For molecules containing a linearly coordinated carbonyl group, relationships linking C-13 and O-18 isotopic effects on the CO stretching vibration to the force constant of the M-C coordination bond are proposed. These relationships are rationalized by simple considerations involving the mechanical coupling of the CO and M-C oscillators, tested on model triatomic molecules, and generalized to larger systems. Previous theoretical considerations and several examples presented here show that the long-accepted relation between the shift in the stretching frequency of the coordinated CO with respect to that of isolated CO and the coordination strength has no general predictive power. In contrast, the force constant of the coordination bond can be correlated with the coordination binding energy, and a method for empirically estimating this important parameter from spectroscopic observations of the strongly absorbing CO stretching vibrations of molecular systems or adsorbates is proposed.