Page 160 - Modeling of Chemical Kinetics and Reactor Design

130 Modeling of Chemical Kinetics and Reactor Design

 (1− X ) −+ 1  X A
n
−
 A  = kC n AO 1 t (3-80)
 1− n 0 
( 1− X A ) 1−n −= kC n AO 1 ( 1− ) n t (3-81)
−
1

Table 3-2 gives solutions for some chemical reactions using the
integration method.

METHOD OF HALF-LIFE t 1/2

As previously discussed, the half-life of a reaction is defined as the
time it takes for the concentration of the reactant to fall to half of its
initial value. Determining the half-life of a reaction as a function of
the initial concentration makes it possible to calculate the reaction
order and its specific reaction rate.
Consider the reaction A → products. The rate equation in a constant
volume batch reaction system gives

− ( r ) = −dC A = kC n (3-82)
A A
dt
Rearranging and integrating Equation 3-82 with the boundary
conditions t = 0, C = C and t = t, C = C gives
A AO A A

C A t
∫
− ∫ dC A = dt
C n (3-83)
C AO A 0

n
C −+1  C A
−  A  = kt (3-84)
 −+1  C AO
n
1 C { A } C A
−
1 n
( n − 1) C AO = kt (3-85)
C { 1− n − C } = ( −
kt n 1)
1−
n
A AO (3-86)