Rate Laws for Reactions with Parallel Pathways: Use of the Electrical Analogy

The conventional kinetic analysis of the rate law of an overall reaction is limited to a single sequential pathway comprising of a series of consecutive molecular steps that transform the reactants into products. The general approach is based on the time-honored quasi-steady state approximation (QSSA), leading, e.g., to the Temkin relation for the general case. More limiting approaches include the rate-limiting step (RLS), along with the quasi-equilibrium hypothesis (QEH), i.e., the Langmuir-Hinshelwood-Hougen-Watson (LHHW) algorithm. The electrical analogy of the network comprising a sequence of resistors representing the elementary steps is often utilized in this regard in visualizing a RLS. Here we describe a topological approach based on the analogy between reaction-route (RR) graphs described by us earlier and electrical circuits that extends such QSSA analysis to the case of systems involving parallel pathways, and is amenable to RLS/QEH analysis as well. It is illustrated here for the simple case of gas-phase hydrogen-bromine reaction, but is useful for catalytic and enzymatic reactions networks as well.