The hydrogenation of alkynes is an important reaction in the synthesis of both fine and bulk chemicals. Palladium-based catalysts are widely used and therefore size-selected Pd nanoclusters may provide enhanced performance. An investigation of the adsorption and desorption of the molecules involved in the reaction can shed light on the activity and selectivity of the catalysts. We employ ab initio calculations to investigate the binding energies of all the molecules related to the hydrogenation of 1-pentyne (1-pentyne, 1-pentene, cis-2-pentene, trans-2-pentene and pentane) on a comprehensive set of possible binding sites of two Pd147 and Pd561 cuboctahedral nanoclusters. We extract the site and size dependence of these binding energies. We find that the adsorption of 1-pentyne occurs preferably on the (100) facets of the nanoclusters, followed by their (111) facets, their edges and their vertices. The molecule binds more strongly on the larger nanoclusters, which are therefore expected to display higher activity. The binding energies of the pentenes are found to be lower on the smaller nanoclusters. Therefore, these molecules are expected to desorb more easily and the small clusters should display better selectivity, i.e., partial hydrogenation to 1-pentene, compared with large clusters. Our results provide guidelines for the optimal design of Pd nanocatalysts.