Page 303 - Modeling of Chemical Kinetics and Reactor Design

Introduction to Reactor Design Fundamentals for Ideal Systems 273

A = 1
B (θ − ) 2 2 (5-36)

Putting X = 0 into Equation 5-35 gives
A

1 = Aθ 2 B +Bθ B +C (5-37)

Putting X = θ /2 into Equation 5-35 yields
B
A
 θ 
1=C 1− B (5-38)
 2 

or

C= 2 (5-39)
2 − θ B

Substituting Equations 5-36 and 5-39 into Equation 5-37 gives

θ 2 2
1 = B 2 + θ B + (5-40)
B
θ
(θ B − 2) ( 2 − )
B
B=− 2
B (θ − ) 2 2 (5-41)

The integral of Equation 5-34 between the limits becomes

X A=09 .
I = ∫ dX A 2
− (1 X )(θ −2 X )
X A=0 A B A
X A X A
= 1 ∫ dX A − 2 ∫ dX A
B (θ − ) 2 2 0 1 − X A B (θ − ) 2 2 0 B (θ − 2 X )
A

X A
2 dX A
+ ∫ 2 (5-42)
(2 − θ B) 0 B (θ −2 X )
A