Page 152 - Modeling of Chemical Kinetics and Reactor Design

122 Modeling of Chemical Kinetics and Reactor Design

Equation 3-42 is resolved into partial fractions as

1 ≡ p + q
A[
C ( C BO − C ) + C A] C A C ( [ BO − C ) + C A] (3-43)
AO
AO
1 ≡ ( [ BO − C AO ) + C A ] + qC A (3-44)
pC

Equating the coefficients of C and the constant on both the right
A
and left side of Equation 3-44 gives
“Const” 1 = p(C BO –C AO )

“C ” 0 = p + q
A
where

p = 1/(C BO – C AO ) (3-45)

and

q = –1/(C –C ) (3-46)
BO AO
Substituting p and q into Equation 3-43 and integrating between the
limits gives

 C A C A 


−  ∫ dC A − ∫ ) ( [ dC A 

C (C BO −C AO )C A (C BO −C AO C BO −C AO )+C A ]
 AO C AO
t
∫
= kdt (3-47)
0

   C ( 
1  C AO  BO − C )+ C A  
AO
 =
 ln
C ( BO − C )  C A + ln     C (   BO − C AO + C )  kt (3-48)
AO 

AO
   C  C (  − C ) + C 
A 
ln   AO   BO AO  = kC ( BO − C ) t (3-49)
AO


   C BO  C A 