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 Zn2+ cation forming a Lewis acid site is determined. In the most stable Zn-MOR structures Zn2+ 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 Zn2+ interacts with only one Al site. The simulated adsorption of H-2 and CH4 shows that adsorption strength decreases with increasing stability of the Zn2+ Lewis site. A higher adsorption strength is observed for Zn2+ deposited in the 5MR than for the 6MR. The reactivity of a series of stable Zn2+ Lewis sites is tested via the dissociative adsorption of H-2 and CH4. The heterolytic dissociation of the adsorbed molecule on the extraframework Zn2+ cation produces a proton and an anion. The anion binds to Zn2+ and proton goes to the zeolite framework, restoring a Bronsted acid site. Because bonding of the anion to Zn2+ is almost energetically equivalent for Zn2+ 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 Zn2+ the most favorable proton-accepting O sites are not those of the ring where Zn2+ 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 Zn2+ Lewis sites not all represent reaction pathways for dehydrogenation. For all of them the dissociation of H, is an exothermic process. In structures exhibiting the highest reactivity the Al/Si substitutions are placed at a large distance and the Zn2+ 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 CH4 molecule.