An Overview of Chemical Reaction Analysis - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 93

NaOH Fat

H 2 COC(O)(CH 2 ) 14 CH 3

Fat

HCOC(O)(CH 2 ) 14 CH 3
H 2 COC(O)(CH 2 ) 14 CH 3

Soap: NaOC(O)(CH 2 ) 14 CH 3
Glycerol: HOCH 2 CH(OH)CH 2 OH

FIGURE 3.1 Well-mixed reaction vessel for soap production.

the concentration of the sample taken at 8 am is the same as that of the sample taken at 2 pm.
Because the species concentrations are constant and therefore do not change with time,

d C j
d t ¼ 0

(E3-1.3)

for any four species involved. Substitution of E(3-1.2) into (E3-1.1), however, would lead to
r j ¼ 0 (E3-1.4)

which is incorrect because glycerol and soap are being formed from NaOH and fat at finite
rates. Consequently, the rate of reaction as defined by Eqn (E3-1.1) cannot apply to a flow
system and is incorrect if it is defined in this manner.

Example 3.1 has touched on the issue of reaction rate for different species involved in the
same reaction. One can imagine that all the rates are related as there is only one reaction; in
this example, the rate of formation of ethanol should be the same as the rate of formation of
sodium acetate. In general, the rates can be related through stoichiometry, i.e. atom balance
involving the reaction system. For convenience and clarity, we define a reaction rate specific
form based on a given stoichiometry by

r j
n j

r ¼ (3.28)

To avoid confusion in multiple reaction systems, the reaction rate for each reaction is given by

r ij
n ij

r i ¼ (3.29)

While r j or r ij does not change, r or r i does change with stoichiometry. In other words, how
you write the reaction will influence the stoichiometry-based rate form.

3.3.2. Rate of a Single Irreversible Reaction
It is found by experiment that rates almost always have power-law dependences on the
densities (such as concentration, density on a surface, or partial pressure) of chemical species.