First principles based density functional methods and theoretical models have been used to investigate thereactivity of different RhCu alloys toward molecular hydrogen dissociation. For pure Rh(111), it is predictedthat H2 can either dissociate spontaneously or be physisorbed as molecular hydrogen. These predictions agreewith recent experimental findings. The simple addition of a Cu atom to a Rh-rich environment is enough toeliminate the presence of the energy minimum associated with molecularly adsorbed hydrogen and to convertH2 dissociation in an activated process. From the present results it is concluded that increasing the Cu contentmay lead to a change in the active site and permits us to speculate about the enhancement on the irreversiblehydrogen uptake on going from Rh to RhCu alloys with a small Cu content.