Low-energy N2 molecules easily dissociate on W(100) but not on W(110). In this Letter, the six-dimensional potential energy surface for the dissociation of N2 molecules on W(110) has been determined by density functional calculations. Results are compared to those of N2 dissociation on W(100). The difference in reactivity between the two faces is shown to arise from the characteristics of the potential energy surface far from the surface (>3 A) and not from the properties of a precursor well or those of the final atomic adsorption sites.