A two-dimensional lattice gas model with square symmetry is investigated by using the real-space renormalization group (RSRG) approach. Using the RSRG transformation with a cluster of 20 spins, we have investigated the influence of pairwise nearest and next nearest neighbor pair interactions as well as three- and four-particle interactions on the chemical adatom diffusion coefficient. In addition we have analyzed adsorption isotherms and adatom density fluctuations. We have also studied how interactions in the activated state influence surface diffusion.