Analysis of reaction schemes using maximum rates of constituent steps

Abstract

We show that the steady-state kinetics of a chemical reaction can be analyzed analytically in terms of proposed reaction schemes composed of series of steps with stoichiometric numbers equal to unity by calculating the maximum rates of the constituent steps, r max,i , assuming that all of the remaining steps are quasi-equilibrated. Analytical expressions can be derived in terms of r max,i to calculate degrees of rate control for each step to determine the extent to which each step controls the rate of the overall stoichiometric reaction. The values of r max,i can be used to predict the rate of the overall stoichiometric reaction, making it possible to estimate the observed reaction kinetics. This approach can be used for catalytic reactions to identify transition states and adsorbed species that are important in controlling catalyst performance, such that detailed calculations using electronic structure calculations (e.g., density functional theory) can be carried out for these species, whereas more approximate methods (e.g., scaling relations) are used for the remaining species. This approach to assess the feasibility of proposed reaction schemes is exact for reaction schemes where the stoichiometric coefficients of the constituent steps are equal to unity and the most abundant adsorbed species are in quasi-equilibrium with the gas phase and can be used in an approximate manner to probe the performance of more general reaction schemes, followed by more detailed analyses using full microkinetic models to determine the surface coverages by adsorbed species and the degrees of rate control of the elementary steps.chemical kinetics | catalysis | microkinetics C hemical reactions take place through sequences of elementary steps, and the dynamics of the overall stoichiometric reaction are typically controlled by key steps in this sequence of steps. For example, in the case of a catalytic reaction, the reaction kinetics are controlled by the energetics of the transition states for the rate-controlling steps and by the energetics of species that are abundant on the active sites (i.e., the Gibbs free energies of these transition states and adsorbed species relative to the reactants and products of the overall stoichiometric reaction). However, whereas the observed reaction kinetics are controlled by a limited number of transition states and adsorbed species, it is typically required to carry out detailed microkinetic analyses to identify the nature of these key transition states and adsorbed species. Thus, a general strategy to elucidate how the reaction kinetics are controlled by a proposed reaction mechanism is first to carry out density functional theory (DFT) calculations to determine the thermodynamic properties of all adsorbed species and transition states, and then to build a microkinetic model to determine the surface coverages by all adsorbed species and the forward and reverse rates of all elementary steps for a range of reaction conditions (1-5). Sensitivity analyses are then carried out using this microkineti...

Evaluation of the degree of rate control via automatic differentiation

“…We first show that AD can reproduce the DRC results of previous reports 11,21 in the first two simple cases. Then, we compare the performance of the FD and the AD on another more complicated reaction mechanism of propylene oxidation.…”

“…Case I was a hypothetical example and it only contained two steps with manually set kinetic parameters, which is relatively simple. In case II, we consider the DRC for a more complicated reaction mechanism for the water‐gas shift reaction 21 which is listed in Table 4. The pressures for the gas‐phase species P CO , , , and are 0.07, 0.21, 0.38, and 0.085 atm, respectively.…”

Theoretical study of the mechanism of 2,5-diketopiperazine formation during pyrolysis of proline

“…Degrees of rate control (X RC ) for all involved transition states were calculated according to the procedure described by Motagamwala 24 (See Supplementary Information for details). Equation ( 1) is used to calculate the degree of rate control of the i-th transition state on a generalized sequence of n steps:…”

“…Now, according to Motagamwala 24 , the degrees of rate control (X RC ) for transition states can be calculated using equations ( 1) and (2) (See details in Supporting Information). Results are summarized in Table 2: These degrees of rate control represent an indicator of how much influence has a transition state on the total reaction rate.…”

Requiem for the Rate-Determining Step in Complex Heterogeneous Catalytic Reactions?

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