Page 108 - Introduction to chemical reaction engineering and kinetics

90 Chapter 5: Complex Systems

5.2 MEASURES OF REACTION EXTENT AND SELECTIVITY

5.2.1 Reaction Stoichiometry and Its Significance

For a complex system, determination of the stoichiometry of a reacting system in the
form of the maximum number (R) of linearly independent chemical equations is de-
scribed in Examples 1-3 and 1-4. This can be a useful preliminary step in a kinetics study
once all the reactants and products are known. It tells us the minimum number (usu-
ally) of species to be analyzed for, and enables us to obtain corresponding information
about the remaining species. We can thus use it to construct a stoichiometric table cor-
responding to that for a simple system in Example 2-4. Since the set of equations is not
unique, the individual chemical equations do not necessarily represent reactions, and
the stoichiometric model does not provide a reaction network without further informa-
tion obtained from kinetics.

Spencer and Pereira (1987) studied the kinetics of the gas-phase partial oxidation of CH,
over a Moo,-SiO, catalyst in a differential PFR. The products were HCHO (formalde-
hyde), CO, C02, and H,O.
(a) Obtain a set of R linearly independent chemical equations to represent the stoi-
chiometry of the reacting system.
(b) What is the minimum number of species whose concentrations must be measured
experimentally for a kinetics analysis?

SOLUTION
(a) The system may be represented by

{(CH,, O,, H,O, CO, CO,, HCHO), (C, 0, H))

Using manipulations by hand or Mathematics as described in Example 1-3, we obtain the
following set of 3 (R) equations in canonical form with CH,, O,, and HZ0 as components,
and CO, CO,, and HCHO as noncomponents:

CH, + ;02 = 2H,O + CO (1)

CH, + 20, = 2H,O + CO, (2)
CH, + 0, = H,O + HCHO (3)

These chemical equations may be combined indefinitely to form other equivalent sets of
three equations. They do not necessarily represent chemical reactions in a reaction net-
work. The network deduced from kinetics results by Spencer and Pereira (see Example
5-8) involved (3), (l)-(3), and (2) as three reaction steps.
(b) The minimum number of species is R = 3, the same as the number of equations or
noncomponents. Spencer and Pereira reported results in terms of CO, CO,, and HCHO,
but also analyzed for O2 and CH, by gas chromatography. Measurements above the min-
imum number allow for independent checks on element balances, and also more data for
statistical determination of rate parameters.