Density functional theory is used to determine transition states and the corresponding energy barriers of the reactions related to C-H bond activation of hydrogen exchange and dehydrogenation of ethane catalyzed by a protonated zeolite as well as hydride transfer between methanol and a methoxide (CH3-zeolite) species. Additionally the C-C bond activation involved in the acid catalyzed cracking reaction of ethane was investigated. The computed activation barriers are 118 for hydrogen exchange, 202 for hydride transfer, 292 for cracking and finally 297 for dehydrogenation, all in kilojoules per mole. For the cracking reaction, two different transition states with the same activation barrier have been obtained, dependent on the approach of the ethane molecule to the zeolite cluster. A study of the relation between acidity and the structure of the zeolite shows that the transition state for the hydrogen exchange reaction is rather covalent and its geometry resembles the well-known carbonium ion, while the others are rather ionic carbenium ions. From the calculated activation barriers as well as vibrational, rotational, and translational partition functions, reaction rate constants have been evaluated by means of the transition state reaction rate theory.