Page 141 - Introduction to chemical reaction engineering and kinetics

6.3 Energy in Molecules 123
activation energy, EA, of the reaction. Figure 6.3(d) indicates atomic configurations
along the reaction coordinate.
In the elementary reaction
0’ + H, 4 OH’ + H’ (6.3-la)

which is part of the reaction mechanism in hydrogen flames and the space shuttle main
rocket engine, the transition state would resemble:

The energy barrier for this reaction is quite low, 37 kJ mol-I. There are many schemes
for the estimation of the barrier height, Et. The simplest of these are based on empirical
correlations. For details see Steinfeld et al., 1989, p. 231.
The reverse reaction (BC + A -+ AB + C) follows the same reaction coordinate
in the opposite direction. The barrier for the reverse reaction occurs at the same place.
The barrier height in the reverse direction is related to the barrier height in the forward
direction by

E$ (reverse) = ES (forward) - AE(forward) (6.3-2)

where AE (forward) is the reaction energy change in the forward direction. For exam-
ple, reaction 6.3-la is endoergic by approximately 9 kJ mol-l, and so the energy barrier
for the reverse reaction is 37 - 9 = 28 kJ mol-l.

6.3.1.3 Relationship Between Barrier Height and Reaction Energy
In reaction 6.3-1, the A-B bond weakens as the B-C bond is formed. If there is a bar-
rier, these two effects do not cancel. However, if the B-C bond is much stronger than
the A-B bond (very exoergic reaction), even partial B-C bond formation compensates
for the weakening of the A-B bond. This explains the observation that for a series of
similar reactions, the energy barrier (activation energy) is lower for the more exoergic
reactions. A correlation expressing this has been given by Evans and Polanyi (1938):

Et = Ei + qAE(reaction) (6.3-3)

where E$ is the barrier for an energetically neutral reaction (such as CH; + CD, 4
CH,D + CDT). The correlation predicts the barriers (Es) for similar exoergic/endoergic
reactions to be smaller/larger by a fraction, 4, of the reaction energy (AE (reaction)).
For one set of H transfer reactions, the best value of q is 0.4. This correlation holds
only until the barrier becomes zero, in the case of sufficiently exoergic reactions; or
until the barrier becomes equal to the endoergicity, in the case of sufficiently endoergic
reactions. Figure 6.4 shows reaction coordinate diagrams for a hypothetical series of
reactions, and the “data” for these reactions are indicated in Figure 6.4, along with the
Evans-Polanyi correlation (dashed line). This and other correlations allow unknown
rate constant parameters to be estimated from known values.