Horiuti’s rule

Horiuti calls H the number of independent intermediates. Temkin (10) describes the equation P = S - H as Horiuti s rule, and the equation R = Q — H as expressing the number of basic overall equations. To avoid confusion, let us confine the term basis and the concept of linear independence to sets of vectors, and let numbers such as H, P, Q, R, S be understood as dimensions of vector spaces. This makes it simple to determine their values and the relations among them, as will be done in Section III. 

Horiuti s rule is valid both for linear and nonlinear mechanisms, though we shall restrict our study to linear mechanisms. 

Chapter 2 describes the evolution in fundamental concepts of chemical kinetics (in particular, that of heterogeneous catalysis) and the "prehis-tory of the problem, i.e. the period before the construction of the formal kinetics apparatus. Data are presented concerning the ideal adsorbed layer model and the Horiuti-Temkin theory of steady-state reactions. In what follows (Chapter 3), an apparatus for the modern formal kinetics is represented. This is based on the qualitative theory of differential equations, linear algebra and graphs theory. Closed and open systems are discussed separately (as a rule, only for isothermal cases). We will draw the reader s attention to the two results of considerable importance. 

Three slices of single-crystal nickel, 10 mm. in diameter and 2 mm. in thickness, respectively, parallel to the (110), (100), and (111) planes were prepared by S. Kaya and denoted, respectively, a, b, and c. They were studied by Matsuda (unpublished) about ten years ago with particular reference to the rates of recombination of hydrogen atoms and to the activation energies for the chemisorption of hydrogen. The latter had been theoretically estimated by Horiuti et ah, as mentioned elsewhere, as functions of the different arrangement of the nickel atoms on the three main crystal planes mentioned above. The relative rates of recombination on the electropolished surfaces of these specimens observed by Matsuda at room temperature followed the qualitative rule ... 

In what follows we discuss these criteria and present the main results. The number of vertices in a KG, JV, is not important for the classification, but it is convenient to introduce this criterion into the coding procedure immediately after the notation for the number of routes. The number of KG edges, E (the mechanism s elementary steps), is not regarded as a criterion because it is determined uniquely by the Horiuti rule M = E — J, where J is the number of linearly independent intermediates. In the case of non-catalytic reactions the number N includes the vertex with the so-called zero reagent. 

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