An Overview of Chemical Reaction Analysis - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 108

and

C j n j

R Y

N S

k b 0 ¼ exp DS R =

k f 0

(3.88)

j ¼1

These relationships require that reactions be elementary, and it is always true that near
equilibrium all reactions obey elementary kinetics. However, we caution once again that in
general kinetics is empirically determined. These arguments show that near equilibrium
the kinetics of reactions must be consistent with thermodynamic equilibrium requirements.
Note also that the description of a reaction as irreversible simply means that the equilib-
rium constant is so large that r f »

r b . The notion of an irreversible reaction is an operational
one, assuming that the reverse reaction rate is sufficiently small compared to the forward
reaction so that it can be neglected. It is frequently a good approximation to assume a reac-
tion to be irreversible when DG R 0 .

Returning to the energy diagrams, Fig. 3.3 , we see that the difference between E f and E b is
the energy difference between reactants and products, which is the heat of the reaction DH R .
The heat of reaction is given by the relation

X

N S

DH R ¼ n j DH fj

(3.89)

j ¼1

0
fj

where DH is the heat of formation of species j. We necessarily described the energy scale

loosely, but it can be identified with the enthalpy difference DH

0
R

in a reaction system at
constant pressure, an expression similar to that derived from classical thermodynamics.
These relations can be used to estimate rate parameters for a back reaction in a reversible
reaction if we know the rate parameters of the forward reaction and the equilibrium proper-
ties DG fj and DH fj .
We emphasize several cautions about the relationships between kinetics and thermody-
namic equilibrium. First, the relations given apply only for a reaction that is close to equilib-
rium and what is “close” is not always easy to specify. A second caution is that kinetics
describes the rate with which a reaction approaches thermodynamic equilibrium, and this
rate cannot be predicted from its deviation from the equilibrium composition, i.e. using argu-
ments from nonequilibrium thermodynamics.
A fundamental principle of bioprocess engineering is that we may be able to find a suitable
catalyst that will accelerate a desired reaction while leaving others unchanged or an inhibitor
that will slow reaction rates. We note the following important points about the relations
between thermodynamics and kinetics:

(1) Thermodynamic equilibrium requires that we cannot go from one side of the equilibrium
composition to the other in a single process.
(2) Kinetics predicts the rates of reactions and which reactions will go rapidly or slowly
toward equilibrium.

One never should try to make a process violate the Second Law of Thermodynamics

G fj alone

( D G 0 and the entropy generation D S 0), but one should never assume that D

predicts what will happen in a chemical reactor.