We have studied the size-dependent reactivity of W-10-W-60 with N-2 under single-collision-like conditions by using a laser-vaporization source, a low-pressure reaction cell and a laser-ionization time-of-flight mass spectrometer. The reaction probability with the first and second Na molecule was measured at two different cluster-source temperatures : room temperature (RT) and liquid-nitrogen temperature (LNT). For the RT clusters, a strong size dependence in the reaction probability was observed in the size range similar to 10-26 atoms, With distinct local maxima at W-16, W-22, and W-23. Upon cooling of the cluster source, the reaction probability increased significantly overall, and the relative variations with size decreased, but persisted. To get an indication of the bond Strength of N-2 onW(n), we heated the cluster products after reaction through irradiation with 4.02 eV photons from a XeCl excimer laser and checked for consequent desorption of adsorbate atoms or molecules. For the LNT clusters, heating with laser light caused a substantial decrease in the abundance of reaction products with nitrogen, whereas no significant change in the abundance of WnN2 was observed for the RT clusters. This indicates that a proportion of the N-2 is relatively weakly bound to the LNT clusters, whereas on W-n produced at RT, only the strongly bound state/states of N-2 exist. Based on comparisons with the N-2-adsorption on W bulk surfaces, we conclude that the weakly and strongly bound states represent molecularly and dissociatively bound N-2, respectively.