Rearrangement reactions of C-4-alkoxides on O-covered Mo(110) have been studied using temperature-programmed reaction spectroscopy and reflection-absorption infrared spectroscopy. Cyclobutoxide on Mo(110), prepared from the corresponding alcohol or bromide, is described for the first time in detail. Several reaction mechanisms are considered for the ring-opening rearrangement of cyclopropylmethoxide during high-temperature annealing. In light of compelling new data, previous results are reinterpreted to support the formation of transient cations near O-covered Mo(110). For the first time, we present strong evidence for clean, heterolytic bond cleavage reactions over a metal surface. Our revised reactivity model is based on spectroscopic and reactivity data that show the rearrangement of cyclopropylmethyl groups to cyclobutyl groups and vice versa. Selectively deuterated 1,1-D-2-cyclopropylmethanol was studied as a test of mechanism and as a probe for the lifetime of reactive intermediates. Isotopic scrambling observed for this substrate is consistent with the formation of a relatively long-lived carbocation during rearrangement. The intermediacy of transient cations is further invoked to explain the rearrangements that are now recognized to occur as alkyl bromides are transformed into alkoxides on Mo(110)-(1 x 6)-O. The observed ring expansion/contraction reactions are characteristic of a cationic process; carbon-centered radicals are not known to rearrange in this manner. However, in none of the cases discussed could contributions from radical pathways be completely ruled out. Our results are compared to analogous reactions in the vapor and solution phases. General trends governing rearrangement mechanisms on Mo(110) are presented with respect to metal-surface coverage, heteroatom incorporation, and temperature. Trends are discussed in the context of heterogeneous hydrocarbon oxidation.