A grandcanonical Monte Carlo (MC) simulation is described for calculating surface coverages of adsorbed hydrogen atoms and ethylidyne species on Pt(111) as a function of temperature and partial pressures of ethane and hydrogen. The MC simulation is based on self-consistent, gradient-corrected density functional theory (DFT) calculations of the energies of adsorption of H atoms and ethylidyne species at various positions on a periodic Pt(111) slab. DFT calculations of lateral interaction energies between pairs of adsorbates at various distances of separation on the Pt(111) slab are reported. The MC simulation results are in agreement with results from microcalorimetric measurements at 300 K and 573-673 K of the heats of hydrogen adsorption versus adsorbate coverage on two silica-supported Pt samples and on Pt powder. The MC simulation results for the coadsorption of H atoms and ethylidyne species on Pt(111) are used to develop analytical expressions that describe the surface coverages by these species over a wide range of temperatures and pressures (i.e., hydrogen pressures from 1 to 101 kPa, ethane pressures from 0.1 to 10 kPa, and temperatures from 550 to 750 K). The application of these results is discussed for modeling the kinetics of ethane hydrogenolysis over Pt catalysts.