micropores becomes very crucial. They act as microreactors where chemisorbed oxygen has a higher probability to be retained and elemental sulfur has a higher probability to be stored.