The versatility of carbon nanostructures makes them attractive as possible catalytic materias, as they can be synthesized in various shapes and chemically modified by doping, functionalization, and the creation of defects in the nanostructure. In this work we report results of Density Functional Theory calculations on the growth of armchair and zigzag graphene edges on a carbon monoxide atmosphere, in the absence of metallic precursors. Using Statistical Mechanics, we consider the conditions at which the conversion of CO to graphene and carbon dioxide is favorable, both in the presence and in the absence of hydrogen. These results are a first step toward developing processes aimed at carbon sequestration and selective oxydation of CO in the presence of hydrogen.