We studied in this work a competitive reaction model between monomers on a catalyst. The catalyst is represented by hypercubic lattices in d = 1, 2 and 3 dimensions. The model is described by the following reactions: A + A -> A2 and A + B -> AB, where A and B are two monomers that arrive at the surface with probabilities yA and yB, respectively. The model is studied in the adsorption controlled limit where the reaction rate is infinitely larger than the adsorption rate. We employ site and pair mean-field approximations as well as static and dynamical Monte Carlo simulations. We show that, for all d, the model exhibits a continuous phase transition between an active steady state and a B-absorbing state, when the parameter yA is varied through a critical value. Monte Carlo simulations and finite-size scaling analysis near the critical point are used to determine the static critical exponents b,n^ and the dynamical critical exponents n||, d, h and z. The results found for this competitive reaction model are in accordance with the conjecture of Grassberger, which states that any system undergoing a continuous phase transition from an active steady state to a single absorbing state, exhibits the same critical behavior of the directed percolation universality class.