Thermodynamics and kinetics of the carbothermal reduction of aluminum sulfate

Article abstract of DOI:10.1080/10426507.2020.1802274

The thermodynamic analysis and kinetics of the carbothermal reduction of aluminum sulfate using anthracite as the reducing agent are reported. The results showed that the reduction reaction was controlled by interfacial chemical reaction when the carbon e

Full text of DOI:10.1080/10426507.2020.1802274

Phosphorus, Sulfur, and Silicon and the Related Elements
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Thermodynamics and kinetics of the carbothermal
reduction of aluminum sulfate
Guangya Zheng , Jupei Xia & Zhengjie Chen
To cite this article: Guangya Zheng , Jupei Xia & Zhengjie Chen (2020): Thermodynamics and
kinetics of the carbothermal reduction of aluminum sulfate, Phosphorus, Sulfur, and Silicon and the
Related Elements, DOI: 10.1080/10426507.2020.1802274
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PHOSPHORUS, SULFUR, AND SILICON AND THE RELATED ELEMENTS
https://doi.org/10.1080/10426507.2020.1802274
Thermodynamics and kinetics of the carbothermal reduction
of aluminum sulfate
Guangya Zhenga, Jupei Xiaa, and Zhengjie Chenb
b
aFaculty of Chemical Engineering, Kunming University of Science and Technology, Kunming, Yunnan, China; Faculty of Metallurgical and
Energy Engineering, Kunming University of Science and Technology, Kunming, Yunnan, China
ABSTRACT
ARTICLE HISTORY
Received 9 March 2020
Accepted 24 July 2020
The thermodynamic analysis and kinetics of the carbothermal reduction of aluminum sulfate using
anthracite as the reducing agent are reported. The results showed that the reduction reaction was
controlled by interfacial chemical reaction when the carbon excess coefficient was 1.15 (aluminum
sulfate, anthracite coal particle size, respectively 100 mesh, 180 mesh) and the reaction tempera-
ture was in the range of 450–600ꢀC. The reaction could be represented using the Erofeev equa-
tion: ln ½ꢁ ln ð1 ꢁ xÞꢂ ¼ n ln t þ ln k and the apparent activation energy was 227.50 kJꢃmolꢁ1. From
the XRD pattern, FTIR spectra and SEM image of the product after reduction was determined at
600ꢀC for 2 h, it was amorphous alumina and the particle size was small, which provided good
conditions for the preparation of metallurgical grade alumina.
KEYWORDS
Carbothermal reduction;
aluminum sulfate;
anthracite; thermodynam-
ics; kinetics
GRAPHICAL ABSTRACT
Introduction
aspects such as ore size, carbon overdose coefficient, and
carbon–oxygen atomic ratio. Chen proposed that the carbo-
thermal reduction barite reaction primarily consists of a gas
phase enclosing barite particles. CO reacts with barium sul-
fate (BaSO4) on the surface of the particles to form the shell
of the BaS product. CO penetrates the product shell, diffuses
into the internal reaction interface, reacts with the particles,
and CO is then diffused. From the thermodynamics and
kinetics, it was concluded that increasing the reaction tem-
perature in the gas phase is conducive to an increased reac-
tion rate, but this assumption has not been studied in
Aluminum compounds such as aluminum sulfate, aluminum
oxide, and aluminum nitrate are important chemical raw
materials and widely used in flocculants, catalysts, mordants,
paper, ceramics, glass, electronics, and other applications.[1–6]
In industrial production, various carbon metal elements are
used for smelting and extraction of valuable metal elements to
produce metal compounds. The quality and purity of these
compounds determine the utilization rate of the raw materials
and economic benefits of the entire chemical industry.[7–13]
Researchers have conducted in-depth studies on carbon
thermal reduction,[14–17] where most have focused on depth.[18] Salem and Osgouei examined the influence of
CONTACT Jupei Xia
Zhengjie Chen
xjp6661@163.com
czjkmust@126.com
Faculty of Chemical Engineering, Kunming University of Science and Technology, Kunming 650500, Yunnan, China;
Faculty of Metallurgical and Energy Engineering, Kunming University of Science and Technology, Kunming 650093,
Yunnan, China.
ß 2020 Taylor & Francis Group, LLC

2
G. ZHENG ET AL.
Table 1. Carbothermal reduction of aluminum sulfate series reaction.
Serial
number
Chemical reaction equation
᭝G ¼ 0
R1
R2
R3
R4
R5
Al2(SO4)3 þ 1.5C(A) ¼ Al2O3 þ 3SO2(g) þ 1.5CO2(g)
Al2(SO4)3 þ 3C(A) ¼ Al2O3 þ 3SO2(g) þ 3CO(g)
C(A) þ CO2(g) ¼ 2CO(g)
24 ꢀC
160 ꢀC
600 ꢀC
–
Al2(SO4)3 þ 3CO(g) ¼ Al2O3 þ 3SO2(g) þ 3CO2(g)
2CO(g) þ SO2(g) ¼ 2CO2(g) þ S
–
particle size distribution on the carbothermal reduction bar-
ite process and found that when the granularity of barite
was reduced from 230 to 400 mesh, its reaction activation
energy was reduced by only 5.4 kJꢃmolꢁ1 [19]
.
Liu et al. used
microwave and conventional heating to study the carbother-
mal reduction reaction of manganese ore powder.[20]
Hlabela and Chen used differential scanning calorimetry-
thermogravimetry (DSC-TG) to study the kinetics of CO
reduction of barite. The CO mass fraction was 4.8% between
850 ꢀC and 1000 ꢀC. The CO reduction barite reaction is a
primary reaction with an average activation energy of
Figure 1. Reactive chemical reaction of Gibbs free energy from R1 to R5.
149 kJꢃmolꢁ1 [21]
.
Jagtap studied the catalytic effects of
Fe(NO3)3 and Na2CO3 on the carbon thermal reduction of
barite.[22] The studies above differ significantly in terms of
ore grades, impurity mass fractions, and reduction condi-
tions. Also, studies on the preparation of alumina via carbon
thermal reduction of aluminum sulfate have not been
reported, and the reaction mechanism remains unclear.
In addition, the temperature of sulfate decomposition by
carbothermal reduction is lower than that of direct calcin-
ation and decomposition of sulfate.[22–27] The reaction activ-
ity of alumina in the reduction product is good and the
alkali dissolution condition is mild, which provides suitable
conditions for the preparation of metallurgical grade alu-
mina in later stages.[10,18]
Figure 2. Effect of reaction temperature on equilibrium composition.
The present study used anthracite as a reducing agent. A
thermodynamic analysis of the reaction process of the car-
bothermal reduction of aluminum sulfate revealed limiting
factors and a kinetic equation of the reduction reaction rate.
These findings should provide theoretical basis for the pro-
cess of the carbothermal reduction of aluminum sulfate to
produce crude alumina and provide conditions for the prep-
aration of metallurgical grade alumina.
the following order: Type R2 > R1 > R4 > R5 > R3. When
the reaction temperature exceeded 600 ꢀC, the order was
changed to R2 > R1 > R4 > R3 > R5. All reduction reaction
rates increased with temperature.
The relationship between the equilibrium composition of
the carbothermal reduction aluminum sulfate reaction sys-
tem and the reaction temperature was calculated using the
equilibrium compositions module in the thermodynamic
software HSC 6.0 (Figure 2). Figure 2 showed that the
Al2O3 system temperature was 150 ꢀC, and its mole balance
varied as the temperature rose. The equilibrium tended to
remain constant until the temperature reached 400 ꢀC.
Theoretically, Al2(SO4)3 can be a complete reduction for
Al2O3. According to this conclusion, when the reaction tem-
perature reached 500 ꢀC, the four experimental groups were
tested using gas chromatography (GC900C) at reaction
times of 5 min, 10 min, 25 min, and 30 min of exhaust gas
monitoring; the results were shown in Figure 3.
Results and discussion
Thermodynamic analysis of the carbothermal reduction
of aluminum sulfate
The carbothermal reduction reaction of aluminum sulfate is
relatively complicated. Although all the reactants are solid,
the reaction system includes a solid reaction and gas-solid
reaction. The main potential chemical reactions are listed in
Table 1. Using the reaction equation module in the thermo-
dynamic software HSC 6.0,[20,22] thermodynamic analyses of
the above chemical reactions were carried out and results
were presented in Figure 1.
Figure 3 indicated that a large amount of CO and a small
amount of CO2 appeared in the system at the beginning
(5 min and 10 min). At this point, the carbon thermal reduc-
Table 1 showed that the initial reaction temperature of tion reaction was in the initial stages. CO only reacted with
R1 was 24 ꢀC, R2 was 160 ꢀC, and R3-5 was 600 ꢀC but the activation center of Al2(SO4)3 with high surface energy
could occur at any temperature between 0 and 1000 ꢀC. As to form a new phase crystal nucleus. At this time, the num-
depicted in Figure 1, reactions at 600–900 ꢀC occurred in ber of activation centers on the surface of aluminum sulfate

PHOSPHORUS, SULFUR, AND SILICON AND THE RELATED ELEMENTS
3
Figure 4. Relationship between alumina yield and reaction time at different
temperatures.
Figure 3. Chromatogram at different residence times.
was limited, created difficulties in generating a three-dimen-
sional seed, and the reaction rate was slow. A large amount
of CO2 and a small amount of CO existed in the system at
25 min and 30 min. At this point, with the generation of the
three-dimensional crystal nucleus, the two-phase interfacial
region gradually increased with the growth of the new crys-
talline phase. The chemical reaction accelerated with an
increase in the boundary area, and the reaction rate reached
its maximum.
reaction process shows various rules unique to the mass
transfer step. Since the diffusion activation energy of gas is
generally only 4–20 kJꢃmolꢁ1, the temperature has little
influence on the reaction rate. When controlled by an inter-
facial chemical reaction, the apparent rate follows various
laws inherent in the chemical reaction. The activation energy
of the reaction is generally greater than 40 kJꢃmolꢁ1, and the
reaction rate can increase significantly as the temperature
increases.[28] Therefore, the limiting step in the reduction
process is either the diffusion process or interfacial chemical
reaction, where either step can be separated by reaction tem-
perature changes.
The carbon excess coefficient in this experiment was 1.15.
As noted earlier, aluminum sulfate and anthracite were
passed through 100 mesh and 180 mesh standard sieves,
respectively, followed by warming and cooling stages under
nitrogen protection (30 mL/min). In the reaction phase, the
atmosphere was switched to a mixed gas containing 10%
oxygen (3 mL O2 þ 27 mL N2, a total of 30 mL/min). The
effects of reaction temperature and time on the Al2O3 yield
were investigated. Experimental results are displayed in
Figure 4. A kinetic model was applied to analyze the rela-
tionship between the yield of Al2O3 and reaction time (see
Figure 4) to evaluate the control steps of the reduc-
tion process.
Overall, when using anthracite as a reducing agent, part
of the carbon in the reactant came into close contact with
aluminum sulfate particles. At a low temperature, carbon
reacted directly with aluminum sulfate to produce a small
amount of CO. Due to the presence of O2 in the system,
incomplete combustion of anthracite occurred (partial CO).
At temperatures less than 450 ꢀC, CO reacted directly with
aluminum sulfate and the solid-solid reaction was given pri-
ority, but in the temperature range of 450–600 ꢀC, the gas-
solid reaction was prioritized. The R2 reaction in Table 1
generated CO. As the temperature increased, the reaction
rate increased and a large amount of CO was produced.
This stage was primarily formed by the reaction of
Al2(SO4)3 on the surface of the particle with CO to form
Al2O3, forming the product shell. CO continued to penetrate
the Al2O3 product layer to the inside of the particle for reac-
tion. The resulting CO2 diffused into the gas phase, followed
by the reaction of C with Al2(SO4)3 to generate CO, and
this process was repeated until Al2(SO4)3 was completely
restored. Therefore, the carbothermal reduction of alumi-
num sulfate may be controlled by two dynamic reaction
regions, namely, diffusion control and interfacial chemical
reaction control.
Kinetic model of the reaction controlled by diffusion step
If the reduction reaction is controlled by the diffusion pro-
cess, then the diffusion conforms to Fick’s Law, and the
dynamic equation is expressed by the Fick’s Law equation
and Ginstling equations, respectively.
h
i
2
1=3
ð
Þ
1 ꢁ 1 ꢁ x
¼ kt
(1)
(2)
Kinetic analysis of carbon thermal reduction of
aluminum sulfate
2=3
ð
Þ
1 ꢁ 2x=3 ꢁ 1 ꢁ x
¼ kt
In theory, the reaction process of the carbothermal reduc-
tion of aluminum sulfate can be divided into two kinetic
reaction regions: diffusion control and interfacial chemical
reaction control. Under diffusion control, the rate of the and 1 ꢁ 2x=3 ꢁ ð1 ꢁ xÞ
where x is the yield of Al2O3, t is the reaction time, and k is
h
i
the rate constant.
2
1=3
According to Equations (1) and (2), the 1 ꢁ ð1 ꢁ xÞ
2=3
curves with respect to time can

4
G. ZHENG ET AL.
Table 2. The rate constant of various temperature sections n and lnk values
at different temperatures.
T (ꢀC)
450
500
550
600
N
2.2156
1.8377
1.0885
0.9854
lnk
ꢁ9.2414
ꢁ6.9939
ꢁ3.5755
ꢁ2.8280
be obtained based on the yield rate of Al2O3 at different
temperatures (see Figure A1a,b).
The general requirement of the linear fitting correlation
coefficient was R2 > 0.99. In Figure A1, when the tempera-
ture exceeded 450 ꢀC, the linear relationship of the data was
poor and it could be controlled by the diffusion step at
lower temperatures. According to standard kinetic laws, the
reaction process was controlled by a chemical reaction at
low temperatures and diffusion at high temperatures. The
above abnormal phenomena preliminarily indicated that the
diffusion process was not the rate-limiting step of the reduc-
tion reaction process; rather, the interfacial chemical reac-
tion was more likely to be the control step.
Figure 5. The relationship between lnk and 1/T.
lnk at different temperatures were calculated using the data
in Figure A2c (as shown in Table 2).
The relationship between the k value of the rate constant
and absolute temperature (T) was subjected to the
Arrhenius equation, and the rate constant k can be deter-
mined as shown in Equation (6):
Kinetic model of the reaction controlled by the interfacial
chemical reaction step
ꢂ
ꢃ
The reaction of aluminum sulfate in carbothermal reduction
is primarily concentrated at either the interface of two crys-
talline phases [Al2(SO4)3 and Al2O3] or in the narrow area
near the interface. Such reactions are usually referred to as
local chemical reactions or regional chemical reactions. In
this case, the kinetic equations describing this situation are
the Austin–Rickett, Hulbert–Klawitter, and Erofeev equa-
tions.[29] The expressions are as follows, respectively:
Ea
k ¼ A exp
ꢁ
(6)
RT
where A is the leading factor (minꢁ1); Ea is the apparent
activation energy (kJꢃmolꢁ1);
R is the gas constant
(kJꢃmolꢁ1ꢃKꢁ1); and T is the absolute temperature (K).
By taking the natural logarithm of both sides of the equa-
tion, the equation is shown as:
ꢀ
ꢁ
Ea
ð
Þ
ln x= 1 ꢁ x ¼ k ln t
(3)
ln k ¼ ln A ꢁ
(7)
RT
2=3
½
ð
Þꢂ
ꢁ ln 1 ꢁ x
¼ k ln t
(4)
(5)
If lnk at different temperatures is used to plot 1/T, a line
can be obtained by linear fitting, as shown in Figure 5. The
linear correlation coefficient R2 ¼ 0.9974 > 0.99, and the
expression of k can be obtained through regression analysis
as:
½
ð
Þꢂ
ln ꢁ ln 1 ꢁ x ¼ n ln t þ ln k
where x is the yield of Al2O3, t is the reaction time, k is the
rate constant, and n is a constant related to the reac-
tion mechanism.
27:3632
According to the above equation, the ln ½x=ð1 ꢁ xÞꢂ,
½ꢁ ln ð1 ꢁ xÞꢂ2=3, and ln ½ꢁ ln ð1 ꢁ xÞꢂ curves with respect to
lnt can be obtained, respectively, by using the data relation-
ship between the conversion rate and reaction time at differ-
ent temperatures. The results were shown in Figure A2.
Figure A2 indicated that only the linear correlation coef-
ficient R2 of the Erofeev equation was greater than 0.99.
Additionally, ln ½ꢁ ln ð1 ꢁ xÞꢂ presented a better linear rela-
tionship with lnt, indicating that the process of carbothermal
reduction of aluminum sulfate was controlled by the inter-
facial chemical reaction in this study.
ln k ¼ 28:5432 ꢁ
(8)
T
As the reaction of aluminum sulfate with carbothermal
reduction was in the control area of interfacial chemical
reaction kinetics, the reduction rate could be effectively
improved by appropriately decreasing the particle sizes of
the reactants to increase the contact area.
Characterization analysis of reduced products
The XRD pattern of the product after reduction was deter-
mined at 600 ꢀC for 2 h presented in Figure 6. According to
the phase diagram, the product contained amorphous sub-
stances, which may favor the main reaction.[29–31] Only the
“bread” peaks can be seen in the trace shown in Figure 6,
and there was no characteristic diffraction peak. From the
Activation energy calculation
Our analysis revealed that the rate-limiting step was intro-
duced in the carbothermal reduction of the aluminum sul-
fate reactions the interfacial reaction at
a
reaction X-ray diffraction standard spectrum of the amorphous alu-
temperature range of 450–600 ꢀC. The rate constants n and mina, it can be judged that this is amorphous alumina.[30]

PHOSPHORUS, SULFUR, AND SILICON AND THE RELATED ELEMENTS
5
Figure 8. SEM image of the product after reduction.
Table 3. Industrial analysis of anthracite.
Figure 6. XRD pattern of the product after reduction.
ꢄ
Composition
Anthracite
Mad
Aad
Vad
Fcad
0.12
0.8
4.56
94.52
provides good conditions for the preparation of metallur-
gical grade alumina.[32]
Experimental
Materials
Raw materials in this study consisted of self-made aluminum
sulfate [Al2(SO4)3ꢃ18H2O] and industrial anthracite. To
eliminate the influence of ash on anthracite, anthracite was
degreased by mixed acid filtration, washed and dried. The
anthracite was taken from a coking plant in Yunnan prov-
ince, China. Industrial analysis was performed using a
HKGF-3000 industrial analyzer, as shown in Table 3.
Figure 7. FTIR spectra of the product after reduction.
Experimental methods
Figure 7 shows the FTIR spectra of the reduction prod-
uct, obtained at 600 ꢀC for 2 h. The absorption peak at
3443 cmꢁ1 is the antisymmetric stretching vibration of struc-
tural water -OH, and that at 1644 cmꢁ1 is the bending vibra-
tion of H-O-H of water. Additionally, the absorption peak
at 612 cmꢁ1 is due to the stretching vibration of Al-O-Al.
However, there is excess anthracite, as indicated by the in-
Preparation of aluminum sulfate
After the bauxite was finely ground and iron-removed, it was
reacted with 98% concentrated sulfuric acid at 200 ꢀC for 1 h,
and the temperature was lowered to about 100 ꢀC. The solution
was filtered with water to obtain an aluminum sulfate solution
(aluminum sulfate 18-hydrate, w[Al2(SO4)3ꢃ18H2O] > 99%),
and the filtrate was crystallized and purified at 110 ꢀC to obtain
a high-purity anhydrous aluminum sulfate crystal. The chem-
plane
vibration
.
of
carbon–hydrogen
bond
at
1401 cmꢁ1 [20,22,25,26]
After the carbothermal reduction prod-
ical reaction is shown in Equation (9)[33,34]
:
uct was alkali-dissolved, the residual carbon would exist in
the form of alkali residue. It can be applied to the produc-
tion of blast furnace iron-making or iron concentrate
according to the content of elements in alkali slag. FTIR
results further confirmed that the reduction product deter-
mined at 600 ꢀC for 2 h was amorphous alumina.
ð
Þ
Al2O3 ꢃ 1 or 3 H2O þ 14H2O þ 3H2SO4
! Al2 SO4 ꢃ 18H2O
ð
Þ
(9)
3
Figure 8 shows the SEM microphotograph of the reduc-
tion product, obtained at 600 ꢀC for 2 h. The surface of the
product was smooth and independent, irregular appearance
as shown in Figure 8. Meanwhile, the particle size of the
product was small, which achieved the requirements of the
Aluminum sulfate dehydrates
Aluminum sulfate (8 mg) was added to a crucible and then
placed into a muffle furnace heated to 500 ꢀC for tempera-
ture dehydration in 5 h. The dehydration rate was calculated
according to the change in mass before and after aluminum
micron size. The product is easily alkali-soluble. This sulfate dehydration.[32,34]

6
G. ZHENG ET AL.
Characterization analysis method
Thermogravimetric analysis
Aluminum sulfate dehydration experiments were carried out
in a thermogravimetric analyzer (TGA; TGA-STA449F3,
NETZSCH, Germany), under nitrogen gas atmosphere, to
investigate the dehydration rate of aluminum sulfate. Reactions
were performed at 100 cm3ꢃminꢁ1 N2 flow, with a heating rate
of 10 ꢀCꢃminꢁ1, from room temperature to 1200 ꢀC. All dehy-
dration experiments were repeated at least with two parallel
runs and the relative errors were less than 5%.
Gas chromatography analysis
Monitoring the tail gas of the reaction with GC900C gas
chromatography.
Figure 9. TG-DSC curves of aluminum sulfate 18-hydrate pyrolysis process.
To investigate the role of Al2(SO4)3ꢃ18H2O in the dehy-
dration process, TG-DSC was used to measure changes in
energy and mass during dehydration. Throughout the heat-
ing process, as the temperature rose, water of crystallization
XRD analysis
At a scanning voltage of 36 kV and a current of 40 mA, the
reaction residue phase was analyzed using a D/max-3B type
was gradually removed and the quality declined. The energy X-ray diffractometer with a scanning angle ranging from 10ꢀ
difference between the sample and the inert reference mater-
to 80ꢀ and a step size of 2ꢀꢃminꢁ1
.
ial varied with temperature. The TG-DSC curve, shown in
Figure 9, depicts changes up to 1200 ꢀC in Al2(SO4)3ꢃ18H2O
throughout the dehydration process.
Scanning electron microscopy
The micromorphology and particle size of the samples were
observed using a Quanta-200 scanning electron microscope
made by FEI Company (magnification: 30-100000).
Anthracite reacts with aluminum and carbon sulfate
Broken, ball-ground anthracite (180 mesh), and aluminum
sulfate (100 mesh) were mixed at a carbon excess coefficient
of 1.15 and placed in a porcelain boat. Then, it was posi-
tioned in a heating device and the heating device used for
this experiment was a TCGC-1700 tube furnace.
First, the furnace was programmed for heating, with nitro-
gen gas (30 mLꢃminꢁ1) as a shielding gas (eliminate the inter-
ference of air in the system). When the temperature reached
specified temperature and then maintained at a constant tem-
perature for 30 min. Second, the boat containing reactants was
placed in the constant temperature zone of the tube furnace, a
mixed gas (27 mL N2 þ 3 mL O2, a total of 30 mLꢃminꢁ1) was
introduced during the reaction phase and the reaction was
started. After the reaction was completed, the boat was natur-
ally cooled to the room temperature under nitrogen protec-
tion (60 mLꢃminꢁ1). The reaction products were weighed and
ground and then used for analysis.
Conclusions
Thermodynamics analysis showed a noteworthy effect of the
reaction temperature on the reaction rate of the carbothermal
reduction of aluminum sulfate. The high-temperature stage
(450–600 ꢀC) primarily generated Al2(SO4)3 through the
reduction reaction of generated CO. The generated CO
reacted with Al2(SO4)3 and the rapid increase in system tem-
perature was conducive to the reaction of carbon-reducing
Al2(SO4)3 and generating CO. The reaction kinetics were also
improved, and the time required for a complete reaction
between carbon and aluminum sulfate was shortened.
Dynamic analysis results showed that at a reaction tem-
perature range of 450–600 ꢀC, the reduction reaction rate
was controlled by the interfacial chemical reaction at an
apparent activation energy of 227.50 kJꢃmolꢁ1. The dynamic
equation can be expressed by the Erofeev equa-
tion: ln ½ꢁ ln ð1 ꢁ xÞꢂ ¼ n ln t þ ln k:
Evaluation indices
The content of Al2(SO4)3 in residue was analyzed by the
BaSO4 gravimetric method in GB/T22660.1-2008 (China).
The Al2O3 yield can be calculated as follows:
The XRD pattern, FTIR spectra and SEM image of the
product determined at 600 ꢀC for 2 h after reduction showed
that it was amorphous alumina and the particle size was
M0w0 ꢁ M1w1
X ¼
(10) small, which provided good conditions for the preparation
M0w0
of metallurgical grade alumina.
where M0 is the mass of the mixtures before the reaction
(g), M1 is the mass of the mixtures after the reaction (g), w0
is the mass fraction of the Al2(SO4)3 mixtures before the
reaction (%), and w1 is the mass fraction of the Al2(SO4)3
mixtures after the reaction (%).
Funding
This work was financially supported by the National Natural Science
Foundation of China (No. 21566018).

PHOSPHORUS, SULFUR, AND SILICON AND THE RELATED ELEMENTS
7
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ORCID
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http://orcid.org/0000-0002-1519-275X
[17] Lombardo, G.; Ebin, B.; St Foreman, M. R. J.; Steenari, B.-M.;
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Appendix A
1=3 2
Figure A1. Relationship between (a) ½1 ꢁ ð1 ꢁ xÞ ꢂ , (b) 1 ꢁ 2x=3 ꢁ ð1 ꢁ xÞ2=3, and t at different temperatures.
Figure A2. Relationship between (a) ln ½x=ð1 ꢁ xÞꢂ, (b) ½ꢁ ln ð1 ꢁ xÞꢂ2=3, (c) ln ½ꢁ ln ð1 ꢁ xÞꢂ, and lnt at different temperatures.