The active site of CO dissociation on a cobalt nanoparticle, relevant to the Fischer-Tropsch reaction, can be computed directly using density functional theory. We investigate how the activation barrier for direct CO dissociation depends on CO coverage for step-edge and terrace cobalt sites. Whereas on terrace sites increasing coverage results in a substantial increase of the direct CO dissociation barrier, we find that this barrier is nearly independent of CO coverage for the step-edge sites on corrugated surfaces. A detailed electronic analysis shows that this difference is due to the flexibility of the adsorbed layer, minimizing Pauli repulsion during the carbon-oxygen bond dissociation reaction on the step-edge site. We constructed a simple first-principles microkinetic model that not only reproduces experimentally observed rates but also shows how migration of carbon species between step-edge and terrace sites contributes to methane formation.