Horiuti numerals

Due to the fulfilment of this law of conservation, the number of linearly independent intermediates is not three but one fewer, i.e. it amounts to two. To the right of mechanism (1) we gave a column of numerals. Steps of the detailed mechanism must be multiplied by these numerals so that, after the subsequent addition of the equations, a stoichiometric equation for a complex reaction (a brutto equation) is obtained that contains no intermediates. The Japanese physical chemist Horiuti suggested that these numerals should be called "stoichiometric numerals. We believe this term is not too suitable, since it is often confused with stoichiometric coefficients, indicating the number of reactant molecules taking part in the reaction. In our opinion it would be more correct to call them Horiuti numerals. For our simplest mechanism, eqn. (1), these numerals amount to unity. 

According to the Horiuti-Polanyi mechanism, isomerization requires the participation of hydrogen. The first addition step, formation of the half-hydrogenated state [Eq. (11.3)], cannot take place without hydrogen. Numerous investigations have supported the role of hydrogen in these so-called hydroisomerizations. 

Horiuti quotes the American chemist Daniels "Despite Eyring and Arrhenius, chemical kinetics is all-in-all confusion. But through all the confusion of complications some promising perspective can be seen. Numerous consecutive, competing and reverse reactions by themselves are simple mono- or bimolecular reactions that in principle obey simple laws. Hence we are fighting not so much with primary steps as with the problem of their mutual coordination to interpret the observed facts and to make practical predictions [13]. Such considerations had been made a very long time ago. 

A different dependence of the parameters in kinetic equations was reported by Horiuti [11] who suggested a method for determining the number of independent parameters. The method consists of the numerical estimation of a rank for some Jacobian matrix. (It is known that this procedure can result in a considerable error.) Later, these problems were analyzed in detail by Spivak and Gorskii [52, 53] but they did not aim at the elucidation of the physico-chemical reasons for the appearance of dependent and undeterminable parameters. It is this aspect that we will discuss below. 

The phenomenological Horiuti Boreskov Onsager equations allow in some cases a first approximation to be made for the kinetic description of catalytic transformations in systems that involve numerous parallel trans formation channels. Consider how these equations can be applied with the process of benzene alkylation with ethylene as an example. 

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