A generalized mathematical treatment is presented that enables a quantitative analysis of various in situ spectroscopic experiments involving detection of solution-phase species generated at the surface of rotating disk and ring-disk, channel, and tube-type electrodes under steady state. This theory is valid for experimental conditions easily realizable in the laboratory and is only applicable to first-order irreversible heterogeneous electron-transfer processes without complications derived from homogeneous phase reactions. Illustrations of the advantages of this formalism are provided, including a rederivation of equations obtained by other authors, an analytic route to the solution of the rotating disk-transparent ring electrode, and various aspects of normal incidence reflection absorption spectroscopy at rotating ring and ring-disk electrodes. The results were in excellent agreement with those of other workers (when available), and in some cases, yielded better accuracy than solutions generated by digital simulation techniques reported in the literature.
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