Quantum chemical calculations employing density functional theory were performed to investigate the interactions of C2Hx(ads) species on Pt-10 clusters and on Pt(111) and Pt(211) slabs. We calculate the binding energies of experimentally observed surface species, such as di-a-bonded ethylene, ethylidyne species, and di-sigma/pi vinylidene species. In addition, we calculate the binding energies of the other species, such as ethyl, ethylidene, and vinyl species, that are postulated to be reactive intermediates in surface reactions. Furthermore, we calculate the activation energies for C-C bond dissociation of various C2Hx(ads) species. We show that the bonding energies are dependent on the geometry of the surface, leading to the observed structure sensitivity of ethane hydrogenolysis. We show that the underlying parameter for understanding the stronger binding of various species on the step edge of Pt(211) compared to Pt(111) is the position of the metal d-band center. With estimates from these DFT calculations of the potential energy surface involved in the formation and reactivity of various C2Hx(ads) species on Pt, we show that the primary reaction pathways for ethane hydrogenolysis on platinum involve highly hydrogenated species, such as C2H5(ads).