Page 213 - Modeling of Chemical Kinetics and Reactor Design

Reaction Rate Expression 183

Solution

The reaction in stoichiometry can be represented as


k
A + 3 B  → Products (3-255)
Assuming that the reaction is second order in a constant volume
batch system, the rate equation is

− ( r A ) = −dC A = kC C B (3-256)
A
dt
From stoichiometry:

A B
Amount at t = 0 C AO C BO
Amount at t = t C A C B
Amounts that have reacted (C AO – C ) (C BO – C )
A
B
and (C – C ) = 3(C – C ). The fractional conversion X is
BO B AO A A
defined as

X = C AO − C A (3-257)
A
C AO
Therefore,

C = C (1 – X ) (3-258)
A AO A
Differentiating Equation 3-258 with respect to time t gives

− dC A = C AO dX A (3-259)
dt dt

The concentration of B is

C = C BO − C ( 3 AO − C ) (3-260)
B
A
In terms of the fractional conversion, the concentration of B is

C = C −3 C X (3-261)
B BO AO A