Thermal Decomposition of Sodium Hydrogen Carbonate and Textural

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Thermal Decomposition of Sodium Hydrogen Carbonate and Textural Features of Its Calcines Miloslav Hartman,*,† Karel Svoboda,† Michael Pohořelý,‡ and Michal Šyc† †

Institute of Chemical Process Fundamentals of the AS CR, v.v.i., Rozvojová 135, 165 02 Prague 6, Czech Republic Department of the Power Engineering, Institute of Chemical Technology, Technická 5, 16628 Prague 6, Czech Republic

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‡

ABSTRACT: The decomposition rate of sodium hydrogen carbonate (NaHCO3) into carbonate (Na2CO3) was determined as weight loss at ambient pressure and elevated temperatures up to 230 °C. A particularly slow increasing-temperature procedure and small samples of fine powders were employed to minimize heat and mass transfer intrusions. Efficient removal of the gaseous products eliminated possible equilibrium constraints. A near-first-order reaction rate equation has been presented for the decomposition reaction and also verified by the data collected by experiment in a constant-temperature mode. This correlation makes it possible to predict the reaction rate as a function of temperature and the extent of decomposition. In combination with its integrated form, it can readily be used, for example, in modeling or design of the decomposition process. Experimental measurements show that the porosity of parent (precursor) solids persists during the calcination process. It is believed that such a highly alkaline porous reactant is sort of ideally suited for the fast sorption of unwanted acid gases. The sintering of the nascent NaHCO3-derived carbonate was explored in a nitrogen environment at temperatures from 120 to 230 °C. An empirical model has been proposed to correlate the experimental results on the most probable pore diameter, the specific surface area, and the micrograin size of calcines in dependence upon the temperature of sintering. In addition to the pore volume, also these textural/ structural features are of considerable importance in assessment of the sorbent suitability.

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INTRODUCTION

Kinetics of the thermal decomposition of sodium hydrogen carbonate was the subject of several studies in the field of basic and theoretical chemistry.7,15−21 However, there are considerable differences among the presented findings. Aside from the origin and history of the parent materials, wide discrepancies between the reported results stem from a number of encountered experimental difficulties (e.g., the sample mass and granulometry, the method of advance of temperature, and the differences in thermal properties of the materials). An employed method of deducing kinetic parameters from measured thermogravimetric data should also be carefully considered. The objective of this work is to acquire a basic knowledge needed for the development of a very efficient alkaline sorbent particularly for near-complete removal of hydrogen chloride from producer gas. Our experience indicates that the phenomenon of sintering should not be overlooked in any gas−solid reaction system. There are many situations in which decomposition, sintering, and other subsequent reactions (e.g., chloridization) take place on a similar time scale.

One of the issues in our current research on biomass gasification is a need for deep removal of hydrogen chloride and/or hydrogen fluoride from the fuel (producer) gas at elevated temperature.1 While the sorption of hydrogen chloride on inexpensive calcium oxide suffers from considerable equilibrium constraints, the reaction with sodium-based solids is thermodynamically capable of reducing the HCl concentrations in the fuel gas below 1 ppm by volume still at temperatures as high as 500 °C.2,3 Potassium-based sorbents have slightly more favorable reaction equilibria but exhibit a tendency to form low-melting point eutectics. As is known for some years, there is a striking difference in reactivity between common, commercial soda ash (the Solvay soda) and the sodium carbonate prepared by the appropriately controlled thermal decomposition of sodium hydrogen carbonate (sodium bicarbonate).4−8 Our experience as well as that of others6,9 shows that such active sodium carbonate is also quite reactive toward noxious NOx and exhibits affinity for persistent odors. In addition to the specific surface area, the pore volume of the solid reactants is also augmented as gaseous products are released in the course of the thermal decomposition of NaHCO3. There are casual links between the low temperature of decomposition of the parent materials and large surface area, pore volume, and high reactivity of their calcines. In light of the grain theory, micrograins comprise a porous particle produced by thermal decomposition. As micrograin sintering occurs, the grains grow larger and the surface area and the pore volume are reduced. These undesirable textural changes have an adverse effect on the reactivity of solids with fluids.10−14 © 2013 American Chemical Society

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PHYSICOCHEMICAL PRINCIPLES The decomposition reaction 2NaHCO3(s) = Na 2CO3(s) + H 2O(g) + CO2 (g)

(1)

is considerably endothermic with ΔHo (298 K) = 135.52 kJ deduced from Barin’s thermochemical data.22 The standard Received: Revised: Accepted: Published: 10619

March 20, 2013 June 5, 2013 July 3, 2013 July 3, 2013 dx.doi.org/10.1021/ie400896c | Ind. Eng. Chem. Res. 2013, 52, 10619−10626

Industrial & Engineering Chemistry Research

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enthalpy of reaction, ΔHo, changes with temperature very little (nonmonotonously) to 134.85 kJ at 500 K (226.8 °C). Thermodynamic constraints imposed on reaction 1 can also be inferred from the thermodynamic data compiled and tabulated by Barin22 and expressed in the form 7080.42 log K = 21.66584 − (1a) T where

K = K p = pH2O ·pCO2

which predict the decomposition temperature, Td, to be as large as 373.70 K (100.55 °C) and, correspondingly, the standard heat of reaction 1, ΔHo, amounts to 127.89 kJ. Structural transformation is involved in reaction 1: the crystalline, monoclinic NaHCO3 is converted into the powdered or cryptocrystalline carbonate. Upon the release of water vapor and carbon dioxide, the pseudomorphs more or less similar to the parent hydrogen carbonate can remain at lower temperature. At higher temperature and/or after some period of time, further transformation or sintering of the carbonate occurs. The decomposition produces a mass of carbonate crystallites that form a porous spongy relic of the parent hydrogen carbonate. The handbook values24,25 for the density of sodium hydrogen carbonate (2.20 g/cm3) and sodium carbonate (2.533 g/cm3) lead to the following molar volumes: VNaHCO3 = 38.185 cm3/g and VNa2CO3 = 41.843 cm3/g. Considering these values, it becomes evident that the hydrogen carbonate crystal is made porous or much more porous by calcining it. The theoretical fractional porosity of the carbonate formed from a nonporous crystal of NaHCO3 amounts to 0.4521, which corresponds to the pore volume as large as 0.3258 cm3/g.

(2)

and the partial pressures pH2O and pCO2 are given in kPa. The dissociation pressure of NaHCO3, p, is given by p = pH2O + pCO2 (3) With respect to the stoichiometry of reaction 1, we get

p = 2K 0.5

(3a)

and consequently 3540.21 (4) T The decomposition temperature, Td, defined as a temperature at which the decomposition pressure, p, is equal to the pressure of the surrounding atmosphere (i.e., p = 101.325 kPa), and predicted by eq 4 amounts to 387.83 K (114.68 °C). Reasonable agreement can be seen in Figure 1 between the theoretical predictions of eq 4 and the experimental equilibrium log p = 11.13395 −

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EXPERIMENTAL SECTION The experimental work includes several parts: material specification and sample preparation, careful and replicated TGA experiments at linearly increasing temperature as well as at constant temperature, and experimental measurements of the pore volume and the pore size distribution in decomposed solids. Material. The experiments were performed with sodium hydrogen carbonate obtained from commercial sources (Analyzed Reagent grade) with purity above 99.5%. Chemical specification of this material is given in Table 1. Table 1. Chemical Characteristics of Sodium Hydrogen Carbonate

data measured by Caven and Sand.23 Their experimental data can be represented by means of eqs 4a and 4b 6680 T

(4a)

log p = 10.94338 −

3340 T

(4b)

amount (wt %) 99.6 0.02 0.01 0.001 0.001 0.01 36.77

For the TGA experiments, minute crystals of hydrogen carbonate were gently ground with an agate mortar and pestle and carefully sieved by hand to provide very fine samples for the kinetics experiments. In order to conform to common practice,26,27 all TGA experiments were run on the very narrowsized fraction between 50 and 70 μm (270−200 mesh by Tyler). For the textural experiments, hydrogen carbonate in powder form was first pressed into cylindrical pellets and then broken or crushed into needed pieces to provide larger samples for the textural experiments. All the samples were stored in a desiccator. Procedure and Apparatus. 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

Figure 1. Equilibrium dissociation pressure of sodium hydrogen carbonate under ambient pressure and at different temperatures. Symbols represent the experimental data obtained by Caven and Sand.23 Solid line shows the predictions of eq 4.

log K = 21.28471 −

constituent NaHCO3 chloride sulfate iron heavy metals insoluble matter weight loss on ignition determined at 600 °C

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effects on the rate of reaction are minimized. Removal of the gaseous product of reaction eliminates a possible effect of equilibrium constraints. On preliminary experiments, we chose the operating conditions as follows: the heating rate as low 1 K/min, the sample mass as small as 8 mg, and a dry nitrogen flow of 40 cm3/min was maintained through the gas space to ward off the gaseous product(s) of reaction. We believe that such operating conditions ensure the relevance of collected data. Thermal decomposition experiments were carried out in a Setsys Evolution, Simultaneous TGA/DTA Analyzer (Setaram Corp.) equipped with an Omni Star Mass Spectrometer (Pfeiffer Vacuum Corp.). Temperature was increased at a preselected constant rate or was maintained constant. Fractional conversions were calculated from the decrease in sample mass, w0 − w(τ), at any time (temperature) and the equation: X (τ ) =

MNaHCO3 w − w(τ ) 2 · · 0 y MH2O + MCO2 w0

(5)

where y is the mass fraction of sodium hydrogen carbonate in the original sample and Mi is the molar mass of species. Complete stoichiometric conversion (i.e., y = 1 and X = 1) corresponds to the relative weight loss Δw/w0 = 0.36917. Pore volumes/porosities of the samples were determined by helium and mercury displacement with the use of Accu Pyc 1330 and AutoPore III instruments (Micromeritics Instrument Corp.). Pore size distributions were determined by measuring the volume of mercury penetrating the pore volume at pressure increasing up to 690 MPa (105 psi).

Figure 2. Fractional extent of the thermal decomposition of sodium hydrogen carbonate, X, in an increasing-temperature experiment. Initial mass of the sample, 8.01 mg; heating rate, 1 °C/min; flow rate of entrainer nitrogen, 40 cm 3 /min. Symbols represent the experimental results. Solid line shows the predictions of eq 11.

⎡ ⎛ E ⎞⎤ dX n ⎟ (1 − X ) = ⎢A exp⎜ − ⎝ RT ⎠⎥⎦ ⎣ dτ

■

(6)

with the initial condition X=0

RESULTS AND DISCUSSION Nonisothermal Kinetics of Decomposition. Preliminary experimental runs indicated that the first traces of the commencing decomposition of sodium hydrogen carbonate became detectable in the vicinity of 355 K (82 °C). The dissociation pressure at this temperature predicted by eq 4 amounts to 14.5 kPa. In light of the experiments of Caven and Sand,23 the corresponding dissociation pressure is as high as 34.3 kPa. The experimental curve of Hu at al.7 measured at a heating rate of 6 K/min suggests an initial temperature of the decomposition process of about 364 K (91 °C). Thus, it can be anticipated that appreciable decomposition of NaHCO3 can hardly occur below approximately 343 K (70 °C). Temperature in our experimental runs was increased at a rate of 1 K/min to a final temperature of 438 K (165 °C) where the decomposition to sodium carbonate was virtually complete. As can be seen in Figure 2, the decomposition of NaHCO3 becomes quite rapid at about 393−403 K (120−130 °C). The data provided by the linearly increasing-temperature procedure, some of which are plotted in Figure 2, were employed as the solid basis for development of a kinetics equation describing the rate of the decomposition reaction 1. Every care was taken to reduce all presumable side effects. In order to minimize random inaccuracies, the experimental runs were always repeated. The presented and treated data are means of five-time replicated measurements. As can be seen, the sigmoid, X vs T dependence shown in Figure 2 seems to be moderately asymmetrical in shape. General experience indicates that the rate of the thermal decomposition of solids, dX/dτ, can advantageously be described by the nth-order, differential equation as follows

at

(6a)

τ=0

Equation 6 is a practical basis for description since it complies with most of the prior nucleation and diffusion models.10,11,26,27 Forty data points at equal temperature (time) intervals were taken to fit this equation. The derivatives dX/dτ were approximated as ΔX/Δτ and estimated from the conversion measured as a function of reaction time and temperature. The values of the apparent (effective) kinetic parameters were computed by the simplex procedure (flexible polyhedron search) using statistical evaluations based upon the Student ts distribution.10,11 Computational results of the regression fitting are given in Table 2. The computed apparent (effective) activation energy, E, is as large as 101.1 kJ/mol. This is between the values of 86.4 and 111.5 kJ/mol reported by Tanaka28 and Yamada and Koga,17 respectively. The estimated apparent order of reaction is n = 1.029, which is very close to the first-order kinetics assumed, for Table 2. Effective Kinetics Parameters for Thermal Decomposition of Sodium Hydrogen Carbonate (eq 6)a effective parameter

value

preexponential factor, A, 1/s activation energy, E, kJ/mol order of reaction, n

1.158 × 10 101.1 1.029

10

95% confidence interval

variance

±2.536 × 10

1.161 × 107

±0.451

0.1894

±0.0319

0.01308

7

Upon the basis of experiments with finely powdered, 8 mg samples in a dry nitrogen flow of 40 cm3/min at a heating rate of 1 K/min, temperatures range from 353 to 428 K, fractional conversions from 0.03 to 0.98. a

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example, by Janković and Adnadević.18 Simple tests also confirmed that the data points in the form of ln[(ΔX/Δτ)/(1 − X)1.029] plotted against the reciprocal of thermodynamic temperature, 1/T, behaved linearly. Figure 3 shows how the rate of the decomposition reaction develops with increasing temperature (and time) using the

∫0

T

⎡ ⎛ E ⎞⎤ RT 2 ⎜⎛ 2RT ⎟⎞ ⎡ ⎜⎛ E ⎟⎞⎤ ⎟ dT = ·⎢exp − 1− ⎢⎣exp⎜⎝ − ⎥ ⎥ RT ⎠⎦ E ⎝ E ⎠ ⎣ ⎝ RT ⎠⎦ (10)

On combining eqs 7, 8, and 10 and rearranging, we have the final solution for the overall conversion, X, 1

X = 1 − [1 − (1 − n)Y )]1 − n

(11)

for n ≠ 1, where the symbol Y denotes the dimensionless function of temperature, T, defined by Y=

⎛ E ⎞ ART 2 ⎛⎜ 2RT ⎞⎟ ⎟ 1− ·exp⎜ − ⎝ ⎠ ⎝ RT ⎠ E βE

(12)

In the case of n = 1, we get for X X = 1 − exp( −Y )

The overall conversions, X, computed for different temperatures, T, and time exposures, τ, from eqs 11 and 12, with the use of the effective kinetics triad, A, E, and, n, shown in Table 2, are in Figure 2 compared to the corresponding values determined at temperatures between 80 and 160 °C. As can be seen, the experimental data plotted in this figure fit the computed sigmoid curve quite well. As shown in Figure 3, the temperature corresponding to the highest rate of reaction amounts to approximately 409 K (136 °C) which by eq 12 leads the dimensionless quantity Y as large as 1.092. The conversions, X, predicted by eq 11 (for n = 1.029) and eq 13 (for n = 1) differ just slightly and amount to X = 0.6587 and X = 0.6645, respectively. We believe that also these quick examinations support consistency of our description. Isothermal Decomposition Kinetics. The rate of the thermal decomposition of sodium hydrogen carbonate was also investigated in the constant-temperature regime. The invarianttemperature experiments were performed in the range of 100− 140 °C which is mostly below the characteristic inflection temperature in the linearly increasing-temperature decomposition mode shown in Figures 2 and 3. It was assumed that, at such moderate temperatures, the unwanted process of sintering of the newly formed solid product could be considerably slowed down or minimized. Moreover, the measured data are less likely to be influenced by heat transfer limitations at such lower temperatures. The results of constant temperature runs are presented in Figure 4. It can be concluded from these measurements that the reaction rates at 100 and 110 °C are rather low for practical purposes. In accordance with temperature-increasing experiments, the decomposition becomes quite rapid at about 120 °C. It should be noticed that, in the range between 120 and 140 °C, the experimental curves level off (i.e., X > 0.95) after about 2−0.5 h exposure. On integration of eq 6, holding temperature, T, constant and rearranging, we get eqs 14 and 15 describing the progress of decomposition in the course of time in the isothermal mode of operation

Figure 3. Rate of decomposition, dX/dT, in the course of an increasing-temperature experiment. Curve shows the model predictions for the operating conditions presented in the caption of Figure 2.

kinetic parameters summarized in Table 2 and eq 6. The maximum rate of reaction, ΔX/Δτ, amounts to 4.76 × 10−4 1/s which is a value considerably lower than that we deduced from an experimental curve of Hu et al.7 However, it should be noted that this value (2.80 × 10−3 1/s) was determined from an experimental run with the much higher heating rate (6 K/min). A corresponding value of ΔX/Δτ inferred from experimental results of other authors18 amounts to approximately 4 × 10−4 1/s under conditions similar to ours. The general equation for the overall conversion of solids takes the form

∫0

X

dX A = β (1 − X )n

∫0

T

⎡ ⎛ E ⎞⎤ ⎟ dT ⎢⎣exp⎜⎝ − ⎥ RT ⎠⎦

(7)

The left-hand side of eq 7 can readily be integrated to get

∫0

X

dX 1 = [1 − (1 − X )1 − n ] (1 − X )n 1−n

(8)

for X ≠ 1 and n ≠ 1 (fractional-order kinetics, e.g., Avrami’s nucleation law) and

∫0

X

dX = −ln(1 − X ) 1−X

(13)

(9)

for X ≠ 1 and n = 1 (first-order kinetics, Mampel’s law). Quick examinations confirm that the values of the primitive function in eq 8 are very close to those of the primitive function in eq 9, when the quantity n is nearing unity from either side. The integral on the right-hand side of eq 7 cannot be evaluated by means of the elementary functions. The procedure proposed by Coats and Redfern,29−31 i.e., a suitable substitution followed by a rapidly convergent expansion, leads to

1

X = 1 − [1 − (1 − n)kτ )]1 − n

(14)

for n ≠ 1 and X = 1 − exp( −kτ )

(15)

for n = 1, where k is the effective reaction rate constant at the temperature of interest as defined in Symbols. It can easily be shown that the predictions of eq 14 converge to those of eq 15 10622



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densely arranged flake-like micrograins. The decomposed particles are porous with smaller, more or less round micrograins. Upon the loss of water vapor and carbon dioxide, the pseudomorphs similar to the parent hydrogen carbonate tend to remain at lower temperatures. At higher temperatures, the recrystallization or sintering of the reaction product occurs. An effort was taken to explore how the volume of the solid phase is changed by decomposition reaction. Since the employed operating temperatures are quite low, it is feasible to assume that no shrinkage takes place and the decomposing particle retains its gross external (apparent) volume. As both the precursor and the reaction product are well-defined compounds, an analytical relationship can be developed between the porosity of the decomposing particle, e, the initial porosity of the parent hydrogen carbonate, ein, the mass fraction of sodium hydrogen carbonate in the precursor, y, and the progress of reaction, X ⎛ ⎞ V e − e in = y⎜1 − Na2CO3 ⎟X 1 − e in 2VNaHCO3 ⎠ ⎝

Figure 4. Fractional extent of the thermal decomposition of sodium hydrogen carbonate, X, in constant-temperature experiments. Initial mass of the samples, 7.94−8.09 mg; flow rate of entrainer nitrogen, 40 cm3/min. Symbols represent the experimental results at different temperatures. Solid curves show the model predictions.

(16)

As is evident, in the simplest case (i.e., for y = X = 1 and ein = 0), eq 16 predicts the porosity as large as e = 0.4521 which is the value mentioned above and estimated from the mere stoichiometry of reaction 1. A characteristic feature of many noncatalytic gas−solid reactions (e.g., sorptions) is that they are accompanied by a significant expansion of the solid phase. In the case of the sorption of HCl(g) on Na2CO3, the expansion factor, f, defined as the ratio of the molar volume of sodium chloride (VNaCl = 26.932 cm3/mol) to the molar volume of sodium carbonate (VNa2CO3 = 41.843 cm3/mol), is equal to 1.2873. A simple conception of the system leads to eq 17

when n → 1. In Figure 4, there are also presented the predictions of eq 14 for the respective temperatures with the use of the effective kinetics parameters deduced from the nonisothermal experimental runs that are given in Table 2. Some differences are apparent between the determined and the predicted conversions. It should be borne in mind, however, that the kinetic equations of Arrhenius type are inherently sensitive to the variations in values of the kinetic parameters and quantities. Also, the different modes of experiments (increasing- and constant-temperature methods) should be taken into consideration. In light of these circumstances, we believe that the predictions and experiment are in fair agreement. The proposed description of the reaction kinetics can be applied to modeling and simulation of appropriate reactors for the thermal decomposition of sodium hydrogen carbonate. The empirical relationships have usual limitations, and they should be applied with caution outside experimental conditions from which they were deduced. It should be recalled that the decomposition reaction is strongly endothermic and that it can be difficult to transfer energy fast enough particularly to a rapidly decomposing particle of the reactant. Of possible heat transfer resistances, gas to particle heat transfer and intraparticle heat transfer need to be taken into consideration. Of course, mass transfer resistances such as pore diffusion within the reaction product cannot generally be overlooked. Textural Characteristics of the Decomposed Solids. Sodium hydrogen carbonate in dispersed form was first pressed into pellets, then crushed, and sieved to secure samples for the textural measurements. The solids were exposed to the stream of dry nitrogen at the temperature of interest. Then, the decomposed particles were stored in airtight containers, and shortly afterward, they were subjected to textural analyses. Pore volume vs pore size data were measured with the aid of a 690 MPa (105 psi) porosimeter (Micromeritics Instrument Corp.) with samples of partially and/or completely decomposed parent material. Microscopic examinations revealed that the precursor (sodium hydrogen carbonate) particles are composed of

e(Xs = 1) = 1 − (1 − e0)f

(17)

which predicts that, for f = 1.2873, the initial porosity of sodium carbonate, e0 = 0.4521, is on complete conversion (Xs = 1) to sodium chloride considerably reduced to e = 0.2947. Nevertheless, this is an important indication that the porous structure of such sorbent (prepared from nonporous NaHCO3) is capable of accommodating all sodium chloride formed by the reaction. This fact deserves to be viewed as a promising circumstance from the stand-point of reactivity and sorption capacity of the reactant. The porosimetry experiments were also performed with particles of a different degree of the conversion (calcination) to porous sodium carbonate. Included in this series, there is also the parent material (i.e., virgin sodium hydrogen carbonate). The determined porosities increase linearly from e = ein = 0.0854 for a pellet of the parent NaHCO3 (i.e., X = 0) to e = 0.4989 for completely decomposed (calcined) solids (i.e., X = 1). The straight lines shown in Figure 5 represent the values computed from eq 16 for different conversions of sodium hydrogen carbonate, and these computed porosities are generally in fairly good agreement with the experimental values. As can be seen, the measured porosities are unequivocally higher than those calculated for a nonporous crystal of NaHCO3 as the precursor. From this analysis, it is evident that, if the calcination process takes place at lower temperatures such as around 100−150 °C, shrinkage of the particles does not occur and the pore volume of the parent material is preserved during its thermal decomposition. 10623



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Figure 6. Pore-radius distribution in the particles calcined at 200 °C: calcination (exposure) time, 120 min. Figure 5. Fractional porosity of decomposing particles for initially nonporous NaHCO3 (ein = 0) and for little-porous pellets of NaHCO3 (ein = 0.0854) as a function of the fractional conversion to Na2CO3, X, (yNaHCO3 = 0.996). Data points are the results of experiments; solid lines show the predictions of eq 16.

Table 3. Physical Characteristics of Parent Sodium Hydrogen Carbonate and Sodium Carbonate Prepared by Its Calcination at 200 °C

Pore-Size Distribution. As our experimental data indicate, the thermal decomposition of the hydrogen carbonate is accompanied/followed with the process of sintering or recrystallization of the nascent carbonate. It takes place quite rapidly at temperatures considerably lower than that suggested by the Tammann temperature which is usually viewed as an index for the onset of significant lattice mobility. The driving force for the mass flux, which occurs between the sites of different surface curvature of the micrograins, is the excess surface energy over some asymptotic value at a given temperature. With respect to the range of experimental temperatures, the surface diffusion/migration of atoms across the grain surface to the necks seems to be the main mechanism of the sintering process. The most sensitive textural parameters affected by sintering are the pore size and the specific surface area. Of course, other sintering mechanisms cannot be ruled out. The experimental results are illustrated in Figure 6 by the pore-size distribution curve for the particles calcined at a temperature of 200 °C. As can be seen, the curve exhibits a sharp peak at the most probable pore diameter, d̅p (by pore volume), as large as 1.991 × 10−5 cm. Illustrative examples of the porosimeter data are given in Table 3. Assuming an assembly of parallel noninterconnected pores, the total pore surface area of the Na2CO3 particles, S, estimated with the aid of

S=

physical property

NaHCO3

apparent density, ρp, g/cm3 pore volume, Vp, cm3/g fractional porosity, e median pore diameter (by pore volume), d̅p, nm surface (total pore) area, S, m2/g mean grain diameter, d̅g, nm

2.012 0.04247 0.08542

Na2CO3 prepared from NaHCO3 by calcination at 200 °C 1.269 0.3930 0.4989 199.1 7.90 299.8

The increase in size of the most probable pores with temperature can be regressed by the relationship 302.34 ln d p̅ = −10.1853 − (20) T for a calcination (exposure) time of 90 min. The coefficients in eq 20 were determined by a least-squares method, and predictions of this equation are compared to the experimental values in Figure 7. It has to be borne in mind that the

4Vp d p̅

(18) 2

amounts to 78 955 cm /g. Presuming further that all micrograins are uniform, nonporous spheres with no overlapping, their mean size, d̅g, can simply be related to the surface area

dg̅ =

6 SρHe

(19) 2

Thus, the above surface area, S = 78 955 cm /g, leads to the grain size as large as d̅g = 3 × 10−5 cm.

Figure 7. Influence of the calcination temperature, t, on the diameter of the most probable pores, d̅p: calcination (exposure) time, 120 min. 10624



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regression equations developed here have the usual limitations and they should be applied with caution outside the experimental conditions from which they were deduced. As is evident, once the mean pore size is determined or predicted by eq 20, the surface area and/or grain size is readily estimated, e.g., for the needs of reaction modeling. The specific surface area of the decomposed solids was also determined by nitrogen adsorption on the basis of the Brunauer−Emmett−Teller theory of isothermal multilayer adsorption (Instrument ASAP 2050, Micromeritics). Surface area measured by this method was very close to that inferred from the cumulative pore volume. For example, Hu et al.7 report a surface area value of 33 000 cm2/g for their calcined solids which is a result more or less similar to our findings. Postlude. The thermal decomposition of sodium hydrogen carbonate can be advantageously carried out in a fluidized-bed reactor with respect to intensive heat and mass transfer in such a swirling reaction milieu. However, it is to be noted that the density of solids undergoes a relevant change which will affect the fluidization characteristics of the material. For example, the estimated minimum fluidization velocity and the terminal (freefall) velocity of 0.5 mm parent particles change by factors of 0.54 and 0.65, respectively, on complete conversion to Na2CO3 at 200 °C.32

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AUTHOR INFORMATION

Corresponding Author

*Tel. +420 220 390 254. Fax: +420 220 661. E-mail: hartman@ icpf.cas.cz. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Thanks are due to the Research Fund for Coal and Steel of the EC for support through Grant No. RFCR-CT-2010-00009 and the Ministry of Education, Youth, and Sport of CR (Support No. 7C11009). Our grateful thanks also go to Mrs. Eva Fišerová for her assistance with the manuscript.

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NOMENCLATURE

Abbreviations

ppm = parts per million by volume wt = weight Symbols

A = preexponential factor, Arrhenius constant, fitted parameter, 1/s d̅g = mean diameter of micrograins, cm d̅p = most probable diameter of pores, cm e = fractional porosity of solid = (ρHe − ρHg)/ρHe e0 = initial fractional porosity of sodium carbonate before sorption in eq 17 ein = fractional porosity of solid prior to calcination E = effective (apparent) activation energy, fitted parameter, J/mol f = relative increase in the solid volume caused by sorption reaction ΔHo = standard heat of reaction 1, kJ/mol of Na2CO3 k = effective reaction rate constant in eqs 14 and 15 = A·exp[−E/(RT)], 1/s K = equilibrium constant for reaction 1, given by eq 2, (kPa)2 Mi = molar (formula) mass of component, g/mol n = effective (apparent) order of reaction, fitted parameter p = dissociation pressure of NaHCO3 given by eqs 3 and 3a, kPa r = pore radius, cm R = ideal gas-law constant = 8.31441 J/(mol K) S = specific surface area of solid, cm2/g t = Celsius temperature, °C T = thermodynamic temperature, K Td = temperature at which the pressure of gaseous product(s) is equal to ambient pressure, K Vi = molar volume of component, cm3/mol Vp = pore volume of particle = (1/ρHg) − (1/ρHe), cm3/g w0 = initial mass of sample, g w(τ) = mass of sample at any moment of time, g Xs = fractional conversion of Na2CO3 to solid product by sorption reaction in eq 17 X = extent of decomposition of NaHCO3 expressed as the fractional conversion of NaHCO3 to Na2CO3 given by eq 5 y = content of NaHCO3 in sample, weight fraction Y = dimensionless function of thermodynamic temperature given by eq 12

CONCLUSIONS

While the decomposition temperature of sodium hydrogen carbonate, predicted on the basis of thermochemical data, is as high as 114.7 °C, its value deduced from the measured dissociation pressures is somewhat lower and amounts to 100.6 °C. In increasing-temperature experiments, the first traces of the commencing decomposition become noticeable at about 82 °C. The maximum rate of reaction, attained at about 136 °C and X = 0.66, was dX/dτ = 4.76 × 10−4 1/s. The proposed rate equation deduced from the increasing-temperature experiments is in fair agreement with the results measured in the constanttemperature mode. The apparent order of reaction is equal to 1.03 which is very near the first-order kinetics in the NaHCO3 mass. The apparent activation energy, E = 101.1 kJ/mol, represents approximately 75% of the standard heat of reaction. Temperatures above 120 °C secure a rapid rate of the decomposition reaction. Aside from chemical reaction, heat and mass transfer rates have to be also taken into consideration in any realistic model of the calcination process. Nonporous monoclinic crystals or little porous pellets of NaHCO 3 are made highly porous by calcining them. Experimental measurements show that the parent particles do not shrink and their original pore volume persists during the calcination process. The largest measured porosity of decomposed solid amounted to approximately 50% (0.39 cm3/g). The particle density needed, for example, in fluidization computations, decreases with the progress of reaction from 2.21 to 1.27 g/cm3. Although the calcination takes place at rather low temperatures, quite far below the Tammann point (aprox. 465 °C), the sintering of the nascent sodium carbonate is significant. Raising the temperature of calcination from 120 to 230 °C increases the most probable pore diameter from 180 to 210 nm, augments the mean micrograin size from 260 to 310 nm, and decreases the specific surface area from 9 to 7.6 m2/g. The sodium carbonate originated from NaHCO3 particles exhibits attractive characteristics for removal of acid components from waste gas.

Greek Letters

β = rate of heating, K/s ρHe = true (helium) solid density, g/cm3 10625



Article

ρHg = apparent (mercury, particle) density, g/cm3 τ = exposure time, s

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Thermal Decomposition of Sodium Hydrogen Carbonate and Textural

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