Page 149 - Introduction to chemical reaction engineering and kinetics

6.4 Simple Collision Theory of Reaction Rates 1 3 1

From (a),

ca = 1.88 X 1025molecules m-3
m A - 28.0/(6.022 X 1023)1000 = 4.65 X 1O-26 kg molecule-’
-
)
Z, = 2(3.8 x lo-” 2 (1.88 X 1025)2[~(1.381 x 10-23)300/4.65 x 10-26]1’2
= 5.4 X 1034m-3s-’
Both parts (a) and (b) of Example 6-1 illustrate that rates of molecular collisions are
extremely large. If “collision” were the only factor involved in chemical reaction, the
rates of all reactions would be virtually instantaneous (the “rate” of N2-O2 collisions in
air calculated in Example 6-l(a) corresponds to 4.5 X lo7 mol L-i s-r!). Evidently, the
energy and orientation factors indicated in equation 6.4-2 are important, and we now
turn attention to them.

6.4.1.2 Requirements for Successful Reactive Collision
The rate of reaction in collision theories is related to the number of “successful” colli-
sions. A successful reactive encounter depends on many things, including (1) the speed
at which the molecules approach each other (relative translational energy), (2) how
close they are to a head-on collision (measured by a miss distance or impact param-
eter, b, Figure 6.10) (3) the internal energy states of each reactant (vibrational (v),
rotational (I)), (4) the timing (phase) of the vibrations and rotations as the reactants
approach, and (5) orientation (or steric aspects) of the molecules (the H atom to be
abstracted in reaction 6.3-4 must be pointing toward the radical center).
Detailed theories include all these effects in the reaction cross-section, which is then
a function of all the various dynamic parameters:

u reaction = o(z?, b, VA, JA, . . .) (6.4-8)

The SCT treats the reaction cross-section as a separable function,

u reaction = (+hard spheref cE)p (6.4-9)

= di,.f@)~ (6.4-10)

where the energy requirements, f(E), and the steric requirements, p, are multiplicative
factors.

6.4.1.3 Energy Requirements
The energy barrier E $ is the minimum energy requirement for reaction. If only this
amount of energy is available, only one orientation out of all the possible collision
orientations is successful. The probability of success rises rapidly if extra energy is

Figure 6.10 Illustration of (a) a head-
on collision (b = 0), and (b) a glancing
collision (0 < b < C&B)