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Rates of Reactions as a Mathematical Consequence of the Permanence of Atoms and the Role of Independent Reactions in the Description of Reaction Kinetics
Linear algebra treatment of the permanence of atoms (mass conservation) naturally leads to the transformation of formation or destruction rates of components of a reaction mixture into rates of reaction steps, which are sufficient to describe the transformations mathematically. These steps form a sc...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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Frontiers Media S.A.
2018
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6073800/ https://www.ncbi.nlm.nih.gov/pubmed/30101143 http://dx.doi.org/10.3389/fchem.2018.00287 |
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author | Pekař, Miloslav |
author_facet | Pekař, Miloslav |
author_sort | Pekař, Miloslav |
collection | PubMed |
description | Linear algebra treatment of the permanence of atoms (mass conservation) naturally leads to the transformation of formation or destruction rates of components of a reaction mixture into rates of reaction steps, which are sufficient to describe the transformations mathematically. These steps form a scheme of independent reactions that can provide a rational basis for elucidating the reaction mechanism (network) while reducing both the component and parametric dimensionality of the description of kinetics. Several particular reaction examples are used to explain the method and show that rates of additional, dependent reactions cannot be unambiguously related to measured component rates. They also illustrate how the rates of dependent reactions can be correctly expressed in terms of the rates of independent reactions. The method starts only with a knowledge of the components of a reaction mixture. It is argued that the design of consistent reaction networks or mechanisms should take into account not only chemistry but also mathematics. |
format | Online Article Text |
id | pubmed-6073800 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2018 |
publisher | Frontiers Media S.A. |
record_format | MEDLINE/PubMed |
spelling | pubmed-60738002018-08-10 Rates of Reactions as a Mathematical Consequence of the Permanence of Atoms and the Role of Independent Reactions in the Description of Reaction Kinetics Pekař, Miloslav Front Chem Chemistry Linear algebra treatment of the permanence of atoms (mass conservation) naturally leads to the transformation of formation or destruction rates of components of a reaction mixture into rates of reaction steps, which are sufficient to describe the transformations mathematically. These steps form a scheme of independent reactions that can provide a rational basis for elucidating the reaction mechanism (network) while reducing both the component and parametric dimensionality of the description of kinetics. Several particular reaction examples are used to explain the method and show that rates of additional, dependent reactions cannot be unambiguously related to measured component rates. They also illustrate how the rates of dependent reactions can be correctly expressed in terms of the rates of independent reactions. The method starts only with a knowledge of the components of a reaction mixture. It is argued that the design of consistent reaction networks or mechanisms should take into account not only chemistry but also mathematics. Frontiers Media S.A. 2018-07-27 /pmc/articles/PMC6073800/ /pubmed/30101143 http://dx.doi.org/10.3389/fchem.2018.00287 Text en Copyright © 2018 Pekař. http://creativecommons.org/licenses/by/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. |
spellingShingle | Chemistry Pekař, Miloslav Rates of Reactions as a Mathematical Consequence of the Permanence of Atoms and the Role of Independent Reactions in the Description of Reaction Kinetics |
title | Rates of Reactions as a Mathematical Consequence of the Permanence of Atoms and the Role of Independent Reactions in the Description of Reaction Kinetics |
title_full | Rates of Reactions as a Mathematical Consequence of the Permanence of Atoms and the Role of Independent Reactions in the Description of Reaction Kinetics |
title_fullStr | Rates of Reactions as a Mathematical Consequence of the Permanence of Atoms and the Role of Independent Reactions in the Description of Reaction Kinetics |
title_full_unstemmed | Rates of Reactions as a Mathematical Consequence of the Permanence of Atoms and the Role of Independent Reactions in the Description of Reaction Kinetics |
title_short | Rates of Reactions as a Mathematical Consequence of the Permanence of Atoms and the Role of Independent Reactions in the Description of Reaction Kinetics |
title_sort | rates of reactions as a mathematical consequence of the permanence of atoms and the role of independent reactions in the description of reaction kinetics |
topic | Chemistry |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6073800/ https://www.ncbi.nlm.nih.gov/pubmed/30101143 http://dx.doi.org/10.3389/fchem.2018.00287 |
work_keys_str_mv | AT pekarmiloslav ratesofreactionsasamathematicalconsequenceofthepermanenceofatomsandtheroleofindependentreactionsinthedescriptionofreactionkinetics |