An Overview of Chemical Reaction Analysis - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 94

For example, the homogeneous reaction of cyclopropane to propylene exhibits a rate of
decomposition that can be written as

r ¼ k ½ cyclopropane (3.30)

while the homogeneous formation of NO 2 from NO and oxygen has a rate

2 ½ r ¼ k ½ NO O 2 (3.31)

where we have used [A] to denote concentrations, i.e.

C

A ¼½

(3.32)

A

In gases, the most used quantity for the density of species j is the partial pressure P j . This
can be related to concentration and mole fraction y j through the relations

n j
P n j ¼

n j
n

y j ¼ (3.33)

and

p j ¼ y j P ¼ C j RT (3.34)

where P is the total pressure and n is the total number of moles in the system. In this equation,
we assume ideal gases (PV nRT) to relate partial pressure to concentration, while for

nonideal gases (not considered here), we would need an equation of state to describe the
density of each chemical species.
For an irreversible reaction, we can frequently describe the rate to a good approximation as

¼

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 is frequently inaccurate, especially with
surface- or enzyme-catalyzed reactions, which are of the main topic of discussion in this
topic.

3.3.3. Rate of an Elementary Reaction
The rate expression (3.35) has been found particularly helpful in many cases although it is
overly simplified. To continue our discussion, let us define an elementary reaction. An
elementary reaction is a reaction whereby the reactants (or reacting molecules) react stoichio-
metrically in each and every instance. For example, if the reaction

(3.36)
is elementary, when A and B meet they can automatically get converted to C without going
through any additional steps. Therefore, elementary reactions are idealized reactions or

A þ B / C