Page 31 - Introduction to chemical reaction engineering and kinetics

1.4 Aspects of Kinetics 13

From this matrix, C = rank(M) = rank(A) = 3; the three components are H,, CO,, and
Hz0 in order. The two noncomponents are CH, and CO. Also, R = N - C = 5 - 3 = 2.
Therefore, a proper set of equations, indicated by the entries in the last two columns, is:

+4H, + lC0, - 2H,O = lCH,

+lH, + lC0, - lH,O = 1CO
in canonical form, or, in conventional canonical form,

4H, + CO, = 2H,O + CH,

H, + CO2 = H,O + CO
In general, corresponding to equation 1.4-7 for a simple system, we may write a set
of chemical equations for a complex system as

g VijAi = 0; j=1,2 >..., R (1.4-10)

where vii is the stoichiometric coefficient of species i in equation j , with a sign conven-
tion as given for equation 1.4-7.
These considerations of stoichiometry raise the question: Why do we write chemical
equations in kinetics if they don’t necessarily represent reactions, as noted in Exam-
ple l-3? There are three points to consider:
(1) A proper set of chemical equations provides an aid in chemical “book-keeping”
to determine composition as reaction proceeds. This is the role of chemical stoi-
chiometry. On the one hand, it prescribes elemental balances that must be obeyed
as constraints on reaction; on the other hand, in prescribing these constraints, it
reduces the amount of other information required (e.g., from kinetics) to deter-
mine the composition.
(2) For a given system, one particular set of chemical equations may in fact corre-
spond to a set of chemical reactions or steps in a kinetics scheme that does repre-
sent overall reaction (as opposed to a kinetics mechanism that represents details
of reaction as a reaction path). The important consequence is that the maximum
!’ number of steps in a kinetics scheme is the same as the number (R) of chemi-
cal equations (the number of steps in a kinetics mechanism is usually greater),
and hence stoichiometry tells us the maximum number of independent rate laws
that we must obtain experimentally (one for each step in the scheme) to describe
completely the macroscopic behavior of the system.
(3) The canonical form of equation 1.4-10, or its corresponding conventional form,
is convenient for relating rates of reaction of substances in a complex system,
corresponding to equation 1.4-8 for a simple system. This convenience arises be-
cause the rate of reaction of each noncomponent is independent. Then the net
rate of reaction of each component can be related to a combination of the rates
for the noncomponents.

For the system in Example 1-3, relate the rates of reaction of each of the two components,
to the rates of reaction of the noncomponents.
rCzH6 md ?-Hz 3