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Analysis of the Reaction Rate Coefficients for Slow Bimolecular Chemical Reactions

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Abstract

Simple bimolecular reactions \(A_1+A_2\rightleftharpoons A_3+A_4\) are analyzed within the framework of the Boltzmann equation in the initial stage of a chemical reaction with the system far from chemical equilibrium. The Chapman-Enskog methodology is applied to determine the coefficients of the expansion of the distribution functions in terms of Sonine polynomials for peculiar molecular velocities. The results are applied to the reaction \(H_2 +Cl\rightleftharpoons HCl+H\), and the influence of the non-Maxwellian distribution and of the activation-energy dependent reactive cross sections upon the forward and reverse reaction rate coefficients are discussed.

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References

  1. I. Prigogine, E. Xhrouet, On the perturbation of Maxwell distribution function by chemical reaction in gases. Physica 15, 913–932 (1949)

    Article  ADS  MATH  Google Scholar 

  2. I. Prigogine, M. Mahieu, Sur la perturbation de la distribution de Maxwell par des réactions chimiques en phase gazeuse. Physica 16, 51–64 (1950)

    Article  ADS  MATH  Google Scholar 

  3. R.D. Present, Note on the simple collision theory of bimolecular reactions. Proc. Natl. Acad. Sci. U.S.A. 41, 415–417 (1955)

    Article  ADS  MATH  Google Scholar 

  4. R.D. Present, On the velocity distribution in a chemically reacting gas. J. Chem. Phys. 31, 747–750 (1959)

    Article  ADS  Google Scholar 

  5. J. Ross, P. Mazur, Some deductions from a formal statistical mechanical theory of chemical kinetics. J. Chem. Phys. 35, 19–28 (1960)

    Article  ADS  Google Scholar 

  6. R.D. Present, Chapman–Enskog method in chemical kinetics. J. Chem. Phys. 48, 4875–4877 (1968)

    Article  ADS  Google Scholar 

  7. B. Shizgal, M. Karplus, Nonequilibrium contributions to the rate of reactions I. Perturbation of the velocity distribution function. J. Chem. Phys. 52, 4262–4278 (1970)

    Article  MathSciNet  ADS  Google Scholar 

  8. B. Shizgal, M. Karplus, Nonequilibrium contributions to the rate of reactions II. Isolated multicomponent systems. J. Chem. Phys. 54, 4345–4356 (1971)

    Article  ADS  Google Scholar 

  9. B. Shizgal, M. Karplus, Nonequilibrium contributions to the rate of reactions III. Isothermal multicomponent systems. J. Chem. Phys. 54, 4357–4362 (1971)

    Article  ADS  Google Scholar 

  10. B.D. Shizgal, Nonequilibrium contributions to the rate of reaction IV. Explicit time-dependent solution. J. Chem. Phys. 55, 76–83 (1971)

    Article  ADS  Google Scholar 

  11. N. Xystris, J.S. Dahler, Kinetic theory of simple reacting spheres. J. Chem. Phys. 68, 345–353 (1978)

    Article  ADS  Google Scholar 

  12. N. Xystris, J. Dahler, Mass and momentum transport in dilute reacting gases. J. Chem. Phys. 68, 354–373 (1978)

    Article  ADS  Google Scholar 

  13. A.S. Cukrowski, J. Popielawski, The effect of viscous flow and thermal flux on the rate of chemical reaction in dilute gases. Chem. Phys. 109, 215–226 (1986)

    Article  ADS  Google Scholar 

  14. F. Baras, M. Malek Mansour, Validity of macroscopic rate equations in exothermic chemical systems. Phys. Rev. Lett. 63, 2429–2432 (1989)

    Article  ADS  Google Scholar 

  15. A.S. Cukrowski, J. Popielawski, L. Qin, J.S. Dahler, A simplified theoretical analysis of nonequllibrium effects in bimolecular gas phase reactions. J. Chem. Phys. 97, 9086–9093 (1992)

    Article  ADS  Google Scholar 

  16. B.V. Alexeev, A. Chikhaoui, I.T. Grushin, Application of the generalized Chapman–Enskog method to the transport-coefficient calculation in a reacting gas mixture. Phys. Rev. E 49, 2809–2825 (1994)

    Article  ADS  Google Scholar 

  17. B.D. Shizgal, D.G. Napier, Nonequilibrium effects in reactive systems: The effect of reaction products and the Chapman–Enskog method. Physica A 223, 50–86 (1996)

    Article  ADS  Google Scholar 

  18. V. Giovangigli, Multicomponent flow modeling (Birkhäuser, Boston, 1999)

    Book  MATH  Google Scholar 

  19. G.M. Alves, G.M. Kremer, Effect of chemical reactions on the coefficients of binary mixtures. J. Chem. Phys. 117, 2205–2215 (2002)

    Article  ADS  Google Scholar 

  20. M. Bisi, M. Groppi, G. Spiga, Grad’s distribution functions in the kinetic equations for a chemical reaction. Contin. Mech. Thermodyn. 14, 207–222 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. A.S. Cukrowski, S. Fritzsche, M.J. Cukrowski Jr., A large nonequilibrium effect of decrease of the bimolecular chemical reaction rate in a dilute gas. Chem. Phys. Lett. 379, 193–201 (2003)

    Article  ADS  Google Scholar 

  22. A.S. Cukrowski, Relations between the Arrhenius activation energy and threshold energy for simple models of the reactive cross sections in a dilute gas. Acta Phys. Pol. B 37, 1715–1726 (2006)

    ADS  Google Scholar 

  23. G.M. Kremer, M. Pandolfi Bianchi, A.J. Soares, A relaxation kinetic model for transport phenomena in a reactive flow. Phys. Fluids 18, 037104 (2006)

    Article  Google Scholar 

  24. B.D. Shizgal, A. Chikhaoui, On the use temperature parameterized rate coefficients in the estimation of non-equilibrium reaction rates. Physica A 365, 317–332 (2006)

    Article  ADS  Google Scholar 

  25. A.W. Silva, G.M. Alves, G.M. Kremer, Transport phenomena in a reactive quaternary gas mixture. Physica A 374, 533–548 (2007)

    Article  ADS  Google Scholar 

  26. G.M. Kremer, A.J. Soares, Effect of reaction heat on Maxwellian distribution functions and rate of reactions. J. Stat. Mech. P12003 (2007)

  27. A.W. Silva, G.M. Alves, G.M. Kremer, Enskog’s kinetic theory of dense gases for chemically reacting binary mixtures I. Reaction rate and viscosity coefficients. Physica A 387, 1733–1749 (2008)

    Article  ADS  Google Scholar 

  28. A.W. Silva, G.M. Alves, W. Marques Jr., G.M. Kremer, Enskog’s kinetic theory of dense gases for chemically reacting binary mixtures, II: light scattering and sound propagation. Physica A 388, 295–310 (2009)

    Article  ADS  Google Scholar 

  29. R. Brun, Introduction to reactive gas dynamics (Oxford University Press, New York, 2009)

    Book  MATH  Google Scholar 

  30. E. Nagnibeda, E. Kustova, Non-equilibrium reacting gas flows: kinetic theory of transport and relaxation processes (Springer Verlag, Berlin, 2009)

    Book  MATH  Google Scholar 

  31. G.M. Kremer, A.W. Silva, G.M. Alves, On inelastic reactive collisions in kinetic theory of chemically reacting gas mixtures. Physica A 389, 2708–2718 (2010)

    Article  ADS  Google Scholar 

  32. G.M. Alves, G.M. Kremer, W. Marques Jr., A.J. Soares, A kinetic model for chemical reactions without barriers: transport coefficients and eigenmodes. J. Stat. Mech. P03014 (2011)

  33. W. Stiller, Arrhenius equation and non-equilibrium kinetics (Teubner, Leipzig, 1989)

    Google Scholar 

  34. G.M. Kremer, An introduction to the Boltzmann equation and transport processes in gases (Springer, Berlin, 2010)

    Book  Google Scholar 

  35. Landolt-Börsnstein, Transportphänomene I, II. Band, 5. Teil, Bandteil a (Springer-Verlag, Berlin, 1969)

    Google Scholar 

  36. Landolt-Börsnstein, Transportphänomene II, II. Band, 5. Teil, Bandteil b (Springer-Verlag, Berlin, 1968)

    Google Scholar 

  37. I. Prigogine, Introduction to thermodynamics of irreversible processes, 3rd edn. (Interscience, New York, 1967)

    Google Scholar 

  38. S.R. de Groot, P. Mazur, Non-equilibrium thermodynamics (Dover, New York, 1984)

    Google Scholar 

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Acknowledgements

GMK acknowledges the support of the CNPq and TGS acknowledges the support of the CAPES.

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Correspondence to Gilberto M. Kremer.

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Dedicated to Professor I-Shih Liu on the occasion of his 70th birthday.

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Kremer, G.M., Silva, T.G. Analysis of the Reaction Rate Coefficients for Slow Bimolecular Chemical Reactions. Braz J Phys 42, 400–409 (2012). https://doi.org/10.1007/s13538-012-0086-x

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