Page 139 - Introduction to chemical reaction engineering and kinetics

6.3 Energy in Molecules 121

The minimum energy on the curve corresponds to the most stable configuration
where the bonding is most effective, and thus to the stable A-B diatomic molecule. In
the specific case of a pair of iodine atoms, this minimum is 149 kJ mol-l below that of
the separated atoms. Therefore, to dissociate an isolated I, molecule at rest, I2 + 21*,
149 kJ mol-i must be supplied from outside the molecule. This elementary reaction
is said to be endoergic (energy absorbing) by this amount, also known as the bond
dissociation energy. This energy can be supplied by absorption of light energy, or by
transfer of kinetic energy from other molecules. This energy can also be thought of as
the height of an energy barrier to be scaled in order for reaction to occur. The path
along the potential energy curve can be thought of as a path or trajectory leading to
reaction, which is described as the “reaction coordinate”.
Now consider the reverse reaction, 21’ + I,. The reaction coordinate in this case is
just the reverse of that for the dissociation reaction. The reaction is exoergic (energy
releasing), and for the I, molecule to come to rest in its most stable configuration, an
amount of energy equal to the bond energy must be given off to the rest of the sys-
tem. If not, the molecule has enough energy (converted to internal kinetic energy) to
dissociate again very quickly. This requirement to “offload” this excess energy (usually
through collisions with other molecules) is important in the rates of these bimolecular
association reactions. The input of additional energy is not required along the reaction
coordinate for this reaction to occur; the two atoms only have to encounter each other;
that is, there is no energy barrier to this reaction. These concepts form a useful basis for
discussing more complicated systems.

6.3.1.2 Triatomic Systems: Potential Energy Surface and Transition State
Consider a system made up of the atoms A, B, and C. Whereas the configuration of
a diatomic system can be represented by a single distance, the internal geometry of a
triatomic system requires three independent parameters, such as the three interatomic
distances rAu, ?-no, and ?-CA, or rAa, r,,, and the angle 4ABc. These are illustrated in
Figure 6.2.
The potential energy is a function of all three parameters, and is a surface (called the
potential energy surface) in three-dimensional (3-D) space. If we simplify the system
by constraining the atoms to remain in a straight line in the order A-B-C, the potential
energy depends Only on tW0 paraIneterS (i.e., rAn and rgc), and we can Conveniently
represent it as a 2-D “topographical map” in Figure 6.3(a), or as a 3-D perspective
drawing in Figure 6.3(b). At the lower-left corner of Figure 6.3(a), all three atoms are
far apart: there are no bonding interactions. As A approaches B while C remains dis-
tant (equivalent to moving up the left edge of Figure 6.3(a)), a stable AB molecule is
formed (like the I, case). Similarly, a B-C bond is formed if B approaches C with A far
away (moving right along the bottom edge of Figure 6.3(a)). When all three atoms are
near each other, the molecular orbitals involve all three atoms. If additional bonding is
possible, the energy is lowered when this happens, and a stable triatomic molecule can
be formed. This is not the case shown in Figure 6.3(a), since in all configurations where
A, B, and C are close together, the system is less stable than AB + C or A + BC. This
is typical for many systems where AB (and BC) are stable molecules with saturated
bonding. The two partial bonds A-B and B-C are weaker than either complete bond.

Figure 6.2 Representation of configuration of
three-atom system