Page 371 - Elements of Chemical Reaction Engineering Ebook

342 Nonelementary Reaction Kinetics Chap. 7

The overall reaction [Equation (7-4)], for which the rate expression is nonele-
mentary, consists of the sequence of elementary reactions, Equations (7-3,
(7-7), and (7-9).
Nitrogen and ethane are only formed in the reaction given by Equation
(7-9). Consequently, the net rate of formation of nitrogen is

(7- 1 1)

Concentration of A* The concentration of the active intermediate, AZO*, is very difficult to
is difficult to measure, because it is highly reactive and very short-lived s). Conse-
measure and needs
to be replaced in quently, evaluation of the reaction rate laws, (7-8), (7-lo), and (7-11), in their
the rate law present forms becomes quite difficult, if not impossible. To overcome this dif-
ficulty, we need to express the concentration of the active intermediate, CAzo*,
in terms of the concentration of azomethane, Cao. As mentioned in Chapter
3, the total or net rate of formation of a particular species involved in many
simultaneous reactions is the sum of the rates of formation of each reaction for
that species.
We can generalize the rate of formation of species j occurring in n differ-
ent reactions as
The total rate n
of formation r. = C rji (7-12)
of species j from all I
reactions 1=1
Because the active intermediate, AZO*, is present in all three reactions in the
decomposition mechanism, the net rate of formation of AZO* is the sum of the
rates of each of the reaction equations, (7-5), (7-7), and (7-9):

rate of rate of
formation formation I
of AZO” in of AZO* in of AZO* in
Equation (7-5) Equation (7-9)

‘AZO*(7-5) + ‘AZ0*(7-7) + ‘AZO*(7 - 9)
(7-13)
By substituting Equations (7-6), (7-S), and (7-10) into Equation (7-13), we obtain
Rate of formation
of active (7-14)
intermediate
To express CMOS in terms of measurable concentrations, we use the pseudo-
steady-state hypothesis (PSSH).

7.1.2 Pseudo-Steady-State Hypothesis (PSSH)

In most instances it is not possible to eliminate the concentration of the
active intermediate in the differential forms of the mole balance equations to
obtain closed-form solutions. However, an approximate solution may be
obtained. The active intermediate molecule has a very short lifetime because of