Chemistry Reference
In-Depth Information
The corresponding expression for the thermal effect is
t
end
1
m
Q
=
[
α
(T)S
−
M
ω
b
]
Δ
Tdt
.
(6.8)
0
Expressions for the reaction rate and degree of conversion (omitted for the sake of
brevity) also contain a correction term
M
b
that can be neglected in practice. Since
for commonly used diluents (Al, Al
2
O
3
,SiO
2
and others), the value of parameter
b
in Eq. (6.6) is lower than or equal to 4
ω
10
−
3
Jdeg
−
2
g
−
1
, the following inequality
is always valid for moderate heating rates (
×
10 deg min
−
1
):
ω
≤
M
ω
b
(
T
)
S
<<
1
.
α
Thus, in contrast to the temperature dependence
α
=
α
(
T
) (which is determined in
a special experiment as
S
(
T
), where
S
is the heat-exchange surface; see Chap. 7),
C
=
C
(
T
) can b
e n
eglected in the calculation of
Q
,
α
. In this case, th
e
diluent
heat capacity
C
(
T
) corresponding to the average experimental temperature
T
can be
substituted into the formulae.
Thus, to obtain an intermediate data array including the thermal effect (
Q
) and
sets of values for the temperature (
T
), conversion degree (
η
and ˙
η
) and reaction rate (
˙
)
for a certain time (
t
), one should measure the time dependence of the DTA signal
Δ
η
η
T
=
Δ
T
(
ω
,
t
) and that of the reference substance temperature
T
ref
=
T
ref
(
ω
,
t
).
,
t
) with respect to time,
Q
and
˙
=
˙
) can
be obtained via the following set of equations derived from Eqs. (6.3) and (6.4):
After differentiating
Δ
T
=
Δ
T
(
ω
η
η
(
T
,
η
∞
1
m
Q
=
α
(
T
)
S
Δ
Tdt
,
(6.9)
0
⎡
⎤
t
,
t
)=
1
Qm
⎣
MC
⎦
,
η
=
η
(
ω
Δ
T
+
α
(
T
)
S
Δ
Tdt
(6.10)
0
Qm
MC
(
T
.
,
t
)=
1
T
)+
˙
=
˙
η
η
(
ω
Δ
α
(
T
)
S
Δ
(6.11)
Since the relationship
T
=
T
ref
+
,
t
) is known, Eqs. (6.10) and (6.11) can
be considered a parametric form of the kinetic equation. Indeed, the dependence
˙
Δ
T
=
T
(
ω
=
˙
η
and
t
from them.
Let us graphically illustrate the described analytical approach. The experimental
DTA curves (
η
(
T
,
η
) can be obtained by eliminating
ω
Δ
T
=
Δ
T
(
ω
,
t
)) obtained for various linear heating rates (
ω
1
,
ω
2
,
ω
i
)
and corresponding plots of the working cell temperature against time (
T
=
T
(
,
t
))
are shown in Fig. 6.2a,b. Analysis of these data using Eqs. (6.10) and (6.11) yields
the time dependencies of the conversion degree (
ω
,
t
)) and the reaction rate
η
=
η
(
ω
( ˙
η
= ˙
η
(
ω
,
t
)) for the same linear heating rates (Fig. 6.2c, d). Drawing a straight
