Page 226 - Modeling of Chemical Kinetics and Reactor Design

196 Modeling of Chemical Kinetics and Reactor Design

Table 3-15
Half-life t 1/2 as function of initial concentration C AO
Run number C AO , gmol/l Half-life, t 1/2 min

1 0.025 4.1
2 0.0133 7.7
3 0.01 9.8
4 0.05 1.96
5 0.075 1.30
6 0.025 2.0

Taking the natural logarithm of Equation 3-286 yields

−
ln t ( 12) = ln 2 kn 1) 1 + ( 1− n ) lnC AO (3-287)
−
n 1
(
−
A plot of C AO versus t on log-log paper should give the slope of
1/2
the line equal to (1 – n). However, Equation 3-287 can also be
represented in the form

Y = AX B (3-288)

Linearizing Equation 3-288 gives

ln Y = ln A + B ln X (3-289)

The constants for Equation 3-289 are:

• A = 0.0878
• B = 1.0032
• Correlation Coefficient = 0.97195

The slope of the line B = 1 – n. The computer program PROG1
gives the slope B = –1.003, therefore, the order of reaction n = 2.
When t = 5 min, and C AO = 0.022 gmol/l at 100°C, then from
1/2
Equation 3-286

−
k = 2 n 1 − 1 1
−
100 ( n 1− ) C n 1 t 12
AO