Batch Reactor - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 144

As the stoichiometrical coefficients are true constants for a given reaction, the total number of
moles in the reactor can be computed by adding the number of moles for all the components
(species) up. That is

n ¼ N S

j¼1 n j ¼ N S

n j0 þ n j n A n A0
n A

j¼1

(4.11)

N S

¼ n 0 þ n A n A0
n A

n j

j¼1

Letting n S be the total stoichiometric coefficients, i.e.

N S

n S ¼ n j (4.12)

j¼1

We obtain

n ¼ n 0 þ n S

n A ðn A n A0 Þ

(4.13)

While the above derivation is concise, we often tabularize the stoichiometry to gain a thor-
ough 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 Table 4.1 .
The concentration can be related to the number of moles in the reactor through

n j0 þ n j

n A ðn A n A0 Þ
V

C j ¼ n j

V ¼

(4.14)

which can be further reduced to

r 0 C j0 þ n j

C j ¼ r C A r

r 0 C A0

(4.15)

n A

TABLE 4.1 Stoichiometry of a Reaction System in a Batch Reactor

Species Initial Change At time t

A n A0 n A en A0 n A

n j n j0 ¼ n j n A n A 0
n A

n j ¼ n j0 þ n j n A n A 0
n A

j n j 0

. . . .

N S N S

j¼1 ðn j n j0 Þ¼n S n A n A 0 j¼1 n j ¼ n 0 þ n S n A n A 0

Total n 0

n A n A