Signal analysis in Nuclear Magnetic Resonance spectroscopy is among the most powerful methods to quantify reaction rates in aqueous solutions. To this end, the Swifta??Connick approximations to the Blocha??McConnell equations have been used extensively to estimate rate parameters for elementary reactions. The method is primarily used for 17O NMR in aqueous solutions, but the list of geochemically relevant nuclei that can be used is long, and includes 29Si, 27Al, 19F, 13C and many others of particular interest to geochemists. Here we review the derivation of both the Swifta??Connick and Blocha??McConnell equations and emphasize assumptions and quirks. For example, the equations were derived for CW-NMR, but are used with modern pulse FT-NMR and can be applied to systems that have exchange rates that are shorter than the lifetime of a typical pulse. The method requires a dilute solution where the minor reacting species contributes a negligible amount of total magnetization. We evaluate the sensitivity of results to this dilute-solution requirement and also highlight the need for chemically well-defined systems if reliable data are to be obtained. The limitations in using longitudinal relaxation to estimate reaction rate parameters are discussed. Finally, we provide examples of the application of the method, including ligand exchanges from aqua ions and hydrolysis complexes, that emphasize its flexibility. Once the basic requirements of the Swifta??Connick method are met, it allows geochemists to establish rates of elementary reactions. Reactions at this scale lend themselves well to methods of computational simulation and could provide key tests of accuracy.