(179b) Rates and Reversibilities in Interconnected Reaction Networks

We leverage the pseudo-steady-state hypothesis to develop a generalized approach for expressing the unidirectional forward and reverse rates of interconnected reaction networks in terms of the unidirectional rates of the constituent elementary steps, and we validate this formalism with simulated isotopic exchange rates obtained from microkinetic models. The resulting unidirectional rate expressions show that branches in reaction pathways decrease the forward and reverse unidirectional rates by the same factor such that the functional form of effective reversibility, a thermodynamic parameter, remains independent of the network connectivity. Kinetic resistance, defined as the inverse of reaction rate, provides a physical interpretation for unidirectional rate expressions and demonstrates the analogy between elementary steps in an overall reaction and resistors in an electrical circuit. An overall reaction behaves as a series of resistors, each accounting for either an elementary step involved or a branch in the reaction pathway. The derivation developed herein applies to all reaction systems regardless of the number of elementary steps, number of branches, and values of stoichiometric numbers. Further analysis on interconnected reaction systems indicates the inability to determine net and unidirectional rates of reaction pathways based on species generation rates alone and underscores the necessity of isotopic tracers. The presented work rectifies previously established framework applicable exclusively to single-path reaction sequences, outlines the dichotomy between kinetic (reaction rates) and thermodynamic (reversibility) descriptors, and highlights the potential to validate proposed reaction networks for highly interconnected systems such as CO_x hydrogenation with unidirectional rates.