We report here kinetic and isotopic evidence for the elementary steps involved in dimethyl ether (DME) homologation and for their role in the preferential synthesis of 2,2,3-trimethylbutane (triptane) and isobutane. Rates of methylation of alkenes and of hydrogen transfer, isomerization and beta-scission reactions of the corresponding alkoxides formed along the homologation path to triptane were measured using mixtures of C-13-labeled dimethyl ether (C-13-DME) and unlabeled alkenes on H-BEA. DME-derived C-1 species react with these alkenes to form linear butyls from propene, isopentyls from n-butenes, 2,3-dimethylbutyls from isopentenes, and triptyls from 2,3-dimethylbutenes; these kinetic preferences reflect the selective formation of the more highly substituted carbenium ions and the retention of a four-carbon backbone along the path to triptane. Hydrogen transfer reactions terminate chains as alkanes; chain termination probabilities are low for species along the preferred methylation path, but reach a maximum at triptyl species, because tertiary carbenium ions involved in hydrogen transfer are much more stable than those with primary character required for triptene methylation. Alkenes and alkanes act as hydrogen donors and form unsaturated species as precursors to hexamethylbenzene, which forms to provide the hydrogen required for the DME-to-alkanes stoichiometry. Weak allylic C-H bonds in isoalkenes are particularly effective hydrogen donors, as shown by the higher termination probabilities and C-12 content in hexamethylbenzene as C-12-2-methyl-2-butene and C-12-2,3-dimethyl-2-butene pressures increased in mixtures with C-13-DME. The resulting dienes and trienes can then undergo Diels-Alder cyclizations to form arenes as stable by-products. Isomerization and beta-scission reactions of the alkoxides preferentially formed in methylation of alkenes are much slower than hydrogen transfer or methylation rates, thus preventing molecular disruptions along the path to triptane. Methylation at less preferred positions leads to species with lower termination probabilities, which tend to grow to C8+ molecules; these larger alkoxides undergo facile beta-scission to form tert-butoxides that desorb preferentially as isobutane via hydrogen transfer; such pathways resolve methylation "missteps" by recycling the carbon atoms in such chains to the early stages of the homologation chain and account for the prevalence of isobutane among DME homologation products. These findings were motivated by an inquiry into the products formed via C-1 homologation, but they provide rigorous insights about how the structure and stability of carbenium ions specifically influence the rates of methylation, hydrogen transfer, beta-scission, and isomerization reactions catalyzed by solid acids. (C) 2010 Elsevier Inc. All rights reserved.