Page 154 - Modeling of Chemical Kinetics and Reactor Design

124 Modeling of Chemical Kinetics and Reactor Design

Rearranging Equation 3-50 and integrating between the limits yields

C A −dC t
∫ 2 A = kdt (3-51)
∫
C AO C A 0

C A
 1 
  = kt
 C A  (3-52)
C AO

1 1
− = kt
C A C AO (3-53)

or

1 1
= + kt
C A C AO (3-54)

In terms of the fractional conversion, X , Equation 3-50 becomes
A
C AO dX A = kC (1 − X ) 2
2
dt AO A (3-55)

Rearranging Equation 3-55 and integrating gives

X A dX t
∫ A 2 = kC AO ∫ dt (3-56)
A
0 ( 1− X ) 0
Equation 3-56 yields

 1 
X A
 (  = kC AO t (3-57)
0  1 X− A ) 

Equation 3-57 gives