Kinetic Modeling of the Alkaline Decomposition of Potassium Arsenojarosite

Uma amostra de arsenojarosita de potássio foi sintetizada e completamente caracterizada. A amostra obtida é uma solução sólida de arsenojarosita de potássio, cuja fórmula aproximada é [K0,75(H3O)0,25]Fe1,84[(SO4)1,82(AsO4)0,18][(OH)2,34(H2O)3,66]. O processo de decomposição em meio alcalino foi estudado no período de indução e de conversão progressiva, e a ordem de reação e a energia de ativação foram determinadas para cada caso. Nas condições experimentais utilizadas, os resultados são consistentes com modelo de partícula esférica com núcleo decrescente e controle químico. Em ambos os processos, quatro modelos parciais e dois modelos globais foram desenvolvidos para descrever seu comportamento básico. Os modelos foram validados, e foi provado que descrevem favoravelmente o processo de decomposição em meio alcalino.


Introduction
In many parts of the world, potable water is polluted with arsenic.This element is disposed of by mining and chemical industries, refineries, etc. 1 The presence of arsenic in ground waters can be also natural because of the leaching of rocks and sediments that contain this element. 2hese ground waters contain great amounts of arsenic, and they are consumed by millions of people around the world, in countries like Bangladesh, Cambodia, China, India, Laos, Myanmar, Nepal, Pakistan and Vietnam in Asia. 3 This problem is also present in the American continent, in countries such as Argentina, Mexico, Chile, Peru, United States, Brazil and Canada. 4,5For these reasons, the U. S. Environmental Protection Agency has set the amount of 10 μg L −1 as the maximum level of pollution allowed in potable water. 6Thus, several alternatives have been studied in order to solve this problem. 7Jarosite technology has been applied for 40 years in the zinc industry as a way to control Fe and other impurities, such as As.Therefore, arsenic can be incorporated into the structure of the jarosites, which work as an inerting medium for this toxic element.Regarding this, Dutrizac et al. 8,9 studied the incorporation of arsenic as AsO 4  3− in the lattice of potassium, sodium and lead jarosite at 97 and 150 o C. Patiño et al. [10][11][12][13][14] have thoroughly studied the alkaline reactivity of argentian jarosites in alkaline medium.Although there are several studies related to the alkaline decomposition of jarosite type compounds, only few ones are related to jarosite type compounds with arsenic. 15,16hese works are focused on the characterization of the dissolution residues and on the kinetic study of these compounds.However, regarding the latter, 16 the obtained kinetic models were not verified.Vol. 23, No. 6, 2012   For this reason, in this research work, a kinetic study, which allows to describe and to predict the behavior of this compound, was carried out at different experimental conditions.Reaction rates and dependencies were compared in a wide range of experimental conditions of concentration, temperature and particle size.Partial and global kinetic models of the induction and progressive conversion periods were developed for the alkaline decomposition of the potassium arsenojarosite in NaOH and Ca(OH) 2 media.

Experimental
The potassium arsenojarosite samples were synthesized using the parameters previously described by Dutrizac et al. 8,9 and characterized by different techniques.
The alkaline decomposition experiments in NaOH and Ca(OH) 2 media were carried out under the following conditions: 0.2 g potassium arsenojarosite (38 ± 2 μm) in an initial volume of 0.5 L, stirring rate of 500 min −1 , varying the concentration of OH − , temperature and particle size.The pH value was kept constant during all the experiment in both media by adding small amounts of concentrated NaOH and Ca(OH) 2 , respectively.The OH − concentration was determined by considering the ionization constant of water and pH of the alkaline solution according to the temperatures used in a previous work. 17igure 1 shows a scanning electron microscopy (SEM) image (JEOL JSM-5900 LV) of almost spherical particles, which are formed by soundly soldered rhombohedral crystals.
The alkaline decomposition kinetics was monitored by atomic absorption spectroscopy (AAS) of potassium using a Perkin Elmer Analyst 200 equipment.For all of the performed experiments, the induction period (t ind ) was determined and the experimental rate constant (k exp ) was calculated.The kinetic modeling was carried out with the experimental results of the alkaline decomposition of potassium arsenojarosite.The solids at different decomposition times, as well as those submitted to high temperatures, were analyzed by X-ray diffractometry (SIEMENS D-500), SEM with an accelerating voltage of 20 kV and microanalysis by energy-dispersive X-ray spectroscopy (SEM-EDS in an Oxford Equipment).The objective was to determine their evolving process.Tables 1 and 2 summarize the experimental data that were used in the modeling.

Topology of the reaction
The decomposition of potassium arsenojarosite in NaOH and Ca(OH) 2 media presents an induction period (t ind ), during which the arsenojarosite does not react.Therefore, the SO 4 2− and K + concentrations are found at negligible levels in the solution (Figure 2).The induction period has been observed in the decomposition of jarosites synthesized in the laboratory, as well as in those coming from industrial plants. 18The ion concatenation of the medium with the surface of the particle creates active sites until a reaction front is established, and through which the  ions of the medium and the potassium arsenojarosite start to diffuse.This is followed by a progressive conversion period, when the concentrations of SO 4 2− and K + progressively increase until reaching stabilization (Figure 2), indicating the end of the reaction.
Figure 3a is an SEM image of a partially decomposed potassium arsenojarosite particle, showing an unreacted core surrounded by a reaction front, which is wrapped in an amorphous gel of iron hydroxide with arsenic.This can be confirmed in Figure 3b, which shows a linescan (indicated in Figure 3a) of the partially decomposed particle, from the core to the halo of the amorphous gel.This figure shows how the amount of sulfur and potassium decreased, indicating that these species have diffused from the core to the solution, while iron and arsenic are still distributed throughout the particle.The relative amounts of all the species are constant in the core, which means that it did not react.The residues do not evolve into new crystal phases, not even after reaching total decomposition (0-10 h).This was evidenced by the X-ray diffractograms in Figure 4, in which the decomposition product is observed as an amorphous material.Therefore, the process is given by the following reaction: The decomposition solids were exposed to high temperatures.At 110 and 400 o C, there is no formation of new crystal phases, but sharp diffraction peaks,   characteristic of crystalline hematite, Fe 2 O 3 (01-089-8103), were observed after thermal treatment at 600 °C (Figure 5). 13ll results in NaOH and Ca(OH) 2 media, it can be explained using the spherical particle model with decreasing core, in which the process is controlled by the chemical reaction according to the following expressions: [19][20][21] k exp t = 1 -(1 -X) 1/3 (2) where k exp is the experimental rate constant, X is the fraction that reacted, V M is the molar volume of the solid, c A represents the reactant concentration, r 0 stands for the initial radius of the particle, k q is the rate constant of the chemical reaction and n is the reaction order.Figure 6 presents the experimental results from Figure 2 after applying equation 2, and it can be observed that they are consistent the chemical expression as that controls the reaction rate.

Modeling Arsenojarosite decomposition in alkaline medium
Tables 1 and 2 summarize the experimental results, in which the induction period (t ind ) and experimental rate constant are presented within a wide range of experimental conditions, such as NaOH and Ca(OH) 2 concentrations, temperature and particle size.The initial pH was kept constant along the reaction, and [OH − ] calculated according to the ionic constant of water at the working temperature of each reaction, as previously mentioned in the Experimental section. 17

Induction period (t ind )
For the induction period of the potassium arsenojarosite decomposition in NaOH medium with [OH − ] > 6.4 × 10 −3 mol L −1 , a fractional reaction order of n = 2.65 was obtained.The calculated activation energy in NaOH medium is E a = 84.7 kJ mol −1 .In the case of the Ca(OH) 2 with [OH − ] > 3.1 × 10 −2 mol L −1 , the fractional reaction order is n = 0.24.The calculated activation energy in Ca(OH) 2 medium is E a = 88.3 kJ mol −1 .According to these results, the induction period for NaOH is defined by the following expressions.

Progressive conversion period
For the progressive conversion period corresponding to the potassium arsenojarosite decomposition in NaOH medium with [OH − ] > 6.4 × 10 −3 mol L −1 , a fractional reaction order of n = 1.86 was obtained.The activation energy calculated in NaOH medium is E a = 60.3 kJ mol −1 .Therefore, the kinetic expression for the progressive conversion period in NaOH medium is as follows.
For [OH − ] > 6.4 × 10 −3 mol L −1 : (6)   For the progressive conversion period corresponding to the potassium arsenojarosite decomposition in Ca(OH) 2 with [OH − ] > 1.92 × 10 −2 mol L −1 , a fractional reaction order of n = 1.14 was obtained.The activation energy calculated in Ca(OH) 2 medium is E a = 74.4kJ mol −1 , the kinetic expression for progressive conversion period in Ca(OH) is as follows.In all the kinetic expressions: v M = 153.07cm 3 mol −1 , R = 8.3144 J mol −1 K −1 , r 0 in cm, T in Kelvin, [OH − ] in mol L −1 and t in minutes.
From equations 4 and 6, corresponding to the alkaline decomposition in NaOH medium with [OH − ] > 6.4 × 10 −3 mol L −1 , a general expression can be established in order to determine the total reaction time needed for obtaining a definite conversion of the potassium arsenojarosite.The kinetic model is the following: (8)   Figure 10 shows the total reaction time needed for obtaining a potassium arsenojarosite conversion of X = 0.75 (calculated according to equation 8) vs. the same experimentally obtained parameters.It can be concluded that equation 8 is consistent with the experimental results because the experimental and the calculated data do not show any considerable differences.
For equations 5 and 7, corresponding to the decomposition in Ca(OH) 2 medium, an expression was   Figure 11 shows the total reaction time needed for obtaining a conversion of X = 0.75 (calculated according to equation 9) vs. the same parameter (experimentally obtained).It can be concluded, therefore, that equation 9 is consistent with the experimental results of the decomposition in Ca(OH) 2 medium.

Conclusions
The decomposition solids do not evolve into new crystal phases after reaching total decomposition.However, after being heated at 600 o C, the decomposition product evolves into a new crystal phase, which was identified as hematite (Fe 2 O 3 ).The general mathematical models for the decomposition of potassium arsenojarosite in NaOH and Ca(OH) 2 media during the induction and progressive conversion periods are presented as follows: NaOH Ca(OH) 2 These models describe the of alkaline decomposition of the potassium arsenojarosite.They will also allow to predict its behavior at different temperature (20-60 °C) and concentration conditions (0.1-2.7 × 10 −4 mol L −1 for NaOH and 2.3 × 10 −2 -7 × 10 −4 mol L −1 for Ca(OH) 2 ).

Figure 1 .
Figure 1.Particle size distribution of the synthesized potassium arsenojarosite.

Figure 6 .
Figure 6.Representation of the decreasing core model with chemical control of the data in Figure 2.

Figure 5 .
Figure 5. X-ray diffractograms of the total decomposition product heated at 110, 400 and 600 o C for 1 h, including the identification of the phase formed at 600 o C.

ForFigure 7
Figure 7 is a plot of the development of the kinetic model according to equations 4 and 5, showing the experimental induction period (t ind-exp (min)) vs. the calculated induction (t ind-calc (min)).Since the induction and progressive conversion are at different magnitude orders, the base 10 logarithms of the calculated and experimental induction periods were plotted.

Figure 8
Figure 8 presents the development of equation 6, being a plot of the experimental rate constant vs. the calculated rate constant, e.g., k exp (min −1 ) vs. k calc (min −1 ) in NaOH medium.Likewise, Figure9depicts the development of

Figure 7 .
Figure 7. Induction period.Alkaline decomposition of the potassium arsenojarosite.Comparison between the calculated and experimental data in NaOH and Ca(OH) 2 media.

Figure 10 .
Figure 10.Alkaline decomposition in NaOH medium.Plot of the reaction total time obtained at an X = 0.75 conversion (experimental vs. calculated).

Figure 11 .
Figure 11.Alkaline decomposition in Ca(OH) 2 medium.Plot of the reaction total time obtained at an X = 0.75 conversion (experimental vs. calculated).

Table 1 .
Decomposition of potassium arsenojarosite in NaOH medium: n = 2.65, E a = 84.7 kJ mol −1 for the induction period; n = 1.86,E a = 60.3 kJ mol −1 for the progressive conversion period

Table 2 .
Decomposition of potassium arsenojarosite in Ca(OH) 2 medium: n = 0.24, E a = 88.3 kJ mol −1 for the induction period; n = 1.14, E a = 74.4kJ mol −1 for the progressive conversion period