Page 306 - Modeling of Chemical Kinetics and Reactor Design

276 Modeling of Chemical Kinetics and Reactor Design

for the reaction assuming that A and B are ideal gases, and starting
with pure A at N AO . Derive a general expression for time t in terms
of the fractional conversion X for an nth order reaction expressed
A
by A → bB.

Solution

Since the volume depends on conversion or time in a constant
pressure batch reactor, consider the mole balance in relation to the
fractional conversion X . From the stoichiometry,
A

Component A B
At time t = 0 N 0
AO
At time t = t N N
A B
Amount reacted (N – N ) N
AO A B
From the stoichiometry,
2N ( AO − N )= N B (5-47)
A

the fractional conversion X is
A
X = N AO − N A
A (5-8)
N AO
From Equation 5-8, the amount reacted in terms of the fractional
conversion and the initial moles is

N AO − N = N AO X A (5-48)
A
and

N = N (1 − X ) (5-9)
A
A
AO
Differentiating Equation 5-9 gives

dN =− N AO dX A (5-10)
A
Therefore, the amount of component B is