Thermal decomposition kinetics of aluminum sulfate hydrate

Article abstract of DOI:10.1007/s10973-009-0389-5

The kinetics of individual stages of thermal decomposition of Al ₂(SO₄)₃?18H₂O were studied by TG method. It is found that Al₂(SO₄)₃? 18H₂O decomposes to Al₂

Full text of DOI:10.1007/s10973-009-0389-5

J Therm Anal Calorim (2009) 98:855–861
DOI 10.1007/s10973-009-0389-5
Thermal decomposition kinetics of aluminum sulfate hydrate
G u¨ lbanu Koyundereli C¸ ılgı Æ Halil Ceti s¸ li
Received: 2 December 2008 / Accepted: 23 July 2009 / Published online: 13 August 2009
Ó Akad e´ miai Kiad o´ , Budapest, Hungary 2009
Abstract The kinetics of individual stages of thermal
decomposition of Al (SO ) ꢀ18H O were studied by TG
it is very difficult to define a single equation for kinetics of
thermal decomposition events.
2
4 3
2
method. It is found that Al (SO ) ꢀ18H O decomposes to
For many decades aluminum sulfate, has been the
standard raw material of the water treatment industry. It is
large molecular size and weight, combined with low cost,
make it an excellent flocculants for the treatment of both
drinking water and industrial waste water. In addition to
water treatment, aluminum sulfate finds use in a diversity
of other areas including construction products, oil and fat
processing, and paper manufacturing.
2
4 3
2
Al O in four major stages, all of endothermic. Some of
2
3
these major stages are formed by sub-stages. The first three
major stages are dehydration reactions in which two, ten
and six moles water are lost, respectively. The last major
stage is sulfate decomposition. In this study the kinetic
parameter values of these major and sub-stages were cal-
culated by integral and differential methods. The alterations
of activation energies with respect to the decomposition
ratio and to the method were investigated.
The thermal decomposition of sulfate compounds have
been studied for many years [3–6]. Chou and Soong
studied thermal decomposition of anhydrous aluminum
sulfate and aluminum sulfate hydrate compounds under
isothermal and dynamic conditions.
Keywords Thermal decomposition ꢀ Aluminum sulfate ꢀ
Thermogravimetric analysis ꢀ Activation energy
They investigated the effects of various reaction con-
ditions on decomposition kinetic, such as different heating
rates and sample weights [7, 8]. But they did not calculate
activation energy values and determine reaction models for
every decomposition stages.
Introduction
The processes which occur during solid decompositions are
complex leading to experimental observations which can
be very different under even slightly changed conditions.
These problems arise from the great variety of possibly
uncontrolled systems variables, such as the nature of the
solid reactant (single crystal, powder), its pretreatment
In this study, the kinetics of thermal decomposition of
Al (SO ) ꢀ18H O compound has been reexamined in detail
2
4 3
2
from a fresh point of view. Activation energies of decom-
position stages are calculated via, Ozawa, KAS (Kissinger–
Akahira–Sunose), Isoconversional and Friedman model free
equations. The alterations of activation energies with respect
to the decomposition fraction and to the method were
investigated. The reaction enthalpy values of major and sub-
stages were calculated with the help of DTA peak areas.
(
grinding, annealing, etc. which influence the defect con-
tent and its nature), sample mass or size (which affect mass
and energy transfer) and experimental conditions (rate of
temperature rise, pressure, nature of the surrounding
atmosphere, removal or otherwise evolved gases) [1, 2]. So
Thermal decomposition kinetics
G. K. C¸ ılgı (&) ꢀ H. Ceti s¸ li
Department of Chemistry, Faculty of Science and Arts,
Pamukkale University, 20070 Denizli, Turkey
e-mail: gkcilgi@gmail.com
The experimental data for the kinetic analysis of hetero-
geneous solid–gas reactions can be obtained under
123

8
56
G. K. C¸ ılgı, H. Ceti s¸ li
different conditions. The non-isothermal thermogravimetry
TG) with a linear temperature growth is a method fre-
For a = const., the plot of ln da/dt versus 1/T, obtained
from curves, which are recorded at several heating rates,
should be a straight line with a slope that allows an eval-
uation of the activation energy.
(
quently used to characterize materials from their thermal
behavior standpoint. In addition, it enables to determine
apparent kinetic parameters of heterogeneous reactions (the
reaction order n, the activation energy E and the frequency
factor A). Considerable attention is paid to the kinetic
parameters calculation from TG curves. New calculation
methods are still being published [9, 10].
Experimental
Aluminum sulfate-18 hydrate was obtained from Aldrich.
All of the thermogravimetry (TG), derivative thermo-
gravimetry (DTG) and differential thermal analysis (DTA)
curves were obtained simultaneously by using a Shimadzu
DTG-60H Thermal Analyzer. The measurements were
carried out in a flowing nitrogen atmosphere with a flow
We here analyse the data obtained under non-isothermal
conditions, with a linear regime of temperature increase in
time (b = dT/dt = const., where b is the heating rate, T is
the temperature and t is the time). Under such conditions,
for a heterogeneous solid–gas reaction, which occurs in a
single stage, the reaction rate is expressed by the well-
known general equation:
-1
rate of 25 mL min and a temperature ranged from 25 to
1
000 °C in an alumina crucible. The heating rate (b) varied
-1
oa
oT
b ¼ AeꢁE=RT fðaÞ
as 8, 6, and 4 °C min , where the sample mass (w
o
) was
ð1Þ
ranged from 10 to 12 mg. All of the experiments were
performed twice for repeatability and the results showed
good reproducibility with the smaller variations in the
kinetic parameters. Finally, highly sintered Al O was used
where a is the degree of conversion, A is the frequency
factor, E is the activation energy, f(a) is the differential
conversion function and R is the gas constant. Equation 1
may also lead to the corresponding equations of the Ozawa,
KAS, Isoconversional after integration form and Friedman
method after logarithmic form [11–23].
2
3
as the reference material.
Results and discussion
Ozawa equation;
ꢀ
ꢁ
AE
E 1
The thermal analysis results from the evaluation of curves
obtained at all heating rates are summarized in Table 1.
However, only the curve that is obtained at heating rate of
ln b ¼
ꢁ 5:3305 ꢁ 1:05178 R T
ð2Þ
RgðaÞ
For a = const., the plot of ln b versus 1/T, obtained from
curves, which are recorded at several heating rates, should
be a straight line with a slope that allows an evaluation of
the activation energy.
-
1
4
°C min is presented in Fig. 1 as an example. It is found
that aluminum sulfate-18 hydrate’s decomposition consists
of four major steps, all endothermic. Some of these major
steps are formed by sub-stages.
KAS equation;
The 18 moles of water in the compound leaves the body
at three major stages. The peak temperatures for the
dehydration reaction at Stage-I and II, and the temperature
range for the reaction increase with the increase of heating
rate-b, which is programmed during the thermal analysis.
While split of the peaks occurs for the first stage (I)
dehydration event (320.75 K) and for the second stage (II)
dehydration event (336.08 K) at a heating rate of
b
AR
E 1
ln ¼ ln
T2
ꢁ
ð3Þ
gðaÞE R T
2
For a = const., the plot of ln b/S versus 1/T, obtained
from curves, which are recorded at several heating rates,
should be a straight line with slope that allows an evalua-
tion of the activation energy.
Isoconversional equation;
-
1
4
°C min , the peaks of dehydration reaction for Stage-I
A
Ea 1
-1
and II overlaps at highest heating rate (8 °C min ). If two
consecutive physical or chemical events exist, events can
be observed as a single event in the curve for higher
heating rates. Hence, the dehydration reaction enthalpy of
the Stage-I was able to be determined only at lower heating
rates. It is proved by the dehydration reaction enthalpy
ꢁ
ln t ¼ ln
ꢁ
ð4Þ
gðaÞ R T
For a = const., the plot of –ln t versus 1/T, obtained from
curves, which are recorded at several heating rates, should
be a straight line with a slope that allows an evaluation of
the activation energy.
-
1
of the Stage-I at lower heating rate (72.93 kJ mol ),
Friedman equation;
which is higher than the evaporation enthalpy of the water
-
1
40.60 kJ mol ), that the water molecules chemically
oa
ln ¼ ln b dT ¼ ln AfðaÞ ꢁ
ot
da
E
(
ð5Þ
RT
bounded to the compound.
1
23

Thermal decomposition kinetics of aluminum sulfate hydrate
857
123

8
58
G. K. C¸ ılgı, H. Ceti s¸ li
DTA
uV
(a) 80
TG/%
00.0
(
b) 220
160
1
Ozawa
KAS
0.0
320.75
Iso.
Ozawa
KAS
Iso.
Friedman
6
4
2
0
0
0
Friedman
5
61.64
3
36.08
6
29.77
80.0
60.0
40.0
20.0
−20.0
−40.0
100
397.40
40
0
.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
α
α
1091.19
−60.0
−80.0
1
029.14
(c)
(d) 390
2
1
00
40
Ozawa
KAS
Iso.
Temperature/K
265
140
15
4
00.0
600.0
800.0
100.0
1200.0
Ozawa
KAS
Iso.
80
-
1
Friedman
Fig. 1 TG and DTA curves of Al
2
(SO
4
)
3
ꢀ18H
2
O in 4 °C min
20
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
The reaction activation energy values are calculated
using the Ozawa, KAS, Isoconversional and Friedman
methods for all stages and for the values of decomposition
ratios a varying from 0.05 to 1.00. The calculated values
for the activation energies of the dehydration reaction at
Stage-I with respect to the decomposition ratio are pre-
sented in Fig. 2a.
α
α
(
e)130
(f)
Ozawa
KAS
Iso.
525
95
325
60
Ozawa
KAS
Iso.
Friedman
25
125
It is observed that the activation energy values, which
are calculated using these four methods, correlate with
each other and result with an average value of
0
0.2
0.4
0.6
0.8
1
0.0
0.2
0.4
0.6
0.8
1.0
α
α
(
g) 375
-
1
3
6.23 kJ mol . It is also found that, the variations of
2
1
50
25
activation energy values with respect to the decomposition
ratio are similar. The activation energy decreases with an
increase in decomposition ratio, and it reaches to a mini-
mum value for decomposition ratio ranging in between
Ozawa
KAS
Iso.
0
0
0.2
0.4
0.6
0.8
1
0
.45 and 0.55. After reaching to the minimum value, the
α
activation energy increases with the increase in decompo-
sition ratio.
Fig. 2 Variation of activation energy values with decomposition
ratio a, a major reaction step I, b major reaction step II, c reaction step
I ? II (combined step), d major reaction step III, e sub-stage IIIa,
f sub-stage IIIb, g sub-stage IIIc
Since there is not any available information on the
compound-Al (SO ) ꢀ16H O, which is the product of
2
4 3
2
dehydration reaction for the Stage-I, it is supposed that this
compound forms at reaction stage and is not stable at
ambient conditions. In other words, it is found that the
dehydration reaction at Stage-I is reversible.
The activation energy values of dehydration reaction at
Stage-II are calculated by using these four different
methods and the variation with respect to decomposition
ratio a is plotted in Fig. 2b. While calculating the activa-
tion energy, the Ozawa and KAS methods provide per-
fectly compatible results, however, the value of activation
energy obtained by using Isoconversional method is found
to be approximately the twice of the value calculated by
using these two models. Activation energy values calcu-
lated by Friedman’s method may deviate from the activa-
tion energy values calculated by the other methods. This is
due to the fact that Friedman’s method is based on dif-
ferential unlike the others use integrals. The decomposition
ratio a dependence of activation energy values determined
by first three methods show similar tendencies. They all
increase with an increase in decomposition ratio, reach to a
maximum for decomposition ratio values in between 0.50
Al ðSO Þ ꢀ18H O $ Al ðSO Þ ꢀ16H O þ 2H O
2
4 3
2
ðsÞ
2
4 3
2
ðsÞ
2
ðgÞ
ðIÞ
Al2ðSO4Þ ꢀ16H2O ! Al2ðSO4Þ ꢀ6H2O þ 10H2OðgÞ
3
ðsÞ
3
ðsÞ
ðIIÞ
The endothermic peak of dehydration reaction for the
Stage-II is obvious in curves for all heating rates and more
limited variation is observed for the peak temperature with
respect to the heating rate. This reaction occurs at a tem-
perature range of 354–458 K and approximately at peak
temperature value of 400.6 K. It is found that the calcu-
lated value of dehydration enthalpy at lower heating rate is
close to the dehydration enthalpy of the Stage-I and is
-
1
-1
7
4.64 kJ mol water .
1
23

Thermal decomposition kinetics of aluminum sulfate hydrate
859
and 0.55. After reaching to the maximum, the values of
activation energy decrease gradually. The average value of
activation energy that is obtained by using these four
A sub-product, Al (SO ) ꢀ3H 0, forms with the leave of
2
4 3
2
three moles of water from the compound Al (SO ) ꢀ6H 0.
2
4 3
2
The endothermic decomposition of this sub-product is
obvious in all three heating rates resulting with a closer
peak temperature values for all three heating rates, which
has a value of 630 K. The first half of departing water
molecules leaves the compound (IIIb) in a narrow tem-
perature range (approximately 60 °C), while other half
leave the compound (IIIc) slowly in a wide temperature
range (approximately 330 °C) to form dehydrated alumi-
num sulfate. The anhydrous Al (SO ) arises at 980 K at
-
1
methods, is 117.03 kJ mol , which is higher than three
times the average value for the Stage-I.
The variation of calculated activation energy for this
combined dehydration reaction with respect to the
decomposition ratio is plotted in Fig. 2c.
Al2ðSO4Þ ꢀ18H2O ! Al2ðSO4Þ ꢀ6H2O þ 12H2OðgÞ
3
ðsÞ
3
ðsÞ
ðI?IIÞ
2
4 3
the end of these sub-stage.
It is more appropriate supposing that dehydration reactions
at Stage-I and II as a single reaction with regard to the
stable aluminum sulfate compounds. The calculated
enthalpy of dehydration reaction, if two stages are sup-
posed as a single stage, does not vary with respect to the
heating rate b, and results in an average value of
Hence the endothermic peak areas are too small to
measure during dehydration reaction of Al (SO ) ꢀ6H 0,
2
4 3
2
reaction enthalpy values for major and sub stages are not
able to be calculated. The values of activation energy for
the dehydration reaction at Stage-III that is calculated by
using four methods and its variation with respect to the
-
1
-1
8
4.23 kJ mol water
.
2
decomposition ratio are plotted in Fig. 2d. Hence lower r
While calculating the activation energy, the Ozawa and
values are obtained in regression analysis of the Stage-III
when compared with to those of first and second dehy-
dration step; the existence of different regions in activation
energy a graph enforced us to evaluate the third dehydra-
tion step in three sub-stages.
KAS methods provide perfectly compatible results with
each other, however, using the Isoconversional method
results in 80% larger values than these two methods. It is
observed that, the variation of calculated activation energy
with respect to the decomposition ratio is similar. At the
beginning, the variation slightly decreases then tends to
increase with the increase in decomposition ratio with
reaching a maximum value in the range of 0.55–0.65. After
reaching to the maximum value, the activation energy
gradually decreases with the increase in decomposition
ratio. The average value of activation energy that is cal-
culated by using three methods, averages a values of
The activation energy values of each sub-stages, IIIa,
IIIb, and IIIc, calculated by using different methods and
their variation behavior with respect to the decomposition
ratio are presented in Fig. 2e–g, respectively. The value of
the average activation energy and the tendency in the
variation of the activation energy with respect to the
decomposition ratio prove that dehydration occurs with
different mechanisms in each sub-stage. The activation
energy values are nearly constant, which require lower
activation energy, during the most of the sub-stage IIIa and
starts rapidly increase by the end of this stage. The ten-
dency in the increase of the activation energy continues till
to the half of the sub-stage IIIb. The findings from thermal
analysis and activation energy presents that dehydration in
the sub-stage IIIb is quite different than the dehydration at
other sub-stages.
-
1
1
06.12 kJ mol , which is slightly lower than the average
value of Stage-II.
As a result of dehydration reaction at Stage-II (or
combined step), Al (SO ) ꢀ6H 0, which is a stable hydrate
2
4 3
2
salt, forms. At Stage-III, the dehydration reaction of
Al (SO ) ꢀ6H 0 occurs at three sub-stages (Fig. 1;
2
4 3
2
Table 1).
Al ðSO Þ ꢀ6H O ! Al ðSO Þ ꢀ3H O þ 3H O
2
4 3
2
ðsÞ
2
4 3
2
ðsÞ
2
ðgÞ
The average activation energy values calculated by
ðIIIaÞ
using Ozawa, KAS, Isoconversional methods are 49.20,
-1
2
Al ðSO Þ ꢀ3H O ! Al ðSO Þ ꢀ3H O þ 3H O
2
4 3
2
ðsÞ
4
4 6
2
ðsÞ
2
ðgÞ
350.66, and 199.04 kJ mol for dehydration reactions at
ðIIIbÞ
sub-stages IIIa, IIIb, and IIIc, respectively. The differences
of activation energy values prove that dehydration reaction
takes place in different sub-stages with different
mechanisms.
Al4ðSO4Þ ꢀ3H2O ! 2Al2ðSO4Þ3ðsÞþ3H2OðgÞ
ðIIIcÞ
ðIIIÞ
6
ðsÞ
Al2ðSO4Þ ꢀ6H2O ! Al2ðSO4Þ3ðsÞþ 6H2OðgÞ
3
ðsÞ
Findings of the thermal analysis and activation energy
do not provide complete information to identify the exact
temperature, at which the dehydrated aluminum sulfate
formed.
During the first sub-stage of dehydration at Stage-III, three
moles of water leaves the compound gradually, so active
endothermic properties are not observed. The water that
leaves the compound is observed such a continuation of the
water molecules that left the compound at Stage-II.
Thermal decomposition of the dehydrated aluminum
sulfate, which was formed as a product of dehydration
123

8
60
G. K. C¸ ılgı, H. Ceti s¸ li
reaction, presents splitting-up with a loss of mass, which is
Table 2 Average activation energies of all major steps with respect
to applied methods and general average activation energy value
equivalent to 0.50 moles of SO at 965–1050 K tempera-
3
ture range, at lower heating rates. Although an endothermic
peak of the reaction is observed with the first two heating
rates, the same peak is not observed with the highest
heating rate (Fig. 1; Table 1).
Reactions
I
II
III
IV
Tpeak/K
354.17
5.407
5.410
400.57
27.033
27.058
630.45
16.220
16.240
1100.85
36.041
34.828
% Mass loss (Theo.)
As pointed out in the literature, it is identified that the
actual decomposition of the dehydrated aluminum sulfate
starts after a temperature of 1043 K, with an average peak
temperature value of 1100 K. Although the majority
% Mass loss (exp.)
-
1
Average E /kJ mol
a
Ozawa
30.77
26.57
41.09
46.47
36.23
96.41
94.75
139.12
135.67
133.96
146.25
138.75
454.84
460.46
403.21
–
KAS
(
2.25 moles) of the gas product, which forms due to
Isoconversional
Friedman
175.87
101.09
117.03
decomposition, leaves the compound at 1043–1120 K
temperature range, the loss of mass continued until
approximately 1150 K at all heating rates.
Generally average
439.50
It is found that reaction enthalpy values, which are
calculated using the endothermic peak areas belongs to the
decomposition of aluminum sulfate, decreases with the
increase in the heating rate, and has a value of 82 kJ per
The activation energy values of major decomposition
step IV determined by three methods compete with each
other well and give us an average activation energy value,
-
1
mol of produced SO , or an approximate value of
3
439.50 kJmol . This value is higher than the values of
dehydration reactions for all major and sub-stages com-
paratively. Average activation energies of all major steps
with respect to applied methods and general average acti-
vation energy value are summarized in Table 2.
1
72.85 kJ per mol of the decomposed compound.
6
Al2ðSO4Þ3ðsÞ ! Al2O3ðsÞ þ 5Al2ðSO4Þ3ðsÞ þ3SO3ðgÞ
ðIVaÞ
Al O
2
þ 5Al ðSO Þ ! 6Al O
þ 15SO3ðgÞ
The values of thermal analysis and activation energies,
and variation graphs points out that decomposition of sul-
fate occurs in two different sub-stages. For this reason,
activation energy values are calculated for each reaction,
which are defined with IVa and IVb. The variation graphs
for the activation energy with respect to the decomposition
ratio are presented with Fig. 3b and c, respectively.
The average of activation energy values calculated by using
three methods, which are compatible with each other, for the
3ðsÞ
2
4 3ðsÞ
2
3ðsÞ
ðIVbÞ
ðIVÞ
Al2ðSO4Þ3ðsÞ
! Al2O3ðsÞ þ 3SO3ðgÞ
The activation energy values for the thermal decomposition
reaction of the dehydrated aluminum sulfate, which is
defined with the equation IV, are calculated by using all
three methods. However, due to extreme deviation and less
reliability by Friedman method, the values by Friedman
method is not used. The variation graph is also presented
by Fig. 3a.
-1
reaction IVa is 449.81 kJ mol . It is observed that, the
variation of activation energy with respect to the decomposi-
tion ratio is also similar, which persistently increases with the
increase in decomposition ratio and reaches at the end to the
twice of the value at the beginning of the reaction.
(
a) 525
(b) 630
Ozawa
KAS
Iso.
Although the activation energy values of the reac-
tion IVb calculated by using the Ozawa and KAS methods
shows perfect compatibility with each other, the values
calculated by using Isoconversional method quite differs
from values by other two models. The variation of acti-
vation energy calculated by using the Ozawa and KAS
methods with respect to the decomposition ratio are simi-
lar, which reaches a minimum in decomposition ratio
values of 0.10 and 0.65 and are approximately constant for
other values. On the other hand, the variation of activation
energy calculated by using the Isoconversional method
persistently decreases with the increase in the decomposi-
4
2
1
05
85
65
530
Ozawa
KAS
Iso.
430
330
0
.0
0.2
0.4
0.6
0.8
1.0
0
0.2
0.4
0.6
0.8
1
α
α
(
c)540
4
3
1
20
00
80
Ozawa
KAS
Iso.
tion ratio. The average activation energy value, which is
-1
0.0
0.2
0.4
0.6
0.8
1.0
α
260.31 kJ mol
calculated by using Isoconversional
method is almost half of the average value, which is
Fig. 3 Variation of activation energy values with decomposition
ratio a a major reaction step IV, b sub-stage IVa, c sub-stage IVb
-
510.60 kJ mol , calculated by using other two models.
1
1
23

Thermal decomposition kinetics of aluminum sulfate hydrate
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