Page 178 - Modeling of Chemical Kinetics and Reactor Design

148 Modeling of Chemical Kinetics and Reactor Design

Integrating Equation 3-161 between the boundary conditions t = 0,
C = C AO and t = t, C = C gives
A
A
A
α
− 1 ln [C A − ] C A = t (3-162)
k + k C AO
1 2
That is:

α
α
− 1 ln ( [ C A − ) − (C AO − )] = t (3-163)
ln
k 1 + k 2
Substituting Equation 3-160 into Equation 3-163 gives
(
  kC −C )


−  ln C A − 2 AO BO 
  k 1 + k 2 

(
 kC −C )  (3-164)

− ln C AO − 2 AO BO   = (k 1 + )t

k
2
 k 1 + k 2 

 (  k + )C − k C + k C 

k
−  ln  1 2 A 2 AO 2 BO 
  (k 1 + )  (3-165)
k

2

 k C + kC − kC + kC 
2
−ln  1 AO 2 AO + ) AO 2 BO  =(k 1 + )t
k
2

 (k 1 k 2 
( [ { )]
k
k
− ln k 1 + )C A − (C AO − C BO
2
2
(3-166)
ln
− [kC AO + k C BO ]} =(k 1 + )t
k
2
2
1
or
  k 1  
  +1  C A −(C AO −C BO )
−    k 2   1 + )t (3-167)
k
ln
 =(k
2
  k 1 C +C  
   k 2 AO BO   

