The nonparametric determination of the distributions of the rate constant and active sites was studied on the basis of the Fredholm integral of the first kind during the hydrodesulfurization (HDS) of dibenzothiophene. The reactivities of the intermediates accounted for better fitting of the kernel of exp(-kt) rather than 1/ (1 + kt). The two distinct distributions support the fact that two active sites with different activities are present on the Mo sulfide catalysts for the C-S hydrogenolysis and hydrogenation of dibenzothiophene during the HDS reaction. The former active sites are 15-16 times stronger than the latter ones. The distributions of the active sites (k(2)) decreased with the increasing sulfidation temperature. The 573 K-sulfided Mo catalyst contained one strong active site distributed at 52.4% while the other contained weak active sites at 47.6%. The strength and distributions of the active sites of the Mo sulfide catalysts during the HDS of dibenzothiophene are discussed. (c) 2007 Elsevier Ltd. All rights reserved,