Theories of Chemical Kinetics

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. 

---

Larson R S and Kostin M D 1982 Kramers theory of chemical kinetics curvilinear reaction coordinates J. Chem. Phys. 77 5017-25... 

In chemical kinetics, it is often important to know the proportion of particles with a velocity that exceeds a selected velocity v. According to collision theories of chemical kinetics, particles with a speed in excess of v are energetic enough to react and those with a speed less than v are not. The probability of finding a particle with a speed from 0 to v is the integral of the distribution function over that interval... 

Leidler, K.J., 1969, Theories of Chemical Kinetics (McGraw Hill, New York). 

A final comment on the interpretation of stochastic simulations We are so accustomed to writing continuous functions—differential and integrated rate equations, commonly called deterministic rate equations—that our first impulse on viewing these stochastic calculations is to interpret them as approximations to the familiar continuous functions. However, we have got this the wrong way around. On a molecular level, events are discrete, not continuous. The continuous functions work so well for us only because we do experiments on veiy large numbers of molecules (typically 10 -10 ). If we could experiment with very much smaller numbers of molecules, we would find that it is the continuous functions that are approximations to the stochastic results. Gillespie has developed the stochastic theory of chemical kinetics without dependence on the deterministic rate equations. 

After an introductory chapter, phenomenological kinetics is treated in Chapters 2, 3, and 4. The theory of chemical kinetics, in the form most applicable to solution studies, is described in Chapter 5 and is used in subsequent chapters. The treatments of mechanistic interpretations of the transition state theory, structure-reactivity relationships, and solvent effects are more extensive than is usual in an introductory textbook. The book could serve as the basis of a one-semester course, and I hope that it also may be found useful for self-instruction. 

This chapter treats the descriptions of the molecular events that lead to the kinetic phenomena that one observes in the laboratory. These events are referred to as the mechanism of the reaction. The chapter begins with definitions of the various terms that are basic to the concept of reaction mechanisms, indicates how elementary events may be combined to yield a description that is consistent with observed macroscopic phenomena, and discusses some of the techniques that may be used to elucidate the mechanism of a reaction. Finally, two basic molecular theories of chemical kinetics are discussed—the kinetic theory of gases and the transition state theory. The determination of a reaction mechanism is a much more complex problem than that of obtaining an accurate rate expression, and the well-educated chemical engineer should have a knowledge of and an appreciation for some of the techniques used in such studies. 

Isotope effects on rates (so-called kinetic isotope effects, KIE s) of specific reactions will be discussed in detail in a later chapter. The most frequently employed formalism used to discuss KIE s is based on the activated complex (transition state) theory of chemical kinetics and is analogous to the theory of isotope effects on thermodynamic equilibria discussed in this chapter. It is thus appropriate to discuss this theory here. 

The standard theories of chemical kinetics are equilibrium theories in which a Maxwell-Boltzmann distribution of reactants is postulated to persist during a reaction.68 The equilibrium theory first passage time is the TV -> oo limit in Eq. (6), Corrections to it then are to be expected when the second term in this equation is no longer negligible, i.e., when N is not much greater than e — e- )-1. The mean first passage time and rate of activation deviate from their equilibrium value by more than 10% when... 

It is known from the theory of chemical kinetics that a system of S chemical substances in dynamic equilibrium can be described by rate constants of the pseudo-first order, K, a (i = 1, 2,..., S a= 1,2,..., Q). Some of the rates may assume zero values. The rate of depletion of substance A-t in the reaction co(er), Vrw(o), and that of its formation in the reverse reaction a, Vj+tt, must equal each other at equilibrium ... 

---