Page 239 - Modeling of Chemical Kinetics and Reactor Design

Reaction Rate Expression 209

Rearranging Equation 3-317 and integrating between the limits t = 0,
C = C AO and t = t, C = C gives
A
A
A
C A dC t
∫
− ∫ 2 A = kdt (3-318)
C AO C A 0

Integrating Equation 3-318 yields

 1 
C A
  = kt (3-319)
 C A 
C AO

1 1  E 
− = k exp − t (3-320)
C C O  RT 
A AO
Therefore, the concentration of species A in terms of C AO and k is

1 1  E 
= + k exp − t (3-321)
C C O  RT 
A AO
(2) The half-life t equation for the general nth-order reaction is
1/2
2 ( n 1 − 1) C 1− n
−
t = AO (3-322)
(
12 kn 1)
−
Since the reaction order is two, that is n = 2, this can be substituted
in Equation 3-322 to obtain

1
t 12 = C − AO = 1 (3-323)
k kC
AO
where

C AO = n AO = p AO V = p AO (3-324)
V RTV RT

Substituting Equation 3-324 into Equation 3-323 gives