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Theories of Molecular Reaction DynamicsThe Microscopic Foundation of Chemical Kinetics$
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Niels E. Henriksen and Flemming Y. Hansen

Print publication date: 2008

Print ISBN-13: 9780199203864

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780199203864.001.0001

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From microscopic to macroscopic descriptions

From microscopic to macroscopic descriptions

Chapter:
(p.19) 2 From microscopic to macroscopic descriptions
Source:
Theories of Molecular Reaction Dynamics
Author(s):

Niels E. Henriksen

Flemming Y. Hansen

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199203864.003.0002

This chapter discusses bimolecular reactions from both a microscopic and macroscopic point of view. The outcome of an isolated reactive scattering event can be specified in terms of an intrinsic fundamental quantity, the reaction cross-section that can be measured in a molecular beam experiment. It depends on the quantum states of the molecules as well as the relative velocity of reactants and products. The relation between the cross-section and the macroscopic rate constant is derived. The rate constant is a weighted average of the product between the relative speed of the reactants and the reaction cross-section. The chapter concludes with the special case of thermal equilibrium, where the velocity distributions for the molecules are the Maxwell-Boltzmann distribution. The expression for the rate constant at temperature T is reduced to a one-dimensional integral over the relative speed of the reactants.

Keywords:   cross-section, differential cross-section, molecular beam, rate constant, thermal equilibrium

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