Page 169 - Modeling of Chemical Kinetics and Reactor Design

Reaction Rate Expression 139

Rearranging Equation 3-121 and integrating between the limits gives

C A dC t
∫
∫ − A ) = kdt (3-122)
C AO C A (C O −C A 0
Converting the left side of Equation 3-122 into partial fractions gives

1 ≡ p + q
C ( C − C ) C A C − C A (3-123)
O
A
A
O
1 ≡ p(C – C ) + qC
O A A
Equating the coefficients

Constant 1 = pC O

“C ” 0 = –p + q
A
p = q

p = q = 1
C O

Integrating Equation 3-122 between the limits gives

 C A C A  t

−  ∫ 1 dC A + ∫ 1 dC A )  ∫ (3-124)
 = kdt

C C O C A C O (C O − C A  0
 AO C AO
 C 1  C −C  

 1
−  ln A − ln  O A   = kt

C
 O C AO C O  C O −C AO 
 C  C − C   C C


ln  AO  O A   = ln B BO = Ckt
 C A  C − C AO  C A C AO O (3-125)


O
The fractional conversion, X , and the initial reaction ratio, θ =
B
A
C BO /C AO , yields