We present density functional theory (DFT) calculations for N2 dissociation on stepped face-centred cubic (211) surface slabs. By using the same crystal structure, the same adsorption site for atomic nitrogen, and the same transition-state bond length of N2 over a range of pure metal surfaces, a perfectly linear Brønsted-Evans-Polanyi (BEP) relation between the transition-state potential energy and the dissociative chemisorption energy is obtained. The perfect BEP relation, which extends over 12 eV in chemisorption energy, suggests that the manifestation of BEP relations for surface reactions is a general electronic structure effect, and that geometric effects are responsible for the scatter which is normally observed around the BEP line. The BEP relation is also shown to be valid for both surface and bulk alloys. The scatter is, however, larger than for the pure elements. This can be understood as a larger geometrical variance. To analyze the accuracy of the DFT calculations a detailed convergence study is performed for several adsorbates on stepped hexagonal close-packed and face-centred cubic Ru slabs.