Horiuti formulation

Apart from enzyme kinetics, this new trend had also appeared in the kinetics of heterogeneous catalysis. In the 1950s, Horiuti formulated a theory of steady-state reactions [11, 12], many of the concepts of which correspond to the graph theory. Independent intermediates, a reaction route, an independent reaction route, all these concepts were introduced by Horiuti. 

Before we examine the hydrogenation of each type of unsaturation, let us first take a look at the basic mechanism assumed to be operating on metal catalytic surfaces. This mechanism is variously referred to as the classic mechanism, the Horiuti-Polanyi mechanism, or the half-hydrogenated state mechanism. It certainly fits the classic definition, since it was first proposed by Horiuti and Polanyi in 193412 and is still used today. Its important surface species is a half-hydrogenated state. This mechanism was shown in Chapter 1 (Scheme 1.2) as an example of how surface reactions are sometimes written. It is shown in slightly different form in Fig. 2.1. Basically, an unsaturated molecule is pictured as adsorbing with its Tt-bond parallel to the plane of the surface atoms of the catalyst. In the original Horiuti-Polanyi formulation, the 7t-bond ruptures... 

The concept of a mechanism for a reaction, whilst well known and much used by the chemist, is not as yet clearly formulated in a rational analysis. The precise classification of the methods adverted to in Section 6 above, and their extension to sets of reactions are steps that need to be taken. In this connection the work of Horiuti [70] and Christiansen [73], as well as the vast chemical literature (see for example Kondrat ev [77]) will provide much material. It is not to be expected however that all vagueness can be removed for the hypothetical method is intrinsically self-contradictory. 

The application of the concept of "the rate along the basic route provides a possibility of obtaining a new formulation for the quasi-stationary conditions in terms of the Horiuti theory which is different from the ordinary one, i.e. "the formation of an intermediate is equal to that of its consumption . Temkin called the equations obtained "the conditions for the statio-narity of steps . In matrix form they are represented as... 

One must not underestimate, however, the importance of the general results obtained in terms of the steady-state reaction theory. Its informative concepts are used in theoretical kinetics, in particular the concept of Horiuti (stoichiometric) numbers and a new formulation for the steady-state... 

Let us note that the summation in eqn. (44) is taken with respect to the number of all cycles involving the participation of step u. At the same time, in the Horiuti-Temkin equation ("the steady-state step equation ), which is one more formulation for the quasi-steady state conditions [11, 12]... 

This problem, put forward independently by Horiuti (1939) [41] and Bores-kov (1945) [42], can be formulated as follows to find a kinetic equation for a complex reaction in the reverse direction from the known similar expression for the direct reaction rate and applying only thermodynamic relationship for the brutto-reaction. In other words it is necessary to answer the question, in what cases is the equation... 

The concept of stoichiometric number was introduced in electrochemistry by Horiuti and Ikusima [42, 43] for the hydrogen electroreduction reaction. We need to introduce the stoichiometric number V in complex multielectron electrode kinetics in order to distinguish different possible mechanisms. The International Union of Pure and Applied Chemistry (lUPAC) defines the stoichiometric number in electrochemistry as a positive integer that indicates the number of identical activated complexes formed and destroyed in the completion of the overall reaction as formulated with the charge number, n [44, 45]... 

An interpretation in terms of molecular potential—energy curves was advanced almost simultaneously by Horiuti and Polanyi and by Bell, " the two treatments corresponding respectively to a covalent and an ionic formulation. The former is probably closer to reality, and will be followed here. 

The Horiuti-Polanyi model considered only the possibility of proton tunneling in the upper part of the barrier. The possibility of proton tunneling from the lowest unexcited level was not considered. Strictly speaking, this problem could not be formulated correctly within the framework of this model. Indeed, for a subbarrier transition of a particle from one bound state to another, the energies of the initial and the final states must be practically identical. For the Horiuti-Polanyi model, such an identity of energies is improbable (see Figure 3.12). A more probable situation is the one where the zero level of the initial state either lies below the zero level of the final state or corresponds to the... 

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