Page 159 - Modeling of Chemical Kinetics and Reactor Design

Reaction Rate Expression 129

EMPIRICAL RATE EQUATIONS OF THE nth ORDER

IRREVERSIBLE REACTIONS

The rate equation for irreversible reactions for a constant volume
batch system (i.e., constant density) is

− ( r A )= −dC A = kC n A (3-73)
dt
Boundary conditions are: at t = 0, C = C AO and t = t, C = C .
A
A
A
Integrating Equation 3-73 between the limits gives
C A −dC t
∫ A = dt
∫
C n A (3-74)
C AO 0

n
C −+1  C A
−  A  = kt (3-75)
 −+1  C AO
n

1 C { 1 n − C } =
−
−
1 n
( n − 1) A AO kt (3-76)
1− n 1− n = ( n 1)
C − C − kt (3-77)
A AO
The value of n must be found by trial-and-error. In terms of the
fractional conversion, X , the rate equation is
A
dX A n n
− ( r A )=C AO = kC AO (1 − X A ) (3-78)
dt

Boundary conditions are: at t = 0, X = 0, and t = t, X = X .
A
A
A
Rearranging and integrating Equation 3-78 between the limits gives
X A dX t
∫ A n = kC AO ∫ dt (3-79)
n 1−
A
0 ( 1− X ) 0