Abstract
A novel exact derivation for the kinetic constant of a bimolecular reaction according to three well-known models of collision theory is reported. The use of probability density functions, with the introduction of a novel geometry to study the collision process, allows simplifying the derivation to such an extent, that, for a proper statistical background, it is is possible to recover the line-of-centers and the angular dependent line-of-centers models in no more than a couple of lectures. Although the derivation is introduced to recover the temperature-dependent kinetic constant, it is shown that the energy-dependent reactive cross section can be recovered as well. A possible confusion in the interpretation of the pre-exponential factor is commented.
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R.D. Present Kinetic Theory of Gases (McGraw Hill, 1958)
Moore J.W., Pearson R.G.: Kinetics and Mechanism, 3rd edn. Wiley, New York (1989)
Smith I.W.M.: J. Chem. Ed. 59, 9 (1982)
A. Gupta, Groundwork of Mathematical Probability and Statistics. (5th edn. revised; Academic Publishers, Kolkata 2004), pp. 123–124
A. Szabo, N.S. Ostlund, Modern Quantum Chemistry. (1st edn. revised; McGraw Hill: New York, 1989)
Nordman C.E., Blinder S.M.: J. Chem. Ed. 51, 790 (1969)
Blinder S.M.: Advanced Physical Chemistry, pp. 240–241. The Macmillan Ca., New York (1969)
Beuhier R.J., Bernstein R.B.: J. Chem. Phys. 51, 5305 (1969)
Levine R.D., Bernstein R.B.: Chem. Phys. Lett. 105, 467 (1984)
Evans G.T., She R.S.C., Bernstein R.B.: J. Chem. Phys. 82, 2258 (1985)
Houston P.L.: Chemical Kinetics and Reaction Dynamics. Dover, Mineola, NY (2001)
Levine R.D.: Molecular reaction dynamics. Cambridge University Press, Cambridge (2005)
D.R. Herschbach, In Nobel Lectures, Chemistry 1981–1990. (Editor-in-Charge Tore Frängsmyr, Editor Bo G. Malmström, World Scientific Publishing Co., Singapore,1992)
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Monaco, G. A novel derivation of collision theory rate constants for a bimolecular reaction. J Math Chem 49, 1544–1557 (2011). https://doi.org/10.1007/s10910-011-9840-5
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DOI: https://doi.org/10.1007/s10910-011-9840-5