Theory and Practice of Catalysis, Including Concentration Effects

Theory and Practice of Catalysis, Including Concentration Effects 

To include the effect of the concentrations of the reactants and the products into the TOE calculation, we need only to express the steady-state matrix A (Eq. (9.6)) as a function of the weights instead of the rate constants, as explained in Section 9.2.1. In a simple cycle, this translates into the -representation as [30, 31, 46,47] 

Although this equation looks like an alphabet soup, it is actually simple to understand. In the numerator, the second term is nothing more than the reaction 

In the denominator, we define the chemical zones that cover from each intermediate Ij) to each TS T, and multiply them by the concentrations of all the reactants and products that are consumed or produced on each one of those zones. If there is only one significant zone, then we can implement the energy span approximation (akin to Eqs. (9.10) and (9.11)) again, by neglecting all the unimportant terms and the reaction quotient Q (which is typically much smaller than K when far from equihbrium). The resulting energy span approximation is 

we are only including the reactants and products that are consumed or produced in the rate-determining zone (RDZone) [40], that is, from the TDI to the TDTS. 

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