* Corresponding author. Tel.: 1-508-8315250; fax: 1-508-8315853. E-mail address: rdatta@wpi.edu (R. Datta). Chemical Engineering Science 55 (2000) 4029}4043 A thermodynamic approach to the systematic elucidation of unique reaction routes in catalytic reactions Ilie Fishtik, Ravindra Datta* Department of Chemical Engineering, Worcester Polytechnic Institute, Worcester, MA 01609-2280, USA Received 22 January 1998; accepted 4 February 2000 Abstract The directness (uniqueness) of both reaction routes (mechanisms) and overall reactions is deduced from chemical thermodynamics. Namely, starting from general thermodynamic relations, the basic kinetic equation is shown to be identically transformed so as to be decomposable into a sum of contributions originating from a "nite and unique set of reactions called response reactions (RERs). For a general chemical reaction system involving terminal species (reactants and products) and intermediates, the basic kinetic equation may be further partitioned into contributions coming from RERs involving only terminal species and those RERs involving at least one intermediate. When the intermediate are assumed to obey the quasi-steady state approximation, the contributions coming from the RERs involving at least one intermediate vanish. As a result, the basic kinetic equation may be presented as a sum of contributions coming from RERs involving only terminal species, i.e., overall RERs. This approach is shown to provide an adequate physicochemi- cal basis of mechanisms and overall reactions as well as an e!ective algorithm of their enumeration.  2000 Elsevier Science Ltd. All rights reserved. Keywords: Thermodynamics; Kinetics; Heterogeneous catalysis; Mechanisms; Multiple chemical reaction systems; Elementary reactions; Overall reactions 1. Introduction Catalytic reactions proceed through a complex net- work of elementary mechanistic steps involving the react- ants, intermediates, and products. A knowledge, or at least a suspicion, of the set of elementary reactions in- volved in a chemical reaction system is crucial to the understanding of its kinetics. It is, therefore, of funda- mental importance to have a systematic and rigorous way of determining all of the possible elementary reac- tions as well as mechanisms for a given chemical process. One way of solving this problem is a purely mathemat- ical one. Given the set of reactants, reaction products, and intermediates, as well as other constraints on plaus- ible mechanisms (e.g., the overall stoichiometry, the as- sumption that every intermediate is adsorbed on the catalyst, a de"nite number of bond cleavage or formation per step, etc.), various combinatorial algorithms of deriv- ing the mechanisms can be proposed (Sinanoglu, 1975; Valdes-Perez, 1994). A somewhat di!erent approach to this problem is the concept of reactions routes. Given a set of elementary reaction steps which are suspected to occur in the system, one looks for their linear combina- tions such that the intermediate species are eliminated and the net transformation involves only the terminal species, i.e., the reactants and products (Horiuti & Nakamura, 1967; Horiuti, 1973; Temkin, 1973, 1979). These ideas were further developed by introducing the concept of direct mechanisms (Milner, 1964) and direct overall reactions (Happel & Sellers, 1982, 1983, 1989; Sellers, 1984, 1989). Within this approach, a chemical system is regarded as being de"ned by a set of elementary reactions (or elementary steps) under the additional spe- ci"cation as to which species are the intermediates and which are the terminal species. Then the problem is formulated as one of determining a unique set of ways (direct mechanisms) which demonstrate how a unique set of reactions involving only terminal species (direct over- all reactions) can result from elementary reactions. The problem of enumerating all possible direct mechanisms and direct overall reactions has been extensively dis- cussed in the literature (Happel & Sellers, 1982, 1983, 0009-2509/00/$ - see front matter  2000 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 0 0 ) 0 0 0 5 0 - 6