Chemistry Reference
In-Depth Information
Table 2.1
Values of
ʱ
m
and
ʱ
p
corresponding, respectively, to the maximum of the
y
(
ʱ
) and
z
(
ʱ
)
functions for different kinetic models [
37
]
Kinetic model
ʱ
m
ʱ
p
R2
0
0.750
R3
0
0.704
F1
0
0.632
A2
0.393
0.632
A3
0.283
0.632
SB
a
m
/(
n
+
m
)
?
b
D2
0
0.834
D3
0
0.704
a
SB stands for the truncated Sestak-Berggren equation (Eq. 2.32)
b
There is no general analytical solution for
ʱ
p
Fig. 2.15
Some
y
(
ʱ
) plots
built by normalizing the
f
(
ʱ
)
functions of the respective
reaction models (Table 1.1)
A2
A3
1.0
R2
0.8
R3
0.6
0.4
0.2
D2, D3
0.0
0.0
0.2
0.4
0.6
0.8
1.0
α
The
z
(
ʱ
) master plots are derived by combining the differential and integral
forms of the reaction models. The temperature integral in Eq. 2.8 can be replaced
with one of the multiple approximations [
17
],
π
(
x
), as follows:
AE
R
π
()
,
x
g
()
α
=
exp(
−
x
)
(2.35)
β
x
where
x
=
E
/
RT
. Combining Eqs. 2.35 and 2.2 and performing some rearrangements
allow one to arrive at the
z
(
ʱ
) function as follows:
d
d
α
π
β
()
.
x
T
=
2
(2.36)
z
() ()()
ααα
=
f
g
T
α
t
α
α
The last term in the brackets of Eq. 2.36 can be neglected [
70
] as it does not practi-
cally affect the shape of the
z
(
ʱ
) plot. Therefore, the
z
(
ʱ
) values can be calculated
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