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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.
Chemical Kinetics
Published in Achintya Mukhopadhyay, Swarnendu Sen, Fundamentals of Combustion Engineering, 2019
Achintya Mukhopadhyay, Swarnendu Sen
The collection of elementary reactants is called the reaction mechanism. For elementary reactions, order or molecularity of reactions refers to the molecules of reactants that interact with each other. This reaction order refers to the number of molecules that collide with each other. For example, for the reaction in Equation (3.4), two molecules (one each of Hand O2) collide to form products. The order of reaction m and n denotes the influence of H2 and O2 concentrations on the reaction rate. Thus, the empirically determined exponents refer to the reaction order and not reaction molecularity. The reaction orders denote reaction molecularities only for elementary reactions. However, for global reactions where the reactants and the products are the starting and the final products of a reaction mechanism, the reaction orders determine the integrated effects of the molecularities of the individual elementary reactions and thus can have fractional values. The most common elementary reactions are bimolecular in nature, though unimolecular and termolecular reactions are also encountered.
A simplified simulation of the reaction mechanism of NOx formation and non-catalytic reduction
Published in Combustion Science and Technology, 2018
Free radical reactions involve initiation, propagation or H-abstraction, and termination steps. The reactions scheme taken into account is also an important input parameter. It is assumed that the reactions are elementary and therefore the order corresponds to the molecularity and rate coefficients obey Arrhenius relationship. In various works it is often used to describe radical reaction, the modified Arrhenius relationship (Battin-Leclerc, 2008; Glassman et al., 2014; Turányi and Tomlin, 2014). Thus the kinetic Equation (17) is used in this model.