Page 124 - Introduction to chemical reaction engineering and kinetics

106 Chapter 5: Complex Systems

Thus, the maximum yield of B, on substitution for t,,, from 5.5-8, is

(YB,A)max = 5 = L!$ exp [ Pk~‘~k~‘kl’ ] = 2 ($+ = (i?)“;; (5.5-9)
2 1
5.6 COMPLEXITIES COMBINED

56.1 Concept of Rate-Determining Step (rds)
In a kinetics scheme involving more than one step, it may be that one change occurs
much faster or much slower than the others (as determined by relative magnitudes of
rate constants). In such a case, the overall rate, and hence the product distribution, may
be determined almost entirely by this step, called the rate-determining step (rds).
For reactions in parallel, it is the “fast” step that governs. Thus, if A 2 B and A %
C are two competing reactions, and if kAB B kAC, the rate of formation of B is much
higher than that of C, and very little C is produced. Chemical rates can vary by very large
factors, particularly when different catalysts are involved. For example, a metal catalyst
favors dehydrogenation of an alcohol to an aldehyde, but an oxide catalyst often favors
dehydration.
For reactions in series, conversely, it is the “slow” step that governs. Thus, for the
scheme A 3 B % C, if k, >> k2, the formation of B is relatively rapid, and the forma-
tion of C waits almost entirely on the rate at which B forms C. On the other hand, if
k, > k,, then B forms C as fast as B is formed, and the rate of formation of C is de-
termined by the rate at which B is formed from A. These conclusions can be obtained
quantitatively from equation 5.5-7. Thus, if k, B k2,

dc,ldt = [ k2klcAol(k2 - k,)] (eLkIt - eek2’) (5.6-1)
= k2cAoe -kzr (k, > k2) (5.6-la)

so that the rate of formation of C is governed by the rate constant for the second (slow)
step. If k, > kl,

dc,ldt = klcAoe-kl’ (k2 >> kl) (5.6-lb)

and the rate of formation of C is governed by the rate constant for the first step.
Since the rates of reaction steps in series may vary greatly, the concept of the slow
step as the governing factor in the overall rate of reaction is very important. It is also a
matter of everyday experience. If you are in a long, slowly moving lineup getting into
the theater (followed by a relatively rapid passage past a ticket-collector and thence to
a seat), the rate of getting seated is largely determined by the rate at which the lineup
moves.

5.6.2 Determination of Reaction Network
A reaction network, as a model of a reacting system, may consist of steps involving some
or all of: opposing reactions, which may or may not be considered to be at equilibrium,
parallel reactions, and series reactions. Some examples are cited in Section 5.1.
The determination of a realistic reaction network from experimental kinetics data
may be difficult, but it provides a useful model for proper optimization, control, and
improvement of a chemical process. One method for obtaining characteristics of the