Bloch Equations for Proton Exchange Reactions in an Aqueous Solution.

The extension of the Bloch equations for acid-base reactions in an aqueous solution is revisited. The acid-base reactions are second-order, and several reactions catalyzed by distinct catalysts may happen simultaneously. By constructing pseudo first-order reactions and assuming fast dissemination of protons from catalysts to solvent water, this extension converges to the well-known Bloch-McConnell equations for a two-site first-order exchange. Thus, explicit relationships between the parameters appearing in the reactions and the Bloch-McConnell equations are established. The dependencies of exchange rates and chemical exchange saturation transfer effects on pH were numerically and experimentally investigated for representative examples.