Page 215 - Modeling of Chemical Kinetics and Reactor Design

Reaction Rate Expression 185

Equating the coefficients of the constant and X gives
A
“Const” 1 = Aθ + B (3-268)
B
“X ” 0 = –3A – B (3-269)
A
Adding simultaneous Equations 3-268 and 3-269 gives 1 = A(θ – 3).
B
Therefore, A = 1/(θ – 3) and B = –3A = –3/(θ – 3). Equation 3-
B
B
267 is now expressed as

t

1  X A dX A − X A 3 dX A  kdt
∫
∫
∫
 =

B (
B (
31 X−
C AO  0 θ − )( A ) 0 θ − 3 θ )( B − 3X )  0


A

−
= 1  − (1 X A ) − 3  −  1 ln ( B − 3X A ) = kt
θ
 ln
θ
3
C AO ( B − )   3  
 θ −3X ) 
1
=  ln ( B A  = kt (3-270)
3
C θ − )  − (1 X ) 
AO ( B  A 
Introducing the initial concentrations of A and B, that is, C AO and
C BO into Equation 3-270 gives
1   C BO C AO − 3X  
  =
A
 ln

 C    1 X A  kt (3-271)
−


C AO BO − 3 
 C AO 
 3X 
1 C BO C AO − A  =
C ( − 3C ) ln  1 X )  kt (3-272)
− (

BO AO  A 
Rearranging Equation 3-272 gives
 C C − 3 X 
ln  BO AO A  = kt C ( BO −3 C ) (3-273)
AO
 1 − X A 