Low-energy (10-90 eV) atomic ions of group IIIA, IVA, VA, VIA, and VIIA elements (E) undergo reactions with a fluorinated self-assembled monolayer surface to give fluoride cations, EF(n)(+). One, two, or three fluorine atoms can be abstracted. Ion/surface reactions are also observed with polyatomic ions of these elements, but in general, atomic ions are much more reactive and react at lower collision energies than the corresponding polyatomic species. The higher collision energies reflect increased energy consumption needed for fragmentation. Most of the ion/surface reactions investigated in this study are endothermic and are driven by the translational energy of the projectile, although there remains a high degree of thermochemical control over reactivity. Thermochemical control over neutralization of the primary beam is also evident; ions with high recombination energies, like N+ and O+, completely neutralize at the fluorocarbon surface. In addition, certain general trends in behavior have been observed for elements within the same periodic group. The reactions occur in single scattering events, and they are not associated with electron transfer from the surface to the ion, as are the well-known hydrogen and alkyl group abstractions by organic radical ions. In most cases, the ion/surface reaction seems to occur after, or in concert with, dissociation of the polyatomic projectile. When multiple abstractions occur, the fluorine atoms can be lost from the same alkyl chain; evidence for this is the enhanced intensity of specific sputtering products, e.g. C3F3+, upon collisions of ions such as Sb+, which readily abstract more than one fluorine atom. Ion/surface reactions in which new bonds are formed in the surface alkyl group are also observed; such reactions give rise to unusual product ions which are sensitive to the chemical nature of the projectile. Examples include chlorine-for-fluorine atom substitution at the surface and PCF2+ formation in p(+) collisions. These processes suggest the possibility of selective chemical modification of the outermost monolayers of surfaces using low-energy reactive ion beams.