Temkin rule

Symbols Z and Z denote two types of sites. For the sake of simplicity, an irreversible reaction is considered. One can see that for scheme (7.222) there are 5 intermediates in the spirit of Temkin considerations (Z, Z, ZH, Z H+ and ZRH ), three steps, one route and thus according to the Horiuti-Temkin rule (eq. 4.3, 4.4) there should be three balance equations. As there are two types of sites in (7.222) then these balance equations take the form... 

There are 3 steps in scheme 7.270, two intermediates (adsorbed hydrogen and vacant sites), one balance equation which relates these two intermediates, and then respectively two independent routes according to the Horiuti-Temkin rule. Steps 1, 2 and 3 are usually referred as Volmer, Tafel and Heirovsky reactions respectively acknowledging the names of researches who emphasized the importance of these processes. 

In Scheme (6.121), the numbering of steps correspond to numbers in Fig. 6.61. The number of independent routes can be calculated following the Horiuti-Temkin rule (Eq. 4.4). There are six steps in this mechanism (the far right vertical line in Fig. 6.61 is the same as step 3), four intermediates (Ei, EiS, E2, E2S) and one balance equation (the sum of all free enzyme and enzyme-substrate concentrations is equal to the total enzyme concentration). This gives three independent routes. The dependent zero routes relate the constants of steps. These routes can be obtained from the independent ones in the following way — isf As the overall... 

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. 

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. 

In several experiments, in particular the study by Temkin and co-workers [224] of the kinetics in ethylene oxidation, slow relaxations, i.e. the extremely slow achievement of a steady-state reaction rate, were found. As a rule, the existence of such slow relaxations is ascribed to some "side reasons rather than to the purely kinetic ("proper ) factors. The terms "proper and "side were first introduced by Temkin [225], As usual, we classify as slow "side processes variations in the chemical or phase composition of the surface under the effect of reaction media, catalyst deactivation, substance diffusion into its bulk, etc. These processes are usually considered to require significantly longer times to achieve a steady state compared with those characterizing the performance of chemical reactions. The above numerical experiment, however, shows that, when the system parameters attain their bifurcation values, the time to achieve a steady state, tr, sharply increases. 

As Temkin (32) has shown, the adsorption laws always agree with the assumption analogous to the Brensted rule saying that the change of activation energy of adsorption is a part of the change of heat of adsorption. Then, the activation energy of adsorption is... 

According to the Temkin-Horiuti rule the mechanism (4.94) contains 3 steps, two surface intermediates Z and COZ and one balance equation, therefore only two independent routes, as... 

The are six intermediates in scheme 7.231, five steps and only one reaction route. According to the rule of Horiuti-Temkin there should be two balance equations. One is die balance for coverage of surface species ... 

Following the rule of Florinti-Temkin for 11 elementary steps and eight intermediates (E, EB, EAB, EA, ECD, EC, ED, EBC) with one balance equation (ie, the total balance of enzyme species), the total number of routes is equal to 4, eg, routes ISP ... 

According to the rule ofHoriuti-Temkin, the number of independent routes can be determined by subtracting from the number of steps, equal to 21 (T to 6 , li to 6i, In to 6 , 7, 8 and 9), number of intermediates, equal to 20 (six in each of three cycles in addition to complexes 3 and 4) and adding the number of balance equations. One balance equation relates concentration of ah rhodium-containing intermediates. FoUowing this rule, it can be concluded that there should be another hnk equation, which must relate concentration of species 4 with other reaction intermediates. It can be easily seen that because in step 9 (Fig. 5.32) equimolar amounts of 1-0 and 4 are produced, such balance equation links species 4 with the sum of species of type 1 ... 

---