The local stability of Al atoms replacing Si in the zeolite framework is compared for all inequivalent tetrahedral (T) sites in mordenite. For Al/Si substitutions in two T sites the stable location of the compensating extraframework Zn(2+) cation forming a Lewis acid site is determined. In the most stable Zn-MOR structures Zn(2+) is located in a small ring (5MR, 6MR) containing two Al/Si substitutions. In less stable structures the Al atoms are placed at larger distances from each other and Zn(2+) interacts with only one Al site. The simulated adsorption of H(2) and CH(4) shows that adsorption strength decreases with increasing stability of the Zn(2+) Lewis site. A higher adsorption strength is observed for Zn(2+) deposited in the 5MR than for the 6MR. The reactivity of a series of stable Zn(2+) Lewis sites is tested via the dissociative adsorption of H(2) and CH(4). The heterolytic dissociation of the adsorbed molecule on the extraframework Zn(2+) cation produces a proton and an anion. The anion binds to Zn(2+) and proton goes to the zeolite framework, restoring a Brønsted acid site. Because bonding of the anion to Zn(2+) is almost energetically equivalent for Zn(2+) in any of the extraframework positions the dissociation is governed by stabilizing bonding of the proton to the framework. Those structures which can exothermically accommodate the proton represent reaction pathways. Due to the repulsion between the proton and Zn(2+) the most favorable proton-accepting O sites are not those of the ring where Zn(2+) is deposited, but O sites close to the ring. Large differences are observed for neighboring positions in a- and b-directions and those oriented along the c-vector. Finally, among the stable Zn(2+) Lewis sites not all represent reaction pathways for dehydrogenation. For all of them the dissociation of H(2) is an exothermic process. In structures exhibiting the highest reactivity the Al/Si substitutions are placed at a large distance and the Zn(2+) cation interacts with O-atoms next to Al in the T4 site of the 5MR. This Lewis site is strong enough to break the C-H bond in the CH(4) molecule.