Page 173 - Introduction to chemical reaction engineering and kinetics

7.1 Simple Homogeneous Reactions 155

7.1 SIMPLE HOMOGENEOUS REACTIONS

7.1.1 Types of Mechanisms

A reaction mechanism may involve one of two types of sequence, open or closed
(Wilkinson, 1980, pp. 40,176). In an open sequence, each reactive intermediate is pro-
duced in only one step and disappears in another. In a closed sequence, in addition to
steps in which a reactive intermediate is initially produced and ultimately consumed,
there are steps in which it is consumed and reproduced in a cyclic sequence which
gives rise to a chain reaction. We give examples to illustrate these in the next sections.
Catalytic reactions are a special type of closed mechanism in which the catalyst species
forms reaction intermediates. The catalyst is regenerated after product formation to
participate in repeated (catalytic) cycles. Catalysts can be involved in both homoge-
neous and heterogeneous systems (Chapter 8).

7.1.2 Open-Sequence Mechanisms: Derivation of Rate Law from Mechanism
The derivation of a rate law from a postulated mechanism is a useful application of
reaction mechanisms. It shows how the kinetics of the elementary reaction steps are
reflected in the kinetics of the overall reaction. The following example illustrates this
for a simple, gas-phase reaction involving an open sequence. The derivations typically
employ the stationary-state hypothesis (SSH) to eliminate unknown concentrations of
reactive intermediates.

The decomposition of N,O, to NO, and 0, is a simple system (if we ignore dimerization
of NO, to N,O,) and a first-order reaction:

2N,O, +4NO, + 0, (A)

r02 = kobsCN205
A proposed mechanism (Ogg, 1953) is as follows:
N,O, $NO, + NO, (1)
1

NO,+NO,~NO+O,+NO, (2)

NO + NO, %2NO, (3)
(a) Show how the mechanism can be made consistent with the observed (overall) stoi-
chiometry.
(b) Derive the rate law for this mechanism so as to show consistency with the observed
form, and to interpret kobs in terms of the rate constants for the individual steps.
(c) Relate the experimental activation energy, EA,Obs, to the activation energies of the
individual steps, if (i) step (2) is fast, and (ii) step (2) is the rate-determining step.

SOLUTION
(a) We note first that the reactive intermediates in the mechanism are NO3 and NO, which
do not appear either in the overall stoichiometry (reaction (A)) or in the observed rate law.