The adsorption dynamics of diatomic molecules on solid surfaces is examined by using a Kinetic Monte Carlo algorithm. Equilibration times at increasing loadings are obtained, and explained based on the elementary processes that lead to the formation of the adsorbed film. The ability of the molecules to change their orientation accelerates the overall uptake and leads to competitive kinetic behaviour between the different orientations. The dependence of the equilibration time on coverage follows the same decreasing trend obtained experimentally for ethane adsorption on closed-end carbon nanotube bundles. The exploration of molecule-molecule interaction effects on this trend provides relevant insights to understand the kinetic behaviour of other species, from simpler molecules to larger polyatomic molecules, adsorbing on surfaces with different binding strength.