Page 27 - Introduction to chemical reaction engineering and kinetics

1.4 Aspects of Kinetics 9

where N is the number of reacting species in the system, vi is the stoichiometric coeffi-
cient for species i [negative (-) for a species written on the left side of = and positive
(+) for a species written on the right side], and Ai is the molecular formula for species
i . For a simple system, if we know the rate of reaction for one species, then we know the
rate for any other species from the chemical equation, which gives the ratios in which
species are reacted and formed; furthermore, it is sometimes convenient to define a
species-independent rate of reaction r for a simple system or single step in a mecha-
nism (Chapter 6). Thus, in Example 1-2, incorporating both of these considerations, we
have
ro,
rso3
rso,
y=-.=---=-
-2 -1 2
where the signs correspond to consumption (-) and formation (+); r is positive.
More generally, for a simple system, the rates Y and ri are related by

r = rilui; i = 1,2,...,N (1.4-8) /

We emphasize that equation 1.4-7 represents only reaction stoichiometry, and has no
necessary implications for reaction mechanism or reaction equilibrium.2 In many cases
of simple systems, the equation can be written by inspection, if the reacting species and
their molecular formulas are known.
A complex reacting system is defined as one that requires more than one chemical
equation to express the stoichiometric constraints contained in element balances. In
such a case, the number of species usually exceeds the number of elements by more
than 1. Although in some cases a proper set of chemical equations can be written by
inspeefion, it is useful to have a universal, systematic method of generating a set for a
system of any complexity, including a simple system. Such a method also ensures the
correct number of equations (R), determines the number (C) and a permissible set
of components, and, for convenience for a very large number of species (to avoid the
tedium of hand manipulation), can be programmed for use by a computer.
A procedure for writing or generating chemical equations has been described by
Smith and Missen (1979; 1991, Chapter 2; see also Missen and Smith, 1989). It is an
extension of the procedure used in Example 1-2, and requires a list of all the species

2We use various symbols to denote different interpretations of chemical statements as follows (with SOa oxi-
dation as an example):
2so2 + 02 = 2so3, (1)
as above, is a chemical equation expressing only conservation of elements S and 0;

2so2 + 02 -+ 2so3 (2)
(also expresses conservation and) indicates chemical reaction occurring in the one direction shown at some
finite rate;
2so* + 02 e 2so3 (3)
(also expresses conservation and) indicates chemical reaction is to be considered to occur simultaneously in
both directions shown, each at some finite rate;
2so2 + o* =2so, (4)
(also expresses conservation and) indicates the system is at chemical equilibrium; this implies that (net rate)
r = ri = 0.