Biomedical Engineering Reference
In-Depth Information
In general, the rate of reaction is a function of concentration and temperature. From
Chapter 3, we learned that the stoichiometry can be applied to relate the amount of every
species in the reaction mixture. The amount change of a component participating in the reac-
tion divided by its stoichiometric coefficient is the universal extent of reaction for a single
reaction. The stoichiometry can be written in a flow reactor as
F
j0
F
j
n
j
F
A
0
F
A
n
A
¼
¼ rV
(5.44)
The total molar flow rate can be computed by adding all the component (species) flow rates
up. That is
F
j0
þ n
j
X
N
S
X
N
S
X
N
S
j¼1
n
j
F
A
F
A
0
n
A
F
A
F
A
0
n
A
F ¼
F
j
¼
¼ F
0
þ
(5.45)
j¼1
j¼1
Letting
n
S
be the total stoichiometric coefficients, i.e.,
X
N
S
j¼1
n
j
n
S
¼
(5.46)
We obtain
F ¼ F
0
þ
n
S
n
A
ðF
A
F
A
0
Þ¼F
0
n
S
n
A
F
A
0
f
A
(5.47)
While the above derivation is concise, we often tabularize the stoichiometry to gain a thorough
understanding of the stoichiometry for every species, either be those involved in the reaction or
those that are not participating in the actual reaction. The stoichiometry is shown in
Tabl e 5 .3
.
The concentration can be related to the molar flow rate through
F
j0
n
j
n
A
F
A
0
f
A
Q
F
j
Q
¼
C
j
¼
(5.48)
The volumetric flow rate
Q
can be a function of temperature and pressure (density
change). Since the mass flow rate does not change if no side inlets or outlets, we have
Q ¼
r
0
r
Q
0
(5.49)
TABLE 5.3
Stoichiometry of a Reaction System with Side Inlets or Outlets
Species
At inlet
Change
At outlet
A
F
A0
F
A
F
A
0
F
A
F
j
F
j0
¼ n
j
F
A
F
A
0
n
A
F
j
¼ F
j0
þ n
j
F
A
F
A
0
n
A
j
F
j
0
.
.
.
.
P
N
s
j¼1
ðF
j
F
j0
Þ¼n
S
P
N
s
F
A
F
A
0
n
A
F
A
F
A
0
n
A
Total
F
0
F
j
¼ F
0
þ n
S
j¼1
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