Thermal Decomposition of Aluminum Chloride Hexahydrate

Ind. Eng. Chem. Res. 2005, 44, 6591-6598

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Thermal Decomposition of Aluminum Chloride Hexahydrate M. Hartman,* O. Trnka, and O. S ˇ olcova´ Institute of Chemical Process Fundamentals, Academy of Sciences of the Czech Republic, 165 02 Prague 6-Suchdol, Czech Republic

The decomposition rate of aluminum chloride hexahydrate (AlCl3‚6H2O) was measured as weight loss at ambient pressure and elevated temperatures up to 270 °C. Such incomplete thermal decomposition produces a porous and reactive basic aluminum chloride [Al2O3‚2HCl‚2H2O or Al2(OH)4Cl2‚H2O] which dissolves in water to give poly(aluminum chloride) used as an efficient flocculation agent. A slowly rising temperature method and very small sample masses, which minimize heat and mass transfer intrusions, were employed to determine intrinsic reaction rates. A fractional order kinetic equation of Arrhenius type was proposed for the decomposition and tested also against the results amassed by experiment in a constant temperature mode. This correlation allows the estimation of the reaction rate as a function of temperature and the extent of decomposition. It can be readily employed in modeling and simulation of the decomposition process. The contents of aluminum and chlorine in the decomposed solids were also explored in the course of the decomposition process. Pore volume (porosity), pore-size distribution, and BET surface area data were also collected on decomposed chloride particles. Introduction

log K ) 85.342 -

Poly(aluminum chloride), PAC, has been known and employed as an effective flocculating agent in water treatment processes. The term PAC denotes an aqueous solution of basic aluminum chloride hydrate (approximately Al2(OH)4Cl2‚H2O or Al2O3‚2HCl‚2H2O), the concentration of which corresponds to about 10 wt % Al2O3. The basic aluminum chloride hydrate, BAC, is formed by the well-controlled, partial thermal decomposition of aluminum chloride hexahydrate (AlCl3‚6H2O) at elevated temperatures.1,2 Aluminum chloride hexahydrate is produced, for instance, by the reaction of aluminum hydroxide with an aqueous solution of hydrogen chloride and by subsequent crystallization. It has been well-established that anhydrous aluminum salts cannot be simply formed by heating the corresponding hydrates because of their amphoteric properties and tendency to hydrolyze. Aluminum chloride hexahydrate should be written as [Al(H2O)6]Cl3 rather than as AlCl3‚6H2O since the interaction force Al-O prevents forming the Al-Cl bonds. At high temperatures,3-5 the following, well-defined, decomposition reaction takes place

1 [Al(H2O)6]Cl3(s) ) Al2O3(s) + 3HCl(g) + 4.5H2O(g) 2 (A) Its standard enthalpy, deduced from Barin’s6 thermodynamic data, is as large as

∆HA° (298 K) ) +996.03 kJ/mol Al2O3 Thermodynamics constraints imposed on reaction A can be expressed by * To whom correspondence should be addressed. Tel.: +420 220390254. Fax: +420 220920661. E-mail: [email protected].

25978.8 T

(1)

where

K ) PHCl3‚PH2O4.5

(2)

The dissociation pressure of AlCl3‚6H2O, P, is taken as

P ) PHCl + PH2O

(3)

With respect to stoichiometry it holds

PH2O ) 1.5 PHCl

(3a)

and we get

log P ) 8.07122 -

3463.84 T

(4)

It should be noted that eqs 1 and 4 are based upon the thermochemical data recently compiled and tabulated by Barin.6 The decomposition temperature, Td, defined as a temperature at which the dissociation pressure, P, is equal to the pressure of the surrounding atmosphere (i.e., P ) 1.01325 bar), and predicted by eq 4 amounts to 429.5 K (156.3 °C). At temperatures below 1000 °C, the less compact γ-Al2O3 (F ) 3.40 g/cm3) is formed. It exhibits the defective, cubic, face-centered structure. This open form constitues the basis of the so-called active aluminum oxide which is frequently used, for example, in catalysis, ion exchange, and chromatography. For the sake of PAC production,1,2 AlCl3‚6H2O as the precursor is incompletely decomposed at about 160-200 °C under ambient pressure. In such operation conditions, the exact decomposition chemistry has not been fully understood yet. The following reaction is usually assumed in the literature4,5 to occur

10.1021/ie058005y CCC: $30.25 © 2005 American Chemical Society Published on Web 07/15/2005

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2[Al(H2O)6]Cl3(s) ) Al2O3‚xHCl‚yH2O(s) + (6 - x)HCl(g) + (9 - y)H2O(g) (B) The stoichiometric coefficients x and y are usually presumed to be near 2. This figure (x ) y ) 2) was employed in all stoichiometric calculations throughout this work. In their recent studies, Park et al.1,2 focused on the bench-scale decomposition of aluminum chloride hexahydrate and the production of poly(aluminum chloride). Little is known about the intrinsic reaction kinetics, chemistry, and the textural features of the reaction product. In this article we present experimental findings on the thermal decomposition of aluminum chloride hexahydrate at elevated temperatures. The purpose of the work was to elucidate the intrinsic kinetics and the chemistry of the decomposition reaction, and the physicochemical properties of the reaction product. Experimental Section Material. The work was carried out with the aluminum chloride hexahydrate, ACHH, (AlCl3‚6H2O) obtained from Sigma-Aldrich, with purity above 99% and the density as large as 2.398 g/cm3. This material was also subjected to X-ray powder diffraction analysis with the use of a model X’Pert Philips Co. (Philips Analytical X-ray B. V.). Results confirmed the presence of a single solid component in the sample. DTA and TGA curves of the employed, finely-ground aluminum chloride hexahydrate were recorded (model TG-750, Stanton-Redcroft Co.). As can be seen in Figure 1, there is a single, large endothermic peak on the DTA curve at about 185-190 °C. It is believed that this massive peak reflects a maximum rate of the formation of the basic aluminum chloride. It should also be noted that the decomposition reaction is strongly endothermic. There is no discernible reason for the minuscule, but noticeable, wave occurring at about 35 °C on the DTA curve. Crystals of the hexahydrate were first crushed, then ground, and finally sieved to provide samples for the kinetics experiments. To conform to common practice (Mu and Perlmutter,7,8 Hartman et al.,9-12 and Kim and Yim13), all experiments were run on finely powdered samples with particle sizes between 50 and 80 µm. Procedure and Apparatus. Decomposition TGA experiments were performed with the finely powdered samples at a constant temperature increase rate of 3 °C/min. Initial sample weights were close to 10 mg, and air flow of 20 mL/min was maintained. Larger samples were only employed for chemical analyses and textural measurements. Also, constant temperature experiments were done under such conditions. In this work, temperature was maintained at a desired level within a range of (0.1 °C. The same apparatus was employed for both nonisothermal measurements and isothermal runs. The TGA module monitors the weight of a sample and its rate of change continuously, when heated in any inert (or reactive) gas, either as a function of increasing temperature or at a preselected temperature. The DTA unit measures the temperature difference between a sample and a reference. The gas space over the sample was as large as about 70 cm3. A special arrangement (a doughnut-shaped baffle) prevented the gas stream from bypassing the

Figure 1. DTA and thermogravimetric results (TGA) for aluminum chloride hexahydrate (AlCl3‚6H2O) amassed at a heating rate of 3 °C/min between room temperature (22 °C) and 270 °C. Initial mass of samples, 20.5 mg; flow rate of entrainer (air), 20 mL/min; standard sample (DTA), Al2O3.

sample. Furthermore, the sample pan contained small holes which permitted gas to flow past the sample. The tip of the thermocouple was located about 1-2 mm below the sample pan. Provided that the chemistry of a decomposition reaction is well-defined, thermogravimetric analysis (TGA) offers solid data under well-controlled laboratory conditions. If small samples, fine-powdered solids, and low heating rates are used, intrusive heat and mass transfer effects on the rate of reaction are minimized. Removal of the gaseous product of reaction eliminates a possible effect of equilibrium constraints. Since the chemistry of the decomposition process of aluminum chloride hexahydrate is not straightforward, thermogravimetric experiments need to be supplemented with chemical analyses. The extent of decomposition of the aluminum chloride hexahydrate (ACHH) was determined as weight loss. With respect to the uncertainties of the reaction chemistry, the measured weight loss was transformed into the conversion of the chloride to the unequivocally defined oxide (Al2O3) by means of the relationship

wo - w(τ) MACHH 2 X) ‚ ‚ z 9MH2O + 6MHCl wo

(5)

The symbols wo and w(τ) are the initial mass of the sample and the mass of the sample at any moment of time, respectively. The symbol z is the weight fraction of AlCl3‚6H2O in the original (initial) reactant (z ) 0.99). Complete conversion of AlCl3‚6H2O to Al2O3 (X ) 1) corresponds to a relative decrease in weight of 0.78095 for z ) 0.99. Provided that this aluminum chloride hexahydrate is completely converted into the basic chloride [Al2(OH)4Cl2‚H2O or Al2O3‚2HCl‚2H2O], the relative weight loss only amounts to 0.5576. The weight loss is a directly and well-determined quantity. That is why it accompanies in any event the data on the conversion in this work.

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thirty points were taken to fit eq 8. When the effective order of reaction, n, was found by a trial and error procedure, the other kinetics parameters were computed by a least-squares method. The activation energy and frequency factor were determined from the slope and the ordinate intercept of the best-fit straight line, respectively. The values of kinetic parameters inferred from the temperature-increasing experiments amount to

ko ) 1.61 × 1014 1/s, E ) 1.359 × 105 J/mol, and n ) 3.56

Figure 2. Thermal decomposition of aluminum chloride hexahydrate (AlCl3‚6H2O) in a temperature-increasing experiment. Initial mass of the sample, 14.82 mg; heating rate, 3 °C/min; flow rate of entrainer (air 20 cm3/min; O, experimental data points. The solid line shows the predictions of eq 6.

Results and Discussion Nonisothermal Decomposition Kinetics. Preliminary experiments indicated that first traces of the commencing decomposition of AlCl3‚6H2O became detectable at about 90 °C. The data provided by the risingtemperature method, some of which are plotted in Figure 2, were employed as the practical basis for development of a kinetics equation describing the rate of the overall decomposition reaction. As can also be seen in Figure 2, the decomposition of AlCl3‚6H2O becomes quite rapid at about 150 °C. It cannot be anticipated that a single kinetic rate equation can describe the thermal decomposition explored in this work. In general, the decomposition of a solid can be represented by a rate expression

dX E ) ko exp (1 - X)n dτ RT

[

(

)]

(6)

with the initial condition

X ) 0 at τ ) 0

(7)

This equation accounts for possible effects of nucleation and diffusion on the rate of decomposition. It reduces to the Jerofeev equation for n ) 1 (Mu and Perlmutter7); it conforms to the three-dimensional and two-dimensional shrinking core models for n ) 1/3 and n ) 1/2, respectively. The equation follows the Avrami nucleation law (constant density of nuclei and onedimensional nucleus growth) with n ) 0 (Mu and Perlmutter;7,8 Hartman et al.14). The experimental data from the decomposition run were tested empirically by fitting to the linearized form of eq 6

ln

E 1 dX/dτ ) ln ko - ‚ n R T (1 - X)

(8)

Values of the reaction rate, ∆X/∆τ, were determined from the curve X vs τ at equal conversion intervals,

Since the above relationship 6 is nonlinear, it is, in general, sensitive to the variations in values of the respective kinetics parameters. The conversions computed for different times of exposure and temperatures from eq 6 with the use of the above-mentioned kinetics parameters are in Figure 2 compared to the corresponding experimental values determined at temperatures between 30 and 270 °C. As can be seen, the experimental data points plotted in this figure fit the computed curve fairly well. Park et al.1,2 assumed that the decomposition reaction is first-order in conversion of the chloride (i.e., n ) 1) and fitted their laboratory-scale data to the integrated form of eq 6

ln

[

]

-ln(1 - X) E 1 ) ln ko - ‚ τ R T

(9)

n)1 From the straight line drawn to fit the data amassed at 160, 180, and 200 °C, the authors1,2 calculated the preexponential factor, ko, and the activation energy, Eo, to be as large as 297.6 1/s and 5.55 × 104 J/mol, respectively. The authors warn that the decomposition is too slow still at 140 °C and eq 9 may not be applicable at such temperatures. Isothermal Decomposition Kinetics. The rate of thermal decomposition of the aluminum chloride hexahydrate was also explored in the constant temperature mode. The constant temperature runs were carried out in the range 90-150 °C. Preliminary tests proved that the particles did not melt at such temperatures. The results of constant temperature runs are shown in Figure 3. As can be seen, there is an appreciable difference in the course of the curves measured at 90110 °C and those obtained at 130-150 °C. While the first three lines are nearly linear, the other three exhibit a sigmoid shape. In accordance with the temperatureincreasing experiments, the decomposition becomes quite rapid at about 140 °C. It should be noticed that in the range 130-150 °C, the experimental curves level off after about 2 h exposure. Also, the weight loss, attained after such a long exposure, slightly augments with the increasing temperature. In Figure 3 are also presented the predictions of eq 6 for 140 °C with the use of the kinetics parameters deduced from the results obtained by the nonisothermal procedure. As can be seen, agreement between the constant temperature results and the predictions appears to be reasonable. The different modes of experiment seem to be among major factors affecting differences between experiment and the predictions in Figure 3. It is a common experience that the results of the temperature-increasing runs

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Figure 3. Thermal decomposition of aluminum chloride hexahydrate (AlCl3‚6H2O) in temperature-constant experiments. Initial mass of the samples, 14.45-15.86 mg; flow rate of entrainer (air), 20 cm3/min. The solid lines represent the experimental curves; O, predictions for the temperature 140 °C of eq 6, the parameters of which were deduced from the temperature-increasing run.

Figure 4. Thermal decomposition of larger samples of aluminum chloride hexahydrate in a muffle furnace. Initial mass of the samples, 3.002-3.006 g; flow rate of entrainer (air), 50 cm3/min; elapsed time of exposure, τ ) 60 min; O, this work, decomposition in a muffle furnace; ×, this work, deduced from the TGA data shown in Figure 3; b, results of Park et al.1

are notoriously sensitive to the rates of heating. Heat transfer can affect the results provided by constant temperature runs, particularly if the rapid rate of decomposition is coupled with the high heat of reaction. Considerable sensitivity of the rate of reaction to temperature also should not be overlooked. In light of such facts the found differences seem to be understandable. It is believed that the proposed kinetic equation can be applied to modeling and simulation of suitable reactors for the thermal decomposition of aluminum chloride hexahydrate. The empirical relationship developed in this work has usual limitations and it should be applied with caution outside the experimental conditions from which it was deduced. Decomposition of Larger Samples. To secure quantities of partially decomposed aluminum chloride hexahydrate needed for chemical and textural analyses, larger samples of the chloride were exposed to elevated temperatures. Crystals of the chloride were crushed and sieved, and the fraction of particles within a sieve size range of 0.50-0.63 mm (d h p ) 0.565 mm) was investigated in this segment of the work. Samples (3 g), dispersed in shallow corundum crucibles, were inserted into a muffle furnace and exposed to the stream of air as a sweep gas at the temperature of interest (150350 °C) for 60 min. Then the decomposed particles were stored in airtight containers, and shortly afterward they were subjected to chemical and textural analyses. The weight loss of each sample was also determined and is shown in Figure 4. For the sake of comparison, some data read from the TGA lines shown in Figure 3 are plotted along with the new decomposition results. As can be seen, the new decomposition curve outlined by the data amassed with the larger samples is distinctly shifted (30-80 °C) toward higher temperatures. The collected data also suggest that even at the highest temperature employed (350 °C), the complete conversion to Al2O3 had not yrt been attained. Park et al.1 explored the extent of decomposition of AlCl3‚6H2O at different temperatures (140-200 °C) using 5-g samples placed in a small flask which was

immersed into a heated silicon oil bath. Some results deduced from the authors’ experimental curves are also incorporated into Figure 4. As can be seen in this figure, Park’s data are not in conflict with the trend of our experimental findings. Amounts of Aluminum and Chlorine in the Partially Decomposed Solids. A natural question arises as to continuous changes in the solids composition in the course of the decomposition process. As apparent, the composition of the evolved gas inherently unfolds from the progress of the decomposition reactions occurring within the particles. The chloride particles, first exposed to different temperatures (150-350 °C) and to the sweep gas for 60 min in the muffle furnace, were then analyzed for aluminum and chlorine. The measured contents of aluminum increased from 12.4 to 44.2 wt %; those of chlorine decreased from 43.2 to 8.9 wt % as the relative weight loss increased from 13.2 to 75.5%. These values of weight loss correspond to the extents of decomposition of 16.7 and 95.7%, respectively. The determined mass fractions of both species are shown in Figure 5 in dependence on the fractional weight loss. The chlorine curve in Figure 5 indicates that hydrogen chloride commences liberating at very early stages of the decomposition reaction. Both curves in Figure 5 become quite steep when the decomposition is nearing completion. As illustrated in Figure 6, the relationship between the content of aluminum and that of chlorine in the decomposing solids is nearly a linear one. The dependence of the molar ratio of Cl to Al in the solids on weight loss shown in Figure 7 exhibits a slightly concave shape. Textural Features of the Decomposed Particles. In the course of the decomposition, water vapor and hydrogen chloride are evolved and consequently numerous pores are formed. Upon the loss of gases, the pseudomorphs similar to the parent chloride tend to remain at lower temperatures.15 At higher temperatures recrystallization or sintering of the reaction product takes place.


Figure 5. Amounts of aluminum (Al) and chlorine (Cl) in the partially decomposed samples as functions of weight loss of the solids. Experimental conditions are the same as those mentioned in the caption for Figure 4.

Figure 7. Molar ratio of chlorine (Cl) to aluminum (Al) present in the partially decomposed solids as a function of the fractional weight loss. Experimental conditions are the same as those mentioned in the caption for Figure 4.

Figure 6. Relationship between the weight fractions of aluminum (Al) and chlorine (Cl) in the partially decomposed solids. Experimental conditions are the same as those mentioned in the caption for Figure 4.

At first, an effort was taken to explore how the volume of the solid phase is changed by the decomposition process. Since the operation temperatures are not high, it is feasible to assume that no shrinkage occurs and the decomposed particle retains its gross external volume. As considerable amounts of gases (water vapor and hydrogen chloride) are evolved in the course of the reaction, it is evident that the porosity/pore volume of the decomposing particle is increased as the decomposition advances. It should be noted, however, that the reaction product is not unambiguously defined. Therefore, an analytical relationship cannot be developed between the porosity of the decomposing particle and the progress of decomposition.16,17

Figure 8. True particle density (FHe) and particle density (FHg) as functions of fractional weight loss. Experimental conditions are the same as those mentioned in the caption for Figure 4.

True and particle density of the decomposed products were determined by helium and mercury pycnometry, respectively. Pore-size distributions were determined by measuring the volume of mercury penetrating the pore volume at increasing pressure. Figure 8 shows the results of the pycnometric measurements in dependence on the extent of decomposition. It is obvious that the measured true densities increase with increasing extent of decomposition. Nevertheless, all values (1.64-1.95 g/cm3) are much lower than the density of γ-Al2O3, which amounts to 3.40 g/cm3. This fact suggests that some pseudomorphous

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Figure 11. Differential pore-size distribution of the particles decomposed at 250 °C. Time of exposure, 60 min. Figure 9. Dependence of the porosity of decomposed particles on the extent of decomposition. Experimental conditions are the same as those mentioned in the caption for Figure 6.

Figure 12. Differential pore-size distribution of the particles decomposed at 350 °C. Time of exposure, 60 min. Figure 10. Differential pore-size distribution of the particles decomposed at 150 °C. Time of exposure, 60 min.

structures can form and persist at the employed temperatures. The curved line shown in Figure 9 displays how the porosity (pore volume) augments with the increasing extent of decomposition. The highest porosity determined with the particles decomposed at 350 °C amounted to 57%. With increase in the porosity of BAC its rate of dissolution in water will most likely increase. The BET surface area of the decomposed particles was on the order of 101 m2/g. The pore size distributions of the solids decomposed at 150, 250, and 350 °C were also determined. The amassed results are illustrated in Figures 10, 11, and 12. The measured curves indicate that the radii of pores are distributed over the 1-104 nm range. The derivative curves shown in these figures exhibit their peaks at the radii of 20, 300, and 400 nm as the most probable pore

sizes in the respective samples. The shift of the most probable pores to larger ones with the increasing temperature of decomposition is most likely linked to sintering or recrystallization of the formed pseudomorphs similar to the parent chloride. The bimodal distribution displayed in Figure 11, with the second maximum at about 1000 nm, was only found at 250 °C. Conclusions Both water vapor and hydrogen chloride are released when aluminum chloride hexahydrate is gradually heated. First noticeable signs of the thermal decomposition of the chloride occur at 90 °C. The results provided by the nonisothermal method showed that the reaction kinetics was more than thirdorder in mass of the chloride up to high extents of decomposition. A reaction rate equation educed from these temperature-increasing thermogravimetric data describes the course of decomposition with fair accuracy.


The results of the isothermal experiments exploring the extent of the decomposition reaction are in reasonable accordance with the predictions of the proposed kinetic relationship based upon the rising-temperature data. The amount of chlorine in the decomposing particles commences decreasing from very early stages of the decomposition process. Thus, the chloride particles decomposed at 350 °C for 60 min still contained 8.9% Cl by weight. Original, dense crystals of the chloride become porous as their decomposition proceeds. The largest measured porosity amounted to 57% (0.63 cm3/g). The true density of decomposed solid slowly increases with the extent of decomposition from 1.65 to 1.95 g/cm3. The particle (apparent) density, needed for fluidization calculations,18 decreased with the progress of reaction from 1.3 to 0.82 g/cm3. The pore-size distributions of the decomposed samples indicate that the radii of pores are distributed over the 1-104 nm range. The most probable pore size in the solids increased from 20 to 400 nm in dependence on the extent of decomposition. Acknowledgment This research was supported by Grant 203/02/0002 from the Grant Agency C ˇ R. The authors thank Mrs. H. Soucˇkova´ and Mrs. H. Sˇ najdaufova´ for the textural measurements. Assistance of Mrs. E. Macha´cˇkova´ and Mr. J. Hora´cˇek in the chemical analyses is also appreciated. Nomenclature Abbreviations ACHH ) aluminum chloride hexahydrate, AlCl3‚6H2O BAC ) basic aluminum chloride, Al2(OH)4Cl2‚H2O or Al2O3‚ 2HCl‚2H2O PAC ) Poly(aluminum chloride); basic aluminum chloride dissolved in water Symbols ∆HA° (298 K) ) standard enthalpy of reaction A at 298.15 K, kJ/mol ∆w ) (weight) mass loss [) wo - w(τ)], g ∆w/wo ) relative (weight) mass loss d h p ) average particle size determined by sieving, mm e ) fractional porosity of solid ) (FHe - FHg)/FHe ) (VpFHe)/ (1 + VpFHe) ) VpFHg E ) effective (apparent) activation energy, fitted parameter, J/mol ko ) preexponential factor, Arrhenius constant, fitted parameter, 1/s K ) quantity defined by eq 2, bar7.5 ln ) base-e, natural (Napierian) logarithm ) 2.30259 log log ) base-ten (Briggsian) logarithm ) 0.434294 ln Mi ) molar mass of species (MH2O ) 18.015; MHCl ) 36.461; MAlCl3‚6H2O ) 241.431; MAl2O3‚2HCl‚2H2O ) 210.913; MAl2O3 ) 101.961; g/mol n ) effective (apparent) order of reaction, fitted parameter ni ) amount of species “i”, mol P ) dissociation pressure given by eq 3, bar PHCl ) partial pressure of HCl, bar PH2O ) partial pressure of water vapor, bar r ) pore radius, nm rp ) radius of pore, nm R ) ideal gas-law constant ) 8.31441, J/(mol K)

t ) Celsius temperature, °C T ) thermodynamic temperature, K Vp ) pore volume ) (1/FHg) - (1/FHe) ) [e/(1 - e)]‚(1/FHe) ) e/FHg, cm3/g wo ) initial (original) mass of sample (τ ) 0), g w(τ) ) mass of sample of any moment of time τ, g X ) fractional extent of decomposition of aluminum chloride hexahydrate (AlCl3‚6H2O) expressed as the fractional conversion of the chloride to aluminum oxide (Al2O3) given by eq 5 z ) mass fraction of species (AlCl3‚6H2O) in original reactant zi ) mass fraction of species “i” in solids Greek Letters F ) solid density, g/cm3, kg/m3 FHe ) skeletal, true (helium) solid density, g/cm3, kg/m3 FHg ) particle, bulk, apparent (mercury) solid density, g/cm3, kg/m3 τ ) exposure time, s, min Subscripts Cl ) chloride(s), (Cl-) Al ) aluminum (Al) i ) species “i”

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Received for review January 3, 2005 Revised manuscript received May 2, 2005 Accepted June 12, 2005 IE058005Y