Molecular diffusion on surfaces does not adhere to the basic assumptions of the adsorbate hopping model. Large molecules such as n-alkanes can bind at more than one site on surfaces. Their diffusion involves multiple hops to various nearest and non-nearest neighbor sites. In a recent study [J. S. Raut and K. A. Fichthorn, J. Chem. Phys. 108, 1626 (1998)], we proposed a simple heterogeneous lattice model to describe the behavior of these molecules on surfaces. In this work, we have carried out kinetic Monte Carlo simulations to verify the model and study the tracer and chemical diffusion of these molecules at different coverages and temperatures. Interestingly the tracer diffusion of a single molecule can be described by a solution of the lattice model obtained using the simplifying assumption of uncorrelated hopping out of different sites. The coverage dependence of tracer diffusion can also be described by a simple lattice model. We compare results from the kinetic Monte Carlo simulations to molecular-dynamics simulations and demonstrate that a lattice-based hopping model does account for all the relevant features of short chain diffusion on surfaces. The chemical-diffusion coefficient increases with increasing coverage, due to a reduction in configurational entropy.