Page 194 - Essentials of physical chemistry

156 Essentials of Physical Chemistry

Henry Eyring
February 20, 1901–December 26, 1981

FIGURE 8.1 Henry Eyring developed the theory of the kinetic transition state. Prof. Eyring published more
than 680 research papers and was an enthusiastic lecturer. Perhaps, his most important contribution to
physical chemistry was the formulation of the ‘‘transition-state’’ concept in chemical reactions. (Courtesy of
the University of Utah, see also http:==www.nap.edu=html=biomems=heyring.html).

then leads to a dissociation to form product(s). It required Eyring’s genius to provide a mathematical
treatment to modify the Arrhenius concept to describe the transition-state process. In what follows,
we may not use exactly the reasoning that Eyring used but still attempt to impart the same clever
process. Schematically, we have

E
K rate ¼ A e ðÞ from Arrhenius
RT
A þ B ! [AB] ! C þ D
z

where we have used the ‘‘z’’ symbol to indicate the activated complex. Eyring generated this new
symbol in chemistry to indicate this transient species, which is the key to the rate-determining step
of a reaction. As such, the decay of the activated complex is essentially a first-order process no
matter how it came to be.
Let us carefully consider the ‘‘ !’’ part of this process. It means that many times, the activated

complex may be formed but then fall apart to go back to the starting materials or sometimes proceed
to the product. This leads to a concept called ‘‘the steady-state approximation,’’ which is a key idea
in several of the examples which follow. The idea is that the reactants (perhaps assisted by solvent
molecules) collide or get near one another long enough to form the activated complex but it may be
an unstable bottleneck in the process. Like any truly dynamic equilibrium, the process rapidly
proceeds in both directions while setting up a steady-state concentration of the activated complex.
Here is a statement of the steady-state idea:
d
[AB] 1 but [AB] 6¼ 0, and since it is so small then [AB] ffi 0or [AB] ffi constant.
z
z
z
z
dt
Eyring’s transition-state theory was developed in the 1930s and strained every computational
capability at that time. Now it is possible to use modern computer programs to study the rearrange-
ment of the reactants along a ‘‘reaction coordinate,’’ which is different from the ‘‘extent of reaction’’