Page 301 - Modeling of Chemical Kinetics and Reactor Design

Introduction to Reactor Design Fundamentals for Ideal Systems 271


k
A + 2 B  → C (5-23)
where component A is the limiting reactant. The material balance on
component A in the batch reactor is

− ( r A )=− 1 dN A (5-7)
V dt
R
where the concentration C = N /V and the rate Equation 5-7 becomes
R
A
A
− ( r A )=− dC A = kC C 2 B (5-24)
A
dt
The concentrations of A and B can be expressed in terms of the
fractional conversion and the stoichiometry of the reaction as:

Component A B
At time t = 0 C AO C BO
At time t = t C C
A B
Amount reacted (C AO – C ) (C BO – C )
A
B
From the stoichiometry,

2C ( AO − C )= C BO − C B (5-25)
A

The concentration of B is expressed as

C = C − C ( 2 − C ) (5-26)
B BO AO A

Using the fractional conversion X at constant volume
A

X = C AO − C A (5-13)
A
C
AO
Therefore, the amount reacted

C AO − C = C AO X A (5-27)
A
or