Ab initio computational quantum chemical methods are used to calculate reduced partition function ratios for all isotopomers of CO, HCO+, and HOC+ involving the nuclides H-1, H-2 (D), C-12, C-13, O-16, and O-18. The ratios are used to calculate equilibrium constants for the reaction pairs HCO+/CO, HOC+/CO, and C+/CO. Both simple proton transfers and more complex isotopic variants involving the breaking and reforming of CO bonds are considered. The probable pathways for the HCO+/CO and C+/CO exchange reactions are explored in detail using high-accuracy quantum chemical calculations. It appears most likely that the HCO+/CO reaction proceeds through exothermic formation of the linear adduct OCHCO+ with D-xh symmetry. Similarly, the C+/CO reaction proceeds along a spin-allowed pathway with exothermic formation of the linear adduct COC+ with D-xh symmetry. An alternate but higher energy spin-allowed pathway for the C+/CO reaction passes through a transition state with only C-s symmetry and a locally stable intermediate with C-2v symmetry. In the ISM these reactions may proceed by these direct pathways or indirectly through coupled exothermic reaction pairs involving other species to achieve C-13/C-12 isotope exchange.