Single route overall rate equation

Single route overall rate equation in applied kinetics 54... 

The overall rate equation of complex single-route reaction with the linear detailed mechanism was derived and analyzed in detail by many researchers. King and Altman (1956) derived the overall reaction rate equation for single-route enzyme reaction with an arbitrary number of intermediates... 

Overall Reaction Rate Equation of Single-Route Complex Catalytic Reaction in Terms of Hypergeometric Series... 

Systems (20a) and (20b) of n+B equations in n+B unknowns and Ri,... Rp, is the equivalent presentation of the original problem (16). For the single-route reaction mechanism vector R has only one element R, which is the overall reaction rate (the rate of net reaction). 

C.J. van Duijn, Andro Mikelic, I.S. Pop, and Carole Rosier, Effective Dispersion Equations for Reactive Flows with Dominant Peclet and Damkohler Numbers Mark Z. Lazman and Gregory S. Yablonsky, Overall Reaction Rate Equation of Single-Route Complex Catalytic Reaction in Terms of Hypergeometric Series A.N. Gorban and O. Radulescu, Dynamic and Static Limitation in Multiscale Reaction Networks, Revisited... 

Equation (1.36) conforms to the relationship deduced by Horiuti and Boreskov in the 1940s for a particular case of stationary single route catalytic reactions [1—4]. This relationship states that the overall rate of such a stepwise catalytic process can be expressed as the difference between the rates of the direct (v ) and reverse (v ) routes of this stepwise process ... 

Since for a single-route mechanism the numerator of the rate does not depend on the details of the mechanism, it can be written directly based on the overall reaction according to the mass-action law. In such a fast derivation of the steady-state rate equation, steps (7) and (8) are omitted. 

Lazman, M.Z., Yablonsky, G.S., 2008. Overall reaction rate equation of single route catal5dic reaction. 

In the range of temperatures and pressures where the reaction is substantially reversible, the kinetics is much more complicated. There is no grounds to consider chemical changes described by (272) and (273) as independent, not interconnected, reactions. Conversely, if processes (272) and (273) occur on the same surface sites, then free sites will act as intermediates of both processes. Thus one must use the general approach, treating (272) and (273) as overall equations of a certain single reaction mechanism. But if a reaction is described by two overall equations, its mechanism should include at least two basic routes hence, the concept of reaction rate in the forward and reverse directions can be inapplicable in this case. However, experiments show that water-gas equilibrium (273) is maintained with sufficient accuracy in the course of the reaction. Let us suppose that the number of basic routes of the reaction is 2 then, as it has been explained in Section VIII, since one of the routes is at equilibrium, the other route, viz., the route with (272) as overall equation, can be described in terms of forward, r+, and reverse, r, reaction rates. The observed reaction rate is then the difference of these... 

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