Page 240 - Modeling of Chemical Kinetics and Reactor Design

210 Modeling of Chemical Kinetics and Reactor Design

t = 1
12
kp AO RT
= RT (3-325)
kp
AO
(3) The decomposition of nitrous oxide (N O) to nitrogen and
2
oxygen is represented by

2NO → 2N + O (3-326)
2 2 2
The half-life t of the general nth order reaction is
1/2
2 ( n 1 − 1) C 1− n
−
t = AO
(
−
12 kn 1)
Therefore, using Equation 3-324 gives

−
−
1 
AO 
n 1
2
t 12 = kn 1− )  p RT  1− n (3-327)
(
Taking the natural logarithm of Equation 3-327 gives
−
ln t ( 12) = ln 2 n 1 − − 1 + ( 1− n) ln   p RT  (3-328)
AO 
kn 1)
(
Equation 3-328 can be expressed in the form

Y = AX B (3-329)

Linearizing Equation 3-329 gives

ln Y = ln A + B ln X (3-330)

where the slope B = 1 – n.
From Table 3-19, we can construct the independent variable p /RT
O
at the constant temperature of 1,015 K and the gas constant R =
0.08206 (l • atm/mol • k) (Table 3-21). The dependent variable is t .
1/2