Horiuti-Temkin relation

If there exists a rate determining step, an isotope tracer method can be used for the determination of a or Urds at equilibrium or near equilibrium conditions. Its basic principle has been expounded systematically by Horiuti, Temkin and Happel. If the exchange rate or rate at equilibrium defined by Wangner is introduced, when the reaction approaches equilibrium, A is close to zero for any elementary step. Consequently, Horiuti-Temkin relation can be deduced ... 

According to the Horiuti-Temkin theorem [9,10], the number of linearly independent RRs is equal to I = p - ranka = p - q. Now, let Ju Ji be the corresponding rates (or, the RR fluxes) along the arbitrarily selected set of linearly independent RRs, namely RRu RR2,..., RRi. Then, within the QSS approximation the following relation between RR fluxes and the rates of individual elementary reaction steps is valid... 

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. 

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