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Spin-polarized density functional theory calculations have been performed to investigate the mechanisms for C_xH_y formation on Fe₃C(100). It is found that H-assisted CO dissociation (CO + H → CHO; CHO → CH + O) has lower barrier than CO direct dissociation (CO → C + O), but surface C_s atom hydrogenation to form surface C_sH is the most favored pathway. As the first C₂ surface species, surface ketenylidene C_sCO rising from CO adsorption is an important intermediate for C₂H_x formation. Initial surface C₂H_x forms from C_sCO hydrogenation instead of direct dissociation. The formation of C_sCH, C_sHCH and C_sH₂CH has close effective barriers and depends on the CO/H₂ ratio. In addition, surface vacancy can activate CO strongly and lower the CO dissociation barrier considerably, and this regenerates the carburized active surface and closes a catalytic cycle.