Page 242 - Modeling of Chemical Kinetics and Reactor Design

212 Modeling of Chemical Kinetics and Reactor Design

The rate constant k can be determined at varying temperature T
T
from the half-life t as follows:
1/2
−
−
t 12 = 2 n 1 − 1   RT   n 1 (3-327)
(
−
kn 1)  p AO 
T
At the initial pressure of 1 atm, p AO = 1 and n = 2. Therefore,
t in Equation 3-327 is t = RT/k and k = RT/t . Table 3-22
T
1/2
T
1/2
1/2
can be constructed from Table 3-20 for values of k , the dependent
T
variable, from varying temperature T and t . Equation 3-331 is of
1/2
the form
Y = Ae BX (3-333)
Linearizing the model Equation 3-333 gives
ln Y = ln A + BX (3-334)

where the constant A = k , and the slope B = –E/R. The computer
O
program PROG1 determines the constants A and B. The constants for
Equation 3-330 are:

• A = 0.3378 × 10 13
• B = –0.29875 × 10 5
• Correlation Coefficient = 0.9999

The gas constant R = 0.08206 l • atm/mol • K.

Table 3-22

 RT 
T(K) t ( sec) 1/T k T   ( l mol• sec )
12
 t 12 
900 5,464 0.00111 0.0135
950 1,004 0.00105 0.0776
1,000 219 0.001 0.3747
1,050 55 0.00095 1.5666