Extraction of Aluminum and Iron Ions from Coal Gangue by Acid Leaching and Kinetic Analyses

: Extracting valuable elements from coal gangue is an important method for the utilization of coal gangue. In order to obtain the suitable technological conditions and the acid leaching kinetic model of leaching aluminum and iron ions from high-iron and low-aluminum coal gangue, the effects of calcination temperature, calcination time, and acid types on the leaching results of aluminum and iron ions are studied. The results show that when the gangue is calcined at 675 ◦ C for 1 h, then the calcined gangue powder is leached by 6 mol/L hydrochloric acid at 93 ◦ C for 4 h, the leaching ratio of iron ions is more than 90%, and that of aluminum ions is more than 60%. Furthermore, the acid leaching kinetic equations at 30 ◦ C, 50 ◦ C, 70 ◦ C, and 90 ◦ C are studied by three kinetic models, and the apparent activation energies of the reactions are calculated by the Arrhenius formula. The results show that the leaching behavior of aluminum and iron ions conformed to the “mixing control” model equation: “(1 − x) − 1/3 − 1 + 1/3ln(1 − x) = kt + b”. The apparent activation energies of aluminum and iron ions are 55.5 kJ/mol and 55.8 kJ/mol, respectively. All these indicate that the acid leaching process is controlled by the “mixing control”.


Introduction
Coal gangue is the waste produced by the coal industry [1], which accounts for 10-20% of the raw coal output [2]. Due to the massive accumulation of coal gangue, it has polluted the atmosphere, water, and soil [3], occupied land, and affected the safety of the ecological environment [4]. The resource utilization of coal gangue is conducive to decreasing its ecological damage and enhancing industrial added value. The common ways to utilize gangue include mine backfilling [5], brick making [6,7], road paving [8], cement making [9], etc. However, these methods cannot make use of coal gangue for highvalue-added applications, so it is imperative to research a method of efficient development and comprehensive utilization of coal gangue [10,11].
The increase in iron content in coal gangue will increase the probability of iron entering the products, which will affect its application fields, and even make it difficult to carry out fine processing directly [22]. In Liupanshui, Guizhou Province, China, more than 10 million

Procedure
As shown in Figure 1, the gangue was crushed and passed through a 160-mesh sieve, then calcined at a high temperature for a certain time to obtain the calcined powder; then, the calcined powder was acid-leached by sulfuric acid or hydrochloric acid at the solid:liquid ratio of 1:3.5, at a temperature of 93 • C, and the stirring speed of 1000 r/min for 1-7 h. After the acid leaching had completed, suction filtration, washing, and drying were carried out. According to the quantity of the filter residue and its chemical components, the extraction ratios of aluminum and iron ions were calculated by the following formulas: yield of residue = (m 2 ÷ m 1 ) × 100% (1) where "m 1 " is the quantity of the calcined powder before leaching, "m 2 " is the quantity of the filter residue, "w 1 %" is the mass fraction of aluminum or iron ions in the calcined gangue powder, and "w 2 %" is the mass fraction of aluminum or iron ions in the filter residue. The compositions of calcined powder before and after acid leaching were detected by XRF, and the concentration of filtrate was calculated accordingly. Then, the USCM was adopted to analyze the leaching kinetics of aluminum and iron ions, and the apparent activation energies were calculated. A 6100 type X-ray diffraction instrument (XRD, Shimadzu Company, Japan) was used for CuKα (λ for Kα = 1.54059 Å), 2θ = 3 • -65 • , with a step width of 0.02 • . The primary chemical elemental components were determined by a Supermini200 type X-ray fluorescence spectrometer (XRF, Rigaku Company, Tokyo, Japan). The morphology of the products was identified by a Zeiss EVO18-type scanning electron microscope (SEM, Jena, Germany). The thermal-chemical properties of coal gangue were characterized by a SDT−Q600 type thermal analyzer (TG-DSC, TA Company, Boston, MA, USA), and analyses were performed under the air atmosphere at a constant flow rate of 100 mL/min, where

Instrumentation and Characterization
A 6100 type X-ray diffraction instrument (XRD, Shimadzu Company, Japan) was used for CuKα (λ for Kα = 1.54059 Å), 2θ = 3°-65°, with a step width of 0.02°. The primary chemical elemental components were determined by a Supermini200 type X-ray fluorescence spectrometer (XRF, Rigaku Company, Tokyo, Japan). The morphology of the products was identified by a Zeiss EVO18-type scanning electron microscope (SEM, Jena, Germany). The thermal-chemical properties of coal gangue were characterized by a SDT−Q600 type thermal analyzer (TG-DSC, TA Company, Boston, MA, USA), and analyses were performed under the air atmosphere at a constant flow rate of 100 mL/min, where the sensitivity of the microbalance was 0.1 μg, the accuracy of temperature measurement was 0.1 °C, and the heating rate was 20 °C/min.

Chemical Components of the Coal Gangue
As shown in Table 1, the contents of SiO2, Al2O3, and Fe2O3 in the gangue accounted for 75.55% of the total quantity. Compared with the coal gangue in other parts of China, the content of the iron element in the sample is higher, whereas the content of the aluminum element is lower.

Chemical Components of the Coal Gangue
As shown in Table 1, the contents of SiO 2 , Al 2 O 3 , and Fe 2 O 3 in the gangue accounted for 75.55% of the total quantity. Compared with the coal gangue in other parts of China, the content of the iron element in the sample is higher, whereas the content of the aluminum element is lower.

XRD Analysis of the Coal Gangue
As seen from Figure 2, the coal gangue is a multiphase mixture [29], and the main phases in the coal gangue are kaolinite, quartz, brookite, montmorillonite, pyrite, and siderite [30], in which kaolinite and quartz are the main components. As shown in Table 1, the iron content is high, but the peaks of the iron-containing materials are lower, which indicates that the crystallinity of the iron-containing materials is low.

XRD Analysis of the Coal Gangue
As seen from Figure 2, the coal gangue is a multiphase mixture [29], and the main phases in the coal gangue are kaolinite, quartz, brookite, montmorillonite, pyrite, and siderite [30], in which kaolinite and quartz are the main components. As shown in Table 1, the iron content is high, but the peaks of the iron-containing materials are lower, which indicates that the crystallinity of the iron-containing materials is low.

Morphology Analysis of the Coal Gangue
It can be seen from Figure 3 that the coal gangue powders are spherical with an uneven particle size. The maximum particle size is more than 30 μm, whereas the minimum is about 1 μm.

Morphology Analysis of the Coal Gangue
It can be seen from Figure 3 that the coal gangue powders are spherical with an uneven particle size. The maximum particle size is more than 30 µm, whereas the minimum is about 1 µm.

TG-DSC Analyses of the Coal Gangue
In order to obtain a suitable thermal activation temperature range, the thermal analyses of coal gangue were carried out by TG-DSC. The results are shown in Figure 4.

TG-DSC Analyses of the Coal Gangue
In order to obtain a suitable thermal activation temperature range, the thermal analyses of coal gangue were carried out by TG-DSC. The results are shown in Figure 4.
In Figure 4, the endothermic valley between 100 and 400 • C is mainly caused by the dehydration of water in coal gangue, but the quantity loss is not obvious within this temperature range, which indicates that the content of crystal water in the coal gangue is low. The exothermic peak near 598 • C is mainly caused by the combustion exothermic of coal, pyrite, and other components. When the temperature is higher than 500 • C, kaolinite begins to decompose into metakaolin [31,32], which is an endothermic reaction. The equation is as follows: The combustion of pyrite is an exothermic reaction, and the reaction is as follows:

TG-DSC Analyses of the Coal Gangue
In order to obtain a suitable thermal activation temperature range, the thermal analyses of coal gangue were carried out by TG-DSC. The results are shown in Figure 4. In Figure 4, the endothermic valley between 100 and 400 °C is mainly caused by the dehydration of water in coal gangue, but the quantity loss is not obvious within this temperature range, which indicates that the content of crystal water in the coal gangue is low. The exothermic peak near 598 °C is mainly caused by the combustion exothermic of coal, pyrite, and other components. When the temperature is higher than 500 °C, kaolinite begins to decompose into metakaolin [31,32], which is an endothermic reaction. The equation is as follows: The combustion of pyrite is an exothermic reaction, and the reaction is as follows: Overall, the total heat release is larger than the heat absorption, which exhibits an exothermic peak. On the TG curve, the quantity decreases significantly for the combustion of coal and pyrite which produce CO2, SO2, H2O, and other volatile substance products [33]. Meanwhile, siderite is decomposed into FexOy, CO2, or CO, and the volatilizations Overall, the total heat release is larger than the heat absorption, which exhibits an exothermic peak. On the TG curve, the quantity decreases significantly for the combustion of coal and pyrite which produce CO 2 , SO 2 , H 2 O, and other volatile substance products [33]. Meanwhile, siderite is decomposed into Fe x O y , CO 2 , or CO, and the volatilizations lead to the quantity loss. When the temperature exceeds 650 • C, kaolin, pyrite, siderite, and other substances have basically produced decomposition, so the quantity is almost unchanged. The low exothermic peak near 800 • C is formed by the continuous combustion and heat release of the residual coal in the coal gangue [34]. The endothermic valley between 900 and 1000 • C is attributed to metakaolin, which is endothermically decomposed into spinel and amorphous silica [35,36]. The main reaction is as follows: 2Al 2 O 3 ·SiO 2 (metakaolin) → Al 4 Si 3 O 12 (spinel) + SiO 2 (amorphous silica) (5)

Phase Analyses of the Calcined Powders at Different Temperatures
As shown in Figure 5, kaolinite and other minerals can be decomposed completely at 600-800 • C. Therefore, it is conducive to the activation of minerals and the combustion of coal gangue components when enhancing the temperature appropriately. However, too high a temperature will not only waste energy, but also lead to the transformations of metakaolin and other substances into other phases. lead to the quantity loss. When the temperature exceeds 650 °C, kaolin, pyrite, siderite, and other substances have basically produced decomposition, so the quantity is almost unchanged. The low exothermic peak near 800 °C is formed by the continuous combustion and heat release of the residual coal in the coal gangue [34]. The endothermic valley between 900 and 1000 °C is attributed to metakaolin, which is endothermically decomposed into spinel and amorphous silica [35,36]. The main reaction is as follows: 2Al2O3·SiO2 (metakaolin) → Al4Si3O12 (spinel) + SiO2 (amorphous silica) (5)

Phase Analyses of the Calcined Powders at Different Temperatures
As shown in Figure 5, kaolinite and other minerals can be decomposed completely at 600-800 °C. Therefore, it is conducive to the activation of minerals and the combustion of coal gangue components when enhancing the temperature appropriately. However, too high a temperature will not only waste energy, but also lead to the transformations of metakaolin and other substances into other phases. There are still crystal inert substances such as quartz and brookite, and the main contents of these substances are silicon and titanium. The gangue rich in aluminum and iron has been transformed into a highly active amorphous state [37], including amorphous Al2O3 and SiO2. Therefore, coal gangue can be activated in the range of 625-750 °C. There are still crystal inert substances such as quartz and brookite, and the main contents of these substances are silicon and titanium. The gangue rich in aluminum and iron has been transformed into a highly active amorphous state [37], including amorphous Al 2 O 3 and SiO 2 . Therefore, coal gangue can be activated in the range of 625-750 • C.

Analyses of the Leaching Effects with Different Acids
Two aliquots with masses of 10 g coal gangue powders were calcined at 750 • C for 2 h, and then the powders were leached by 3.0 mol/L sulfuric acid and 6.0 mol/L hydrochloric acid, respectively. The solid:liquid ratio was 1:3.5, and the whole process was stirred at 93 • C. After the acid leaching reactions, the solid:liquid mixtures were filtered, washed, and dried. After that, the quantities of the filter residues were weighed to obtain the yields of the residues. The results are presented in Figure 6. As seen from Figure 6, the yields of residue decrease with the extension of time. The yields of residue by sulfuric acid leaching are obviously higher than that of hydrochloric acid.
Hydrochloric acid is a common industrial waste acid, although its demand is not as high as sulfuric acid; therefore, using hydrochloric acid could provide a certain reference for industrial production. In addition, coal gangue contains calcium ions, and adding sulfuric acid can easily produce CaSO4. The equation is as follows: CaSO4 is a substance which is slightly soluble in water. It is easy to cover the surface of the particles and affect the diffusion of ions, which is not conducive to metal ion leaching.
The reaction of hydrochloric acid with CaCO3 produces CaCl2, which is soluble in water and conducive to the dissolution of other ions. The equation is as follows: In fact, hydrochloric acid is used very actively in the field of hydrometallurgy, which is used to leach iron or aluminum from coal ash [38], fly ash [39], bauxite [40,41], red mud [42], and coal gangue [43,44]. As can be seen from the results in Figure 6, the effect of hydrochloric acid is significantly better than that of sulfuric acid, so hydrochloric acid was chosen, and the time can be 3-7 h. In order to leach the gangue fully and save energy, the leaching time was determined to be 4 h.
The coal gangue was calcined at 750 °C for 2 h, and after leaching, the phase analyses of the two acid-leached residues are shown in Figure 7. As seen from Figure 6, the yields of residue decrease with the extension of time. The yields of residue by sulfuric acid leaching are obviously higher than that of hydrochloric acid.
Hydrochloric acid is a common industrial waste acid, although its demand is not as high as sulfuric acid; therefore, using hydrochloric acid could provide a certain reference for industrial production. In addition, coal gangue contains calcium ions, and adding sulfuric acid can easily produce CaSO 4 . The equation is as follows: CaSO 4 is a substance which is slightly soluble in water. It is easy to cover the surface of the particles and affect the diffusion of ions, which is not conducive to metal ion leaching.
The reaction of hydrochloric acid with CaCO 3 produces CaCl 2 , which is soluble in water and conducive to the dissolution of other ions. The equation is as follows: In fact, hydrochloric acid is used very actively in the field of hydrometallurgy, which is used to leach iron or aluminum from coal ash [38], fly ash [39], bauxite [40,41], red mud [42], and coal gangue [43,44]. As can be seen from the results in Figure 6, the effect of hydrochloric acid is significantly better than that of sulfuric acid, so hydrochloric acid was chosen, and the time can be 3-7 h. In order to leach the gangue fully and save energy, the leaching time was determined to be 4 h. The coal gangue was calcined at 750 • C for 2 h, and after leaching, the phase analyses of the two acid-leached residues are shown in Figure 7. As shown in Figure 7, the diffraction peaks of the intensity of the quartz and brookite in the filter residue of the leached hydrochloric acid are higher than those of the sulfuric acid, and because more aluminum and iron ions are dissolved by hydrochloric acid, the higher the contents of the remaining quartz and brookite.

Effects of Calcination Temperature on the Yield of Residue
After the reactions, the reduction quantity was calculated. The results are shown in Figure 8. When the calcination temperature was between 550 and 700 °C, the yield tended to be stable, and the minimum yield was at 675 °C. However, when the calcination temperature was raised to 700-750 °C, the yield increased, indicating that the calcined temperature affects the activity of aluminum and iron ions. In order to activate the aluminum and iron components, as well as remove carbon as much as possible, 675 °C was selected as the proper calcination temperature.  As shown in Figure 7, the diffraction peaks of the intensity of the quartz and brookite in the filter residue of the leached hydrochloric acid are higher than those of the sulfuric acid, and because more aluminum and iron ions are dissolved by hydrochloric acid, the higher the contents of the remaining quartz and brookite.

Effects of Calcination Temperature on the Yield of Residue
After the reactions, the reduction quantity was calculated. The results are shown in Figure 8. When the calcination temperature was between 550 and 700 • C, the yield tended to be stable, and the minimum yield was at 675 • C. However, when the calcination temperature was raised to 700-750 • C, the yield increased, indicating that the calcined temperature affects the activity of aluminum and iron ions. In order to activate the aluminum and iron components, as well as remove carbon as much as possible, 675 • C was selected as the proper calcination temperature. As shown in Figure 7, the diffraction peaks of the intensity of the quartz and brookite in the filter residue of the leached hydrochloric acid are higher than those of the sulfuric acid, and because more aluminum and iron ions are dissolved by hydrochloric acid, the higher the contents of the remaining quartz and brookite.

Effects of Calcination Temperature on the Yield of Residue
After the reactions, the reduction quantity was calculated. The results are shown in Figure 8. When the calcination temperature was between 550 and 700 °C, the yield tended to be stable, and the minimum yield was at 675 °C. However, when the calcination temperature was raised to 700-750 °C, the yield increased, indicating that the calcined temperature affects the activity of aluminum and iron ions. In order to activate the aluminum and iron components, as well as remove carbon as much as possible, 675 °C was selected as the proper calcination temperature.

Effect of Calcination Time on the Yield of Residue
The coal gangue powders were calcined at 675 • C for 30 min, 45 min, 60 min, 75 min, 90 min, 105 min, 120 min, and 135 min. The other conditions are the same as above, and the results are shown in Figure 9.

Effect of Calcination Time on the Yield of Residue
The coal gangue powders were calcined at 675 °C for 30 min, 45 min, 60 min, 75 min, 90 min, 105 min, 120 min, and 135 min. The other conditions are the same as above, and the results are shown in Figure 9. As shown in Figure 9, when the calcination time was 30-60 min, the yield of residue decreased with the extension of time because the kaolinite, siderite, pyrite, etc., in the coal gangue underwent chemical reactions to produce a large amount of amorphous Al2O3, SiO2, and FexOy, which improved the activity of the calcined powder, thereby decreasing the yield. When the time was extended more than 60 min, the activity of the calcined powder decreased, which led to the increased yield. Therefore, the calcination time was determined to be 1 h. The components of the acid-leached residue are displayed in Table 2. As seen from Table 2, the primary acid-leached filter residue contained 76.95% of SiO2 and 10.37% of Al2O3. According to the calculations, 91% of iron ions and 66% of aluminum ions have been leached, and the concentration of AlCl3 is 94.26 g/L and that of FeCl3 is 73.13 g/L. The mixed liquid containing aluminum and iron can be used to prepare As shown in Figure 9, when the calcination time was 30-60 min, the yield of residue decreased with the extension of time because the kaolinite, siderite, pyrite, etc., in the coal gangue underwent chemical reactions to produce a large amount of amorphous Al 2 O 3 , SiO 2 , and Fe x O y , which improved the activity of the calcined powder, thereby decreasing the yield. When the time was extended more than 60 min, the activity of the calcined powder decreased, which led to the increased yield. Therefore, the calcination time was determined to be 1 h. The components of the acid-leached residue are displayed in Table 2. As seen from Table 2, the primary acid-leached filter residue contained 76.95% of SiO 2 and 10.37% of Al 2 O 3 . According to the calculations, 91% of iron ions and 66% of aluminum ions have been leached, and the concentration of AlCl 3 is 94.26 g/L and that of FeCl 3 is 73.13 g/L. The mixed liquid containing aluminum and iron can be used to prepare composite coagulants, or to prepare alumina and iron oxide by a step precipitation method. The residue is mainly silicon-and titanium-containing material, which can be used to prepare other products such as zeolites [45], silica, TiO 2 , etc.

Morphology Analysis of Filter Residue
As shown in Figure 10, the particle sizes of the acid-leached filter residues are smaller than that of the ore coal gangue powder, and the largest particle size is about 20 µm. It can also be seen that due to the leaching of iron and aluminum ions, the residue particles become loose, showing flakes and crumbs. composite coagulants, or to prepare alumina and iron oxide by a step precipitation method. The residue is mainly silicon-and titanium-containing material, which can be used to prepare other products such as zeolites [45], silica, TiO2, etc.

Morphology Analysis of Filter Residue
As shown in Figure 10, the particle sizes of the acid-leached filter residues are smaller than that of the ore coal gangue powder, and the largest particle size is about 20 μm. It can also be seen that due to the leaching of iron and aluminum ions, the residue particles become loose, showing flakes and crumbs.

Analysis of Leaching Kinetics
The components of coal gangue are very complex, in which iron oxide comes from FeCO3 and pyrite, as well as other amorphous iron compounds; aluminum primarily comes from amorphous alumina produced by the decomposition of kaolinite. In the leaching process, acid molecules diffuse into the voids or cracks of quartz or amorphous SiO2, and then react with aluminum and iron oxides. With the reactions, products come out from the residual solid layers, and the reaction interface continues to shrink to the core of the mineral particles. Simultaneously, the residual solid layer continues to thicken, and some solid layers may form debris and peel off under stirring. Therefore, the "USCM" is used to describe the leaching kinetics of aluminum and iron ions [46][47][48].
The reaction model of the leaching process is shown in Figure 11. Assuming that the calcined coal gangue powder particles are approximately spherical, and the leaching process is controlled by the "solid film diffusion control", the leaching kinetic equation is as follows:

Analysis of Leaching Kinetics
The components of coal gangue are very complex, in which iron oxide comes from FeCO 3 and pyrite, as well as other amorphous iron compounds; aluminum primarily comes from amorphous alumina produced by the decomposition of kaolinite. In the leaching process, acid molecules diffuse into the voids or cracks of quartz or amorphous SiO 2 , and then react with aluminum and iron oxides. With the reactions, products come out from the residual solid layers, and the reaction interface continues to shrink to the core of the mineral particles. Simultaneously, the residual solid layer continues to thicken, and some solid layers may form debris and peel off under stirring. Therefore, the "USCM" is used to describe the leaching kinetics of aluminum and iron ions [46][47][48].
The reaction model of the leaching process is shown in Figure 11.
Minerals 2022, 12, x FOR PEER REVIEW 10 of 18 composite coagulants, or to prepare alumina and iron oxide by a step precipitation method. The residue is mainly silicon-and titanium-containing material, which can be used to prepare other products such as zeolites [45], silica, TiO2, etc.

Morphology Analysis of Filter Residue
As shown in Figure 10, the particle sizes of the acid-leached filter residues are smaller than that of the ore coal gangue powder, and the largest particle size is about 20 μm. It can also be seen that due to the leaching of iron and aluminum ions, the residue particles become loose, showing flakes and crumbs.

Analysis of Leaching Kinetics
The components of coal gangue are very complex, in which iron oxide comes from FeCO3 and pyrite, as well as other amorphous iron compounds; aluminum primarily comes from amorphous alumina produced by the decomposition of kaolinite. In the leaching process, acid molecules diffuse into the voids or cracks of quartz or amorphous SiO2, and then react with aluminum and iron oxides. With the reactions, products come out from the residual solid layers, and the reaction interface continues to shrink to the core of the mineral particles. Simultaneously, the residual solid layer continues to thicken, and some solid layers may form debris and peel off under stirring. Therefore, the "USCM" is used to describe the leaching kinetics of aluminum and iron ions [46][47][48].
The reaction model of the leaching process is shown in Figure 11. Assuming that the calcined coal gangue powder particles are approximately spherical, and the leaching process is controlled by the "solid film diffusion control", the leaching kinetic equation is as follows: Assuming that the calcined coal gangue powder particles are approximately spherical, and the leaching process is controlled by the "solid film diffusion control", the leaching kinetic equation is as follows: If the control step is the "interface chemical reaction control", the equation is as follows: When the leaching process is jointly controlled by the "solid film diffusion control" and the "interface chemical reaction control" together, it is called the "mixing control", and the equation is [49]: where "k 1 " is the solid-liquid diffusion rate constant, "k 2 " is the rate constant of interfacial chemical reaction, "k 3 " is the rate constant of mixing control reaction, "x" is the leaching ratio, "t" is the leaching time, and "b 1 , b 2 and b 3 " are the constant terms.
In order to determine the control type of hydrochloric acid leaching reactions, the extraction ratios of aluminum and iron ions changing with temperature and time were assessed. The temperature increased from 303.15 K to 363.15 K with a step of 20 K, the time was from 10 min to 5 h, the H + concentration is 6 mol/L, and the stirring speed was 1000 r/min. Since the contents of calcium and magnesium ions in coal the gangue were very low (Cao 0.05%, MgO 0.22%), and TiO 2 (6.22%) did not react with dilute hydrochloric acid, we ignored the effects of calcium, magnesium, and titanium ions on leaching. The results are shown in Figures 12 and 13.
If the control step is the "interface chemical reaction control", the equation is as follows: When the leaching process is jointly controlled by the "solid film diffusion control" and the "interface chemical reaction control" together, it is called the "mixing control", and the equation is [49]: (10) where "k1" is the solid-liquid diffusion rate constant, "k2" is the rate constant of interfacial chemical reaction, "k3" is the rate constant of mixing control reaction, "x" is the leaching ratio, "t" is the leaching time, and "b1, b2 and b3" are the constant terms.
In order to determine the control type of hydrochloric acid leaching reactions, the extraction ratios of aluminum and iron ions changing with temperature and time were assessed. The temperature increased from 303.15 K to 363.15 K with a step of 20 K, the time was from 10 min to 5 h, the H + concentration is 6 mol/L, and the stirring speed was 1000 r/min. Since the contents of calcium and magnesium ions in coal the gangue were very low (Cao 0.05%, MgO 0.22%), and TiO2 (6.22%) did not react with dilute hydrochloric acid, we ignored the effects of calcium, magnesium, and titanium ions on leaching. The results are shown in Figures 12 and 13.  A trial method is used to substitute the obtained results into the kinetic equations of the different control steps, ) versus t, respectively, and then using these three models to fit the obtained data linearly. The results of aluminum ions are shown in Figures 14-16, and so the iron ions are Figure 13. Effects of temperature on the extraction ratios of iron ions.
A trial method is used to substitute the obtained results into the kinetic equations of the different control steps, plotting 1 − 2/3x − (1 − x) 2/3 , 1 − (1 − x) 1/3 and (1 − x) −1/3 − 1 + 1/3ln(1 − x) versus t, respectively, and then using these three models to fit the obtained data linearly. The results of aluminum ions are shown in Figures 14-16, and so the iron ions are shown in Figures 17-19. A trial method is used to substitute the obtained results into the kinetic equations of the different control steps, plotting 1 − 2/3x − (1 − x) 2/3 , 1 − (1 − x) 1/3 and (1 − x) −1/3 − 1 + 1/3ln(1 − x) versus t, respectively, and then using these three models to fit the obtained data linearly. The results of aluminum ions are shown in Figures 14-16, and so the iron ions are shown in Figures 17-19.     0.20        As can be seen from the fitting equations and the R 2 values of these three mathematical models, whether aluminum ion leaching or iron ion leaching, the R 2 values of the mixing control equation at 30 °C, 50 °C, 70 °C, and 90 °C were all better than that of single "solid film diffusion control" or "interface chemical reaction control", and were all closer to 1. Therefore, hydrochloric acid leaching aluminum and iron ions kinetic equations from    Figure 19. Relationships between (1 − x) −1/3 − 1 + 1/3ln(1 − x) and time of iron ions.
As can be seen from the fitting equations and the R 2 values of these three mathematical models, whether aluminum ion leaching or iron ion leaching, the R 2 values of the mixing control equation at 30 °C, 50 °C, 70 °C, and 90 °C were all better than that of single "solid film diffusion control" or "interface chemical reaction control", and were all closer to 1. Therefore, hydrochloric acid leaching aluminum and iron ions kinetic equations from the calcined coal gangue powder are all fitted to accord with the "mixing control" models. As can be seen from the fitting equations and the R 2 values of these three mathematical models, whether aluminum ion leaching or iron ion leaching, the R 2 values of the mixing control equation at 30 • C, 50 • C, 70 • C, and 90 • C were all better than that of single "solid film diffusion control" or "interface chemical reaction control", and were all closer to 1. Therefore, hydrochloric acid leaching aluminum and iron ions kinetic equations from the calcined coal gangue powder are all accord with the "mixing control" models.

Calculation of the Apparent Activation Energy
To obtain the activation energies of aluminum and iron ions extraction under hydrochloric acid leaching conditions, the Arrhenius formula was used to determine the apparent activation energies of the leaching experiments. According to the Arrhenius formula: lnk = −Ea/RT + lnA (12) where "k" is the apparent reaction rate constant, "Ea" is the apparent activation energy, kJ/mol, "R" is the molar   As seen from Figure 20, the correlation fitting degree of the lnk−1/T curve (R 2 = 0.95901) obtained from the "mixing control" fitting is significantly better than that of the diffusion of solid film control (R 2 = 0.91902) and interfacial chemical reaction control (R 2 = 0.79103). Similarly, the correlation coefficient R 2 of the iron ions fitting equation using the "mixing control" model is also better than that of the other two models (Figure 21), which further indicates that the leaching ratios of aluminum and iron ions from calcined coal   As seen from Figure 20, the correlation fitting degree of the lnk−1/T curve (R 2 = 0.95901) obtained from the "mixing control" fitting is significantly better than that of the diffusion of solid film control (R 2 = 0.91902) and interfacial chemical reaction control (R 2 = 0.79103). Similarly, the correlation coefficient R 2 of the iron ions fitting equation using the "mixing control" model is also better than that of the other two models (Figure 21), which further indicates that the leaching ratios of aluminum and iron ions from calcined coal As seen from Figure 20, the correlation fitting degree of the lnk−1/T curve (R 2 = 0.95901) obtained from the "mixing control" fitting is significantly better than that of the diffusion of solid film control (R 2 = 0.91902) and interfacial chemical reaction control (R 2 = 0.79103). Similarly, the correlation coefficient R 2 of the iron ions fitting equation using the "mixing control" model is also better than that of the other two models (Figure 21), which further indicates that the leaching ratios of aluminum and iron ions from calcined coal gangue powder by hydrochloric acid leaching are both affected by the "mixing control".

Conclusions
In the study of extracting aluminum and iron ions from coal gangue, the proper conditions were obtained when the gangue powder was less than 160 mesh, the calcination temperature was 675 • C, the time was 60 min, and the calcined coal gangue was leached by 6 mol/L hydrochloric acid at 93 • C for 4 h, where the leaching ratio of iron ions was 91% and that of aluminum ions was 66%.
The process of leaching aluminum and iron ions from the calcined coal gangue powder with hydrochloric acid conforms to the kinetic model: (1 − x) −1/3 − 1 + 1/3ln(1 − x) = k 3 t + b 3 . According to the Arrhenius equation, the apparent activation energies of the leaching reactions of aluminum and iron are 55.5 kJ/mol and 55.8 kJ/mol, respectively. The leaching process of aluminum and iron ions are controlled by the "mixing control".