Reaction rate theories

This chapter will present theories that are capable of predicting the rate of a reaction, in particular the value of the pre-exponential factor. In Chapter 2 we introduced the Arrhenius equation. 

Concepts of Modem Catalysis and Kinetics. I. ChorkendorfF, J. W. Niemantsverdriet Copyright 2003 WILEY-VCH Verlag GmbH Co. KGaA, Weinheim ISBN 3-527-30574-2 

In his book States of Matter, [(1985), Prentice Hall, Dover] David L. Goodstein writes Ludwig Boltzmann, who spent much of his life studying statistical mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study statistical mechanics. Perhaps it will be wise to approach the subject cautiously.  

To understand how collision theory has been derived, we need to know the velocity distribution of molecules at a given temperature, as it is given by the Maxwell-Boltzmann distribution. To use transition state theory we need the partition functions that follow from the Boltzmann distribution. Hence, we must devote a section of this chapter to statistical thermodynamics. 

Collisions play a tremendously important role in stimulating reacting systems to cross the activation barrier. The theory of Lindemann emphasizes this and provides us with a method to describe the influence of the surrounding medium upon a chemical reaction. It gives important insight into the conditions under which the reaction rate theories discussed here are valid. 

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Johnston Fi S 1966 Gas Phase Reaction Rate Theory (Ronaid)... 

Hanggi P, Talkner P and Borkovec M 1990 Reaction-rate theory fifty years after Kramers Rev. Mod. Phys. 62 251-341... 

Berne B J, Borkovec M and Straub J E 1988 Classical and modern methods in reaction rate theory J. Phys. Chem. 92 3711... 

Talkner P and Hanggi P (eds) 1995 New Trends in Kramers Reaction Rate Theory (Dordrecht Kluwer)... 

Wardlaw D M and Marcus R A 1984 RRKM reaction rate theory for transition states of any looseness Chem. Rhys. Lett. 110 230-4... 

Fleming GR 1986 Chemical Applications of Ultrafast Spectroscopy (Oxford Oxford University Press) Jolmston Ft S 1966 Gas Phase Reaction Rate Theory (Ronald)... 

Hanggi, R, Talkner, P., Borkovec, M. Reaction-rate theory fifty years after Kramers. Revs Modern Phys. 62 (1990) 251-341. 

Mathematical developments of reaction rate theory are given in... 

Electrode kinetics lend themselves to treatment usiag the absolute reaction rate theory or the transition state theory (36,37). In these treatments, the path followed by the reaction proceeds by a route involving an activated complex where the element determining the reaction rate, ie, the rate limiting step, is the dissociation of the activated complex. The general electrode reaction may be described as ... 

Reviews of reaction rate theory by Laidler and Wayne are very helpful. A classic book by Glasstone et al. is still an excellent introduction to the subject. Eyring et al." provide an advanced, detailed treatment of kinetic theory. 

Hill et al. [117] extended the lower end of the temperature range studied (383—503 K) to investigate, in detail, the kinetic characteristics of the acceleratory period, which did not accurately obey eqn. (9). Behaviour varied with sample preparation. For recrystallized material, most of the acceleratory period showed an exponential increase of reaction rate with time (E = 155 kJ mole-1). Values of E for reaction at an interface and for nucleation within the crystal were 130 and 210 kJ mole-1, respectively. It was concluded that potential nuclei are not randomly distributed but are separated by a characteristic minimum distance, related to the Burgers vector of the dislocations present. Below 423 K, nucleation within crystals is very slow compared with decomposition at surfaces. Rate measurements are discussed with reference to absolute reaction rate theory. 

The ratio kq/kf can now be identified as ki9/k9a. We can calculate an upper limit for kl9 from ion-molecule reaction rate theory by assuming that this reaction occurs with a collision efficiency. This leads to k9il < 1 X 109 sec. -1 (7). 

In classical reaction rate theory expressions, this directly follows from the frequency-pre-exponent relationship ... 

Arrhenius proposed his equation in 1889 on empirical grounds, justifying it with the hydrolysis of sucrose to fructose and glucose. Note that the temperature dependence is in the exponential term and that the preexponential factor is a constant. Reaction rate theories (see Chapter 3) show that the Arrhenius equation is to a very good approximation correct however, the assumption of a prefactor that does not depend on temperature cannot strictly be maintained as transition state theory shows that it may be proportional to 7. Nevertheless, this dependence is usually much weaker than the exponential term and is therefore often neglected. 

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