An Overview of Chemical Reaction Analysis - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 133

which is the definition of reaction rate. Bioprocess engineers should be proficient in relating
the change of species in a reactor via mass balance. The direct use of

d C

A

r A

=

(E3-1.1)

d t

for reaction rate is discouraged. The reaction rate is to be obtained from kinetic studies and
the relation of reaction rate to change is obtained by mass or mole balance:

d n j
d t ¼

F j0 F j þ r j V (3.119)

where F j0 is the rate of species j being added to the reactor and F j is the rate of species j being
withdrawn from the reactor.
For bioreactions, reaction rates are normally expressed as the specific rates:
r 0 A ¼

r A
X

(3.25)

where X is the mass concentration of biomass or cells.

r A M A
X

r 0 A M m A ¼

A ¼

(3.27)

where M A is molecular mass of species A.
For an irreversible homogeneous phase reaction, one frequently describes the rate to
a good approximation as

k Y

N S

C O R j
j

r ¼ (3.35)

j ¼1

where O Rj is the order of the reaction with respect to the jth species and the product extends
over all species in the reaction with O Rj ¼ 0 for species that do not affect the rate of reaction.

If the rate is proportional to the concentration of a species raised to a power (O Rj ), we say
that this form of the rate expression is described by “power-law kinetics”. This empirical
function is frequently used to describe reaction rates, but it frequently is not accurate, espe-
cially with surface or enzyme-catalyzed reactions, which are of the main topic of discussion
in this topic.
A reaction is said to be elementary if the rate of reaction follows Eqn (3.35) with the orders
of reaction the same as the stoichiometric coefficients or

Max n

o

O R j ¼ v j ; 0

A reversible reaction can be decoupled into two reactions, one forward and the other back-
ward. The rate of reaction is the summation (or subtraction as the two reactions move against
each other) of the two rates.
The rate of reaction does not followwith the nonequilibrium thermodynamic theory as the
rate expression in Eqn (3.35) is found to be dependent on the concentration not on the chem-
ical activity. However, one may still be able to correlate the reaction rate constants through
nonequilibrium thermodynamic arguments or via the standard Gibbs free energy change.