Page 193 - Essentials of physical chemistry

8 More Kinetics and Some

Mechanisms

INTRODUCTION
In Chapter 7, we tried to form a good foundation for the study of reaction rates using quantitative
measurements. The topic of kinetics deserves a full-semester course, and the classic text is Kinetics
and Mechanism [1] initially by Frost and Pearson with an updated third edition by Moore and
Pearson. Here, we go beyond the straightforward first- or second-order reactions to a few complicated
multistep reactions. The main theme of this chapter is the use of the ‘‘steady-state approximation,’’
which is a pencil-and-paper method to treat reactions, which include transient intermediate species in
the overall reaction. Today, complex reactions are studied using computer modeling, but the pencil-
and-paper steady-state treatment still has educational value in explaining the principles of transition-
state intermediates (Eyring model), chain reactions, and enzyme kinetics. One goal of this chapter is to
learn how to treat reactions according to the Eyring transition-state model to report entropy changes as
well as energy changes in the transition state. Another goal is to appreciate how complicated chain
reactions can be by studying the solvable scheme for the reaction between H 2 and Br 2 . Finally, the
important case of enzyme kinetics is treated by deriving the Michaelis–Menten equation with and
without a competitive inhibitor. These cases and a few others all depend on some form of the steady-
state concept. This admittedly short list of applications was selected as the ‘‘essential’’ topics needed
by students in prehealth science, forensic science, and chemistry. Informal interviews of students
from this course now in industry or graduate studies have helped form this small list over a number
of years. This author always asks graduates of this course, ‘‘Did you use the topics we learned in
physical chemistry?’’ and the list of topics has been adjusted several times. Thus, the topics here are
the result of that selection process.

BEYOND ARRHENIUS TO THE EYRING TRANSITION STATE

Before the invention of copying machines, scientists distributed their work through journal articles
as they do today. But there was no easy way to copy an article then; so when an article appeared, the
author would order a hundred or so ‘‘reprints’’ to be mailed to interested parties upon written
request. There were even special postcards issued by departments to be used by faculty to request
reprints. The reprints themselves were often stapled into very nice covers. As a graduate student
assigned to an inventory task, the author discovered boxes and boxes of nicely bound reprints from
the 15 years of Prof. Henry Eyring’s tenure at Princeton University before he moved to the
University of Utah. Henry Eyring’s name was eventually on over 685 publications, and many
books covering a wide variety of topics in physical chemistry but he is best known for his work on
absolute rate theory. We might add that his lectures were usually very enthusiastic and highly
animated, entertaining as well as full of special insight (Figure 8.1).
Here, we can show Eyring’s genius in reinterpreting the Arrhenius formula. According to
Eyring’s theory, there is in almost every reaction a key ‘‘transition state.’’ Rather than just use the
‘‘extent of reaction’’ in moles to treat the overall reaction turnover, the Eyring treatment imagines
some molecular distortion of the internal coordinates of the combined ‘‘activated complex,’’ which

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