It is well recognized that the standard Butler–Volmer equation is lacking in an adequate description of the kinetics of the hydrogen electrode reaction over the complete range of potentials for the alkaline as well as the acid electrolytes. Further, it is unable to explain the asymmetry in current vs potential observed in the hydrogen evolution reaction (HER) vs the hydrogen oxidation reaction (HOR). In fact, even kinetic descriptions via two-step mechanisms (Volmer–Heyrovsky, Volmer–Tafel, or Heyrovsky–Tafel) are individually applicable only in limited potential ranges. We present an approach that provides explicit rate expressions involving kinetics of all the three steps (Tafel–Volmer–Heyrovsky) simultaneously, as well as more limiting rate expressions based on two-step pathways. The analysis is based on our recently developed graph–theoretic approach that provides accurate rate laws by exploiting the electrical analogy of the reaction network. The accuracy of the resulting rate expressions, as well as their asymmetric potential dependence, for both HOR and HER is illustrated here based on step kinetics provided in the literature for Pt catalyst in 0.5 M NaOH solution.

A theory and algorithm for reaction route (RR) network analysis is developed in analogy with electrical networks and is based on the combined use of RR theory, graph theory, and Kirchhoff's laws. The result is a powerful new approach of "RR graphs" that is useful in not only topological representation of complex reactions and mechanisms but, when combined with techniques of electrical network analysis, is able to provide revealing insights into the mechanism as well as the kinetics of the overall reactions involving multiple elementary reaction steps including the effect of topological constraints. Unlike existing graph theory approaches of reaction networks, the approach developed here is suitable for linear as well as nonlinear kinetic mechanisms and for single and multiple overall reactions. The theoretical approach for the case of a single overall reaction involving minimal kinetic mechanisms (unit stoichiometric numbers) is developed in Part I of this series followed by its application to examples of heterogeneous and enzyme catalytic reactions in Part II.

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