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Steady-State Approximation, Reaction Mechanism and Rate Law of Chain Reactions
Published in Eli Usheunepa Yunana, Calculations in Chemical Kinetics for Undergraduates, 2022
Elementary reactions are characterized by the following: They are either unimolecular (involves a single reactant species) or bimolecular (involves two reactant molecules), but termolecular (involves three reactant molecules colliding simultaneously) are very rare.The order of an elementary reaction corresponds with the stoichiometric coefficients in the balanced equation for that step, although this is not always true for the overall rate law and overall balanced equation in an experiment.The overall rate law of a reaction depends on a single elementary step which is usually the slowest step in the reaction mechanism.They can also be reversible reactions having both forward and reverse processes at equilibrium.
Introduction to dynamic modelling
Published in Karthik Raman, An Introduction to Computational Systems Biology, 2021
The law of mass-action is the all-important model underlying most kinetic models. Building on the work of Guldberg and Waage in 1860s (which they reviewed in [1]), the law has been described in various forms. While Guldberg and Waage speak of the rate of chemical reactions being proportion to the “active masses” of the reactants, in its modern form, the law is taken to state that the rate of a chemical reaction is proportional to the probability of collision between the reactants in a given system. In a system where the concentrations are very low, of the order of a few molecules, such that the collisions are rare, stochastic effects will predominate. On the other hand, in a typical reactor, or in a cell, this probability will be proportional to the concentrations of the participating molecules (reactants) to the power of their respective molecularities. Molecularity refers to the number of colliding molecular entities that are involved in a single elementary reaction step. An elementary reaction is a chemical reaction where one or more chemical species react directly to form product(s) in a single reaction step, with a single transition state.
Introduction to Ordinary Differential Equations
Published in Brian Vick, Applied Engineering Mathematics, 2020
According to the law of mass action of chemical kinetics, the rate of an elementary reaction is proportional to the product of the concentrations of the reactants. We denote the concentrations by lowercase letters x = [X] and a = [A]. Assume that there’s an enormous surplus of chemical A, so that its concentration a can be regarded as constant. Then, the equation for the kinetics of x is dxdt=k1ax−k−1x2
A kinetic model and parameters estimate for the synthesis of 2-phenyloctane: a starting material of bio-degradable surfactant
Published in Indian Chemical Engineer, 2023
Sudip Banerjee, Md Aurangzeb, Amit Kumar
According to Froment et al. [23], the single-event is very useful for obtaining a smooth estimation procedure and significant value of parameters involved in large numbers in a model. The single-event methodology considers the change in symmetry of reactant in the elementary reaction step. Using this methodology, the kinetic rate constant (k) is expressed as the product of the single-event-rate coefficient (k′) of that step and the number of single-event (ne). The latter one is defined as the ratio of the global symmetry of the reactant and activated complex. After incorporating ne in the kinetic rate coefficient (k′) from the transition state theory, the kinetic rate constant is expressed as: Here, and denote the global symmetry of reactant and activated complex, respectively. The number of single-event captures the difference in structure between the reactant and activated complex.
Experimental Study on the Characteristics of the Spontaneous Combustion of Coal at High Ground Temperatures
Published in Combustion Science and Technology, 2022
Huilin Jia, Yang Yang, Wanxing Ren, Zenghui Kang, Jingtai Shi
The results demonstrate that coal exposed to high temperatures for an extended duration undergoes numerous chemical changes. The high temperature changes the functional groups in the coal sample structure, increasing the abundance of hydroxyl and oxygen-containing groups, at the expense of consumable functional groups such as aliphatics. The abundance of functional groups such as carboxycarbonyl groups increases and becomes more reactive, which in turn leads to an increase in the production rate and amount of CO gas. This is because the reaction sequence of CO production is primarily the elementary reaction of the hydroxyl radical to abstract the aldehyde hydrogen, and the elementary reaction of the aldehyde radical to form carbon monoxide. Therefore, when the abundance of aldehydes containing oxygen increases because of high temperatures, CO production also increases. Additionally, the temperature at which CO begins to rapidly increase corresponds to the dry cracking temperature. High ground temperatures thus accelerate the oxidation of coal, and the resulting decrease of the critical temperature, dry cracking temperature, and ignition temperature increases the risk of spontaneous combustion.
A DFT Study of N2O Homogeneous and Heterogeneous Reduction Reaction by the Carbon Monoxide
Published in Combustion Science and Technology, 2022
Ruobing Wang, Chan Zou, Yue Zhang
N2O adsorption on char surface is the first step of the heterogeneous reaction between N2O and CO. From the calculation results in sections 3.2.1, the two optimized structures of CO adsorption on char surface were employed to study the influence of CO on the heterogeneous reduction mechanism of N2O. For the two structures in Figure 4, the N2O molecule is adsorbed on the pre-assembled Char-CO structures 4–1 and 4–2 to form stable intermediate IM1 and IM-1, respectively. It shows that the energy of N2O molecule adsorption on the structure 4–1 is −694.24 kJ/mol, which is lower than that (−640.44 kJ/mol) of N2O adsorption on the structure 4–2. The result indicates that the IM1 is more stable that IM-1, and N2O molecule is more likely to adsorb on the structure 4–1. Subsequently, intermediate IM1 transforms into the intermediate IM2 via the transition state TS1. This reaction step (IM1→TS1→IM2) is an endothermic process with 19.67 kJ/mol and must overcome an energy barrier of 97.96 kJ/mol. The distance between the C atom of CO molecule and C(1) increases gradually for this elementary reaction step: 0.158 nm (IM1)→0.241 nm (TS1)→0.284 nm (IM2). In addition, the elementary reaction step (IM-1→TS-1→IM2) step is an exothermic process with 34.13 kJ/mol, and the five-membered ring in the IM-1 undergoes the dissociation of C(1)-O(5) to form IM2 through the transition state TS-1 after crossing an energy barrier of 119.72 kJ/mol. From the calculation results, it can be concluded that the intermediate IM1 and IM-1 both transform into the intermediate IM2 through the different transition states.