Page 214 - Modeling of Chemical Kinetics and Reactor Design

184 Modeling of Chemical Kinetics and Reactor Design

Substituting Equations 3-258 and 3-261 into Equation 3-256 gives

− dC A = kC AO (1 − X A )(C BO − C AO X A ) (3-262)
3
dt
Substituting Equation 3-259 into Equation 3-262 and rearrang-
ing gives

C AO dX A =
C ( 1− X )( C BO − 3 C AO X ) kdt (3-263)
A
A
AO
Integrating Equation 3-263 between limits t = 0, X = 0 and t = t,
A
X = X gives
A
A
X A dX t
∫
∫ ( X )( A X ) = kdt (3-264)
0 1− A C BO − 3 C AO A 0

Equation 3-264 can be further expressed by

X A dX t
∫
∫ A = kdt (3-265)
0 C ( 1− X )   C BO − 3 X A  0
A
AO
 C AO 
where θ = C /C . Equation 3-265 becomes
B BO AO

X A dX t
∫
∫ C ( A X ) = kdt (3-266)
A
0 AO 1− X )(θ B − 3 A 0
Converting Equation 3-266 into partial fraction gives

1 ≡ A + B
( 1− X A )( B − 3X A ) 1− X A θ B − 3X A (3-267)
θ

A θ − )+ )
A A
1= ( B 3X 1− ( B X