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

Thanassis Dialynas; Nikos Lazarides; Artemis Saitakis

doi:doi:10.11648/j.ajpc.20211004.17

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

Thanassis Dialynas, Nikos Lazarides, Artemis Saitakis

Published in American Journal of Physical Chemistry (Volume 10, Issue 4)

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), 2024. 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.

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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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TY  - JOUR
T1  - Chemical Reaction Rate from a (Semiempirical) Dynamical Point of View
AU  - Thanassis Dialynas
AU  - Nikos Lazarides
AU  - Artemis Saitakis
Y1  - 2021/11/17
PY  - 2021
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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PB  - Science Publishing Group
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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
IS  - 4
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Author Information

Thanassis Dialynas

Department of Physics, University of Crete, Heraklion, Greece
Nikos Lazarides

Department of Physics, University of Crete, Heraklion, Greece
Artemis Saitakis

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

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Plain Text BibTeX RIS

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}
}

Copy | Download

TY  - JOUR
T1  - Chemical Reaction Rate from a (Semiempirical) Dynamical Point of View
AU  - Thanassis Dialynas
AU  - Nikos Lazarides
AU  - Artemis Saitakis
Y1  - 2021/11/17
PY  - 2021
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
SP  - 93
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
IS  - 4
ER  -

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