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Chemical Reaction Rate from a (Semiempirical) Dynamical Point of View

Received: 8 October 2021     Accepted: 2 November 2021     Published: 17 November 2021
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Abstract

The aim of the present paper is to check - or better to confirm - the mathematical validity of chemical reaction rate, faced as a set of differential equations. Firstly one - way elementary reactions are considered, in the most general case. Secondly the same thing is done with two-way (opposing) elementary reactions. At this stage, we show that the two – way reaction, as we mean it, is compatible with the reduction of the total Gibbs energy as expected in every natural process. As an example of a two way elementary reaction of a completely solvable problem we give the hydrolysis of sucrose to glucose and fructose, where the “inversion” of sucrose is examined not only with the initial linear reaction of “Wilhelmy” (1850), but also with the two way nonlinear reaction introduced. Finally the validity of the mathematical model is checked for more complex cases such as the Michaelis-Menten mechanism or reactions in solution, where it is found that the two cases, apparently are four – dimensional while in reality are two – dimensional (after the “subtraction” of the constraints of “motion”) and naturally cannot exhibit chaotic behavior. In all cases the treatment is not one-hundred-percent mathematically austere but it has also arbitrary although reasonable hypotheses.

Published in American Journal of Physical Chemistry (Volume 10, Issue 4)
DOI 10.11648/j.ajpc.20211004.17
Page(s) 93-103
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2021. Published by Science Publishing Group

Keywords

Chemical Reaction Rate, Physical Chemistry, Sucrose, Chaos

References
[1] N. L. Katsanos, Advanced Inorganic Chemistry, 1st Edition, University of Patras, Pa- tras, Greece, 1979.
[2] P. W. Atkins, Physical Chemistry, 1st Edition, Oxford University Press, London, 1996.
[3] M. J. Pilling, P. W. Seakins, Reaction Kinetics, 1st Edition, Oxford University Press, London, 1995.
[4] S. R. Logan, Fundamentals of Chemical Kinetics, 1st Edition, Longman, Harlow, 1996.
[5] E. A. Jackson, Perspectives of nonlinear dynamics, 1st Edition, Cambridge University Press, Cambridge, 1991.
[6] J. K. Hale, Ordinary Differential Equations, 1st Edition, Wiley Interscience, London, 1971.
[7] Lawrence Perko, Differential Eqs. Dynamical Systems, Springer 2000.
[8] P. Erdi & Janos Τoth, Mathematical models of chemical reaction, Manchester University Press, 1989.
[9] Sucrose vs Glucose vs Fructose. What's the difference? Melissa Groves/ June 08, 2018.
[10] Sucrose – Wikipedia [Internet Search].
[11] Inverted sugar syrup – Wikipedia [Internet Search].
[12] Chemical Chaos – Harry L. Swinney - The University of Texas - Austim U.S.A. – J. C. Roux - Centre de Recherché Paul Pascal, Universite de Bordeaux I, Domaine Universitaire, Talence Cedex, France.
[13] Chaos in a chemical system, July 2013: Τhe Εuropean Physical Journal - Special Topics (223 (3-4)). A) Dr Rohit Srivastava, B) P. K. Srivastava, C) Jayeeta Chattopadhyay Amity University India.
[14] Michaelis - Menten kinetics - Wikipedia (internet search)
[15] Reactions in Solutions - Chemical kinetics and Reaction Dynamics, Dordrecht Springer Link dy SK Upadhyay.
Cite This Article
  • APA Style

    Thanassis Dialynas, Nikos Lazarides, Artemis Saitakis. (2021). Chemical Reaction Rate from a (Semiempirical) Dynamical Point of View. American Journal of Physical Chemistry, 10(4), 93-103. https://doi.org/10.11648/j.ajpc.20211004.17

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    ACS Style

    Thanassis Dialynas; Nikos Lazarides; Artemis Saitakis. Chemical Reaction Rate from a (Semiempirical) Dynamical Point of View. Am. J. Phys. Chem. 2021, 10(4), 93-103. doi: 10.11648/j.ajpc.20211004.17

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    AMA Style

    Thanassis Dialynas, Nikos Lazarides, Artemis Saitakis. Chemical Reaction Rate from a (Semiempirical) Dynamical Point of View. Am J Phys Chem. 2021;10(4):93-103. doi: 10.11648/j.ajpc.20211004.17

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  • @article{10.11648/j.ajpc.20211004.17,
      author = {Thanassis Dialynas and Nikos Lazarides and Artemis Saitakis},
      title = {Chemical Reaction Rate from a (Semiempirical) Dynamical Point of View},
      journal = {American Journal of Physical Chemistry},
      volume = {10},
      number = {4},
      pages = {93-103},
      doi = {10.11648/j.ajpc.20211004.17},
      url = {https://doi.org/10.11648/j.ajpc.20211004.17},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajpc.20211004.17},
      abstract = {The aim of the present paper is to check - or better to confirm - the mathematical validity of chemical reaction rate, faced as a set of differential equations. Firstly one - way elementary reactions are considered, in the most general case. Secondly the same thing is done with two-way (opposing) elementary reactions. At this stage, we show that the two – way reaction, as we mean it, is compatible with the reduction of the total Gibbs energy as expected in every natural process. As an example of a two way elementary reaction of a completely solvable problem we give the hydrolysis of sucrose to glucose and fructose, where the “inversion” of sucrose is examined not only with the initial linear reaction of “Wilhelmy” (1850), but also with the two way nonlinear reaction introduced. Finally the validity of the mathematical model is checked for more complex cases such as the Michaelis-Menten mechanism or reactions in solution, where it is found that the two cases, apparently are four – dimensional while in reality are two – dimensional (after the “subtraction” of the constraints of “motion”) and naturally cannot exhibit chaotic behavior. In all cases the treatment is not one-hundred-percent mathematically austere but it has also arbitrary although reasonable hypotheses.},
     year = {2021}
    }
    

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    T1  - Chemical Reaction Rate from a (Semiempirical) Dynamical Point of View
    AU  - Thanassis Dialynas
    AU  - Nikos Lazarides
    AU  - Artemis Saitakis
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    N1  - https://doi.org/10.11648/j.ajpc.20211004.17
    DO  - 10.11648/j.ajpc.20211004.17
    T2  - American Journal of Physical Chemistry
    JF  - American Journal of Physical Chemistry
    JO  - American Journal of Physical Chemistry
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    EP  - 103
    PB  - Science Publishing Group
    SN  - 2327-2449
    UR  - https://doi.org/10.11648/j.ajpc.20211004.17
    AB  - The aim of the present paper is to check - or better to confirm - the mathematical validity of chemical reaction rate, faced as a set of differential equations. Firstly one - way elementary reactions are considered, in the most general case. Secondly the same thing is done with two-way (opposing) elementary reactions. At this stage, we show that the two – way reaction, as we mean it, is compatible with the reduction of the total Gibbs energy as expected in every natural process. As an example of a two way elementary reaction of a completely solvable problem we give the hydrolysis of sucrose to glucose and fructose, where the “inversion” of sucrose is examined not only with the initial linear reaction of “Wilhelmy” (1850), but also with the two way nonlinear reaction introduced. Finally the validity of the mathematical model is checked for more complex cases such as the Michaelis-Menten mechanism or reactions in solution, where it is found that the two cases, apparently are four – dimensional while in reality are two – dimensional (after the “subtraction” of the constraints of “motion”) and naturally cannot exhibit chaotic behavior. In all cases the treatment is not one-hundred-percent mathematically austere but it has also arbitrary although reasonable hypotheses.
    VL  - 10
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    ER  - 

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Author Information
  • Department of Physics, University of Crete, Heraklion, Greece

  • Department of Physics, University of Crete, Heraklion, Greece

  • Science & Technology Park of Crete, Foundation for Research and Technology, Heraklion, Greece

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