Batch Reactor - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 148

is occurring in an isothermal constant pressure batch reactor. The reactor is charged initially
with pure A at 1 bar and 373 K. Determine the time required for the reaction volume to
expand by 50%, i.e. V / V 0 ¼

1.5.
Solution. A sketch of the batch reactor is shown in Fig. E4-2.1 . The stoichiometry of the reac-
tion system is given by

A ! B þ C

t ¼ 0 : n A0 0 0 þÞ ¼ n A0

t ¼ t : n A n B n C þÞ ¼ n T

n A n A0 n A n A0 n A þÞ ¼ 2n A0 n A

Assume ideal gas law applies. The volume of the reaction mixture and concentration of A
in the reactor are given by

V ¼ n T RT
P

2n A0 n A
n A0

¼ V 0 (E4-2.1)

C A ¼ p A

RT ¼ n A

P
RT ¼

n A
2n A0 n A C A0

(E4-2.2)

n T

Based on Eqn (E4-2.1) , we obtain

n A0 ¼ 2 V

n A

(E4-2.3)

V 0

Thus, the extent of reaction is dependent on the volume expansion. Mole balance of A in the
reactor gives

d n A

d

0 0 þ r A V ¼ (E4-2.4)

t

P = 1 bar

t = 0:
p A = = 1 bar

p B = p C = 0
V = V 0

P

A, B, C

T = 373 K

FIGURE E4-2.1 A schematic diagram of a constant pressure batch reactor.