Page 195 - Essentials of physical chemistry

More Kinetics and Some Mechanisms 157

used in Chapter 7. Early calculations by Eyring, Gershinowitz, and Sun [2] as well as by
Hirschfelder, Eyring, and Topley [3] explored the simplest reaction of

H þ H 2 ! H 2 þ H:

Their results and others were reviewed later in 1976 by D. G. Truhlar [4] who also investigated that
reaction with more modern computer programs only to find that the early work by Eyring et al. was
mainly qualitative. Even so, Eyring had an understanding of the basic concepts but not the means to
do accurate calculations.
The ‘‘reaction coordinate’’ is often a tortuous rearrangement of the atoms into a contorted shape
of the activated complex, but the path to the complex can be ‘‘stepped’’ using computer simulations.
Such a path can be shown for reactions such at H 3 mentioned above or the rearrangement of

HOCN þ H ! H þ OCNH or OCNH ! HOCN:

Such reactions may have relatively simple ‘‘reaction coordinates’’ in a line (H 3 ) or on some
relatively simple arc of one H in a plane relative to a fixed linear group like (OCN ). However,

in general, reactions of larger polyatomic molecules involve many simultaneous adjustments in the
atom coordinates to reach the transition-state geometry. We choose to apply the Eyring analysis to
the solvolysis data that we have previously treated using the Arrhenius method. That will allow us to
make a comparison of the Arrhenius results with the Eyring results and we want to apply the method
to a typical organic chemistry reaction. We want to incorporate physical chemistry principles into
organic chemistry.
Usually, it takes some increase in energy to rearrange the atoms into the geometry of the
activated complex, and in particular, the shape requires a change in entropy to go from separate
reactant molecules to a (temporarily) more ordered shape as the activated complex. Thus, Eyring’s
first daring step was to propose that the Arrhenius activation energy is really DG . It may seem that
z
we should use E* ¼ U ¼ H PV but Eyring proposed E* ¼ DG :
z
E* ) DG ¼ DH TDS :
z
z
z
The first modification Eyring made was to rewrite the Arrhenius equation in terms of DG as,
y

(DH z TDS z )
DG z DS z DH z E
k ¼ ( f )e RT ¼ ( f )e RT ¼ ( f )e þ R e RT ¼ A e ðÞ
RT ,
So, Eyring implies

DS z
( f )e þ R ¼ A:

Since the exponential has no units, ‘‘f ’’ has units of inverse time.
As we will see, that yields much more information about the activated complex as well as
satisfies the need to interpret the meaning of the Arrhenius A value. The value and meaning of the
new factor f is some yet-to-be-determined function with inverse time units as befitting a first-order
rate constant. In addition, the usual values of E*and DH are not very different, so the general idea
z
of the activation energy remains the same.
The next step is daring genius on the part of Eyring, the comments here can only speculate at how
he arrived at his final formula. He addressed the question of how the activated complex evolved into
the product. We will study molecular vibrations in a later chapter but we can imagine that the