An Overview of Chemical Reaction Analysis - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 92

where X is the biomass concentration, m X is the dry weight of the biomass, and V is the
volume of the culture. Thus,

r A
X

r 0 A ¼ (3.25)

One commonly used rate in bioprocess engineering is the specific reaction rate or

Mass of species A formed
Time

m A ¼ (3.26)

Mass of Catalyst

That is,

r A M A
X

r 0 A M A ¼

m A ¼ (3.27)

where M A is the molecular mass of species A.
The specific reaction rate is commonly used in biological reactions due to the complexity
of the molecules involved, whereby the number of moles is not easy to measure or compute.
For example, the exact numbers of all the atoms in the living cells or microorganisms are not
easily available and can differ from one particular cell to another at various stages of their
life. Counting the number of cells is not very easy, but it can be done. The lack of exact
composition of all the cells, however, hinders chemical analysis if the number of cells is
used. Mass, on the other hand, can be measured more easily by weighing. Therefore, the
specific rate as defined by Eqn (3.26) is commonly used in cases where biological reactions
are involved.

Example 3-1. Is sodium hydroxide reacting?
The reaction rate is defined by Eqn (3.20) .Ifwenoticethattheconcentration,Eqn (3.21) ,
takes care of both number of moles and volume, we can further simplify the rate
definition to

d C A
d t

r A ¼ (E3-1.1)

In fact, you could find many topics define the reaction rate this way. Before we discuss
whether this definition is correct, let us consider the following operation as illustrated
in Fig. 3.1 .
Sodium hydroxide and fat (triglycerides) are continuously fed to a heated stirred tank in
which they react to form soap (sodium fatty acetate) and glycerol:

3 NaOH þ fat / 3 soap þ HOCH CH ð OH Þ CH OH (E3-1.2)

2 2

One triglyceride (fat) molecule reacts with three sodium hydroxide (NaOH) molecules
produces three sodium fatty acid salt (soap) molecules and one glycerol molecule. The
product stream, containing soap and glycerol, together with the unreacted sodium hydroxide
and fat, is continuously withdrawn from the tank at a rate equal to the total feed rate. The
contents of the tank in which this reaction is taking place may be considered to be perfectly
mixed. Because the system operates at steady state, if we were to withdraw liquid samples at
some location in the tank at various times and analyze them chemically, we would find that
the concentrations of the individual species in the different samples were identical. That is,