Decomposition of Potassium Hydrogen Carbonate: Thermochemistry

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Cite This: Ind. Eng. Chem. Res. 2019, 58, 2868−2881

Decomposition of Potassium Hydrogen Carbonate: Thermochemistry, Kinetics, and Textural Changes in Solids Miloslav Hartman,*,†,‡ Karel Svoboda,†,§ Bohumír Č ech,‡ Michael Pohorě lý,†,| and Michal Š yc† Institute of Chemical Process Fundamentals of the AS Č R, Rozvojová 135, 165 02 Praha 6, Czech Republic ENET Centre, Technical University of Ostrava, 17, Listopadu 15, 708 33 Ostrava, Czech Republic § Faculty of the Environment, University of Jan Evangelista Purkyne, Králova Výsǐ na 7, 400 96 Ú stí nad Labem, Czech Republic | Department of Power Engineering, University of Chemistry and Technology Prague, Technická 5, 166 28 Praha 6, Czech Republic † ‡

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S Supporting Information *

ABSTRACT: To determine unbiased rates of the decomposition of KHCO3, slowly increasing- and constant-temperature TGA methods were employed with small, finely ground samples. Such reaction provides a novel, porous, and highly reactive sorbent for noxious and/or malodorous gases. The bicarbonate commences decomposing at 364 K, and the maximum rate of reaction, attained at 421.9 K, amounts to 5.73 × 10−4 1/s. Taking advantage of the Schlömilch function, an Arrhenius-type relationship is developed by an integral method: the activation energy is as large as 141.3 kJ/mol and the order of reaction amounts to 1.145. While the pore volume made by calcination (0.2309 cm3/g) is not affected by temperature at 403−503 K, the mean pore diameter and the grain size augment with increasing temperature. The diagram presented makes it possible to conveniently predict the conditions to attain near-complete conversion of the bicarbonate and minimize undesirable sintering of the nascent carbonate.

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INTRODUCTION A variety of solid or liquid carbonaceous materials such as (low grade) coal, biomass, or some waste can be exploited more fully by means of gasification.1−4 As is well-established, almost all forms of the omnipresent chlorine (e.g., organic and inorganic chlorides and chlorine ions) are released through the process of gasification in the form of hydrogen chloride gas. With its high reactivity and treacherous corrosiveness, hydrogen chloride and sulfur species belong to most unwanted species.5,6 For example, the presence of HCl also worsens the efficiency of sulfur removal from fuel and waste gas.7−9 In molten carbonate fuel cell processes, hydrogen chloride augments the loss of electrolyte. Current stringent regulations on a limit of HCl require its level in producer gas to be below 1 ppm by volume. For the sake of heat economy, dry and elevated temperature cleaning processes appear to be more feasible than wet ones operated at low temperatures. The efficient contact between gas and solid sorbent can quite easily be realized in the fixed, fluidized,10 or transport bed with recirculation.11 However, a prerequisite for any efficient contacting is to ensure that the sorbent particles do not go soft or sticky because of chemical reaction. A brief thermodynamic analysis using Barin’s12 and Wagmam’s13 tabulated thermodynamic data outlines equilibrium constraints on the chloridization of calcium carbonate, sodium carbonate, and potassium carbonate: e.g., at a temperature of 800 K (527 °C) and in the presence of water vapor and carbon dioxide (yH2O = yCO2 = 0.1), the predicted equilibrium levels of hydrogen chloride gas amount to 493.7, © 2019 American Chemical Society

0.3475, and 0.02418 ppm(v), respectively. The melting points of the considered chlorides (CaCl2, NaCl, and KCl) are as high as 1028, 1074, and 1044 K (755, 801, and 771 °C), respectively.14,15 They all seem to be safely above the temperatures considered as practical for the producer gas dechloridization (∼773 K) (500 °C). As can be seen, K2CO3based sorbents exhibit the particularly favorable reaction equilibria and are capable of separating hydrogen chloride gas extra deeply from producer gas at relatively high operating temperatures. Furthermore, the regenerable system KHCO3/ K2CO3, besides its sodium counterpart, appears to be a most promising material for much needed carbon dioxide sequestration. It can fix and release reversibly CO2 from flue gas at acceptable cost. It is believed that a more reactive potassium analog of active soda16−19 can be prepared from KHCO3 under specific operating conditions. This article is a theoretical and experimental study on the thermal decomposition of potassium bicarbonate particles under well-defined and carefully maintained conditions of experiment. The authors’ aim was to circumscribe the operating conditions for the preparation of a most promising solid reactant with attractive features resulting, for instance, in the virtually complete removal of hydrogen chloride gas from hot (producer) gas and/or in the regenerative capture of CO2 Received: Revised: Accepted: Published: 2868

December 12, 2018 February 1, 2019 February 4, 2019 February 4, 2019 DOI: 10.1021/acs.iecr.8b06151 Ind. Eng. Chem. Res. 2019, 58, 2868−2881

Article

Industrial & Engineering Chemistry Research

Figure 1. Equilibrium dissociation pressure of alkali bicarbonates under ambient pressure and at different temperature: line 1, potassium hydrogen carbonate, regression of the experimental data of Caven and Sand,22,23 r2 = 0.9993; line 2, KHCO3, predictions based upon the thermochemical data collected by Wagman et al.13; line 3, sodium hydrogen carbonate, predictions based upon the thermochemical data collected by Wagman et al.13; line 4, NaHCO3, regression of the experimental data of Caven and Sand,22,23 r2 = 0.9982.

from flue gas. Textural changes brought about by chemical reaction as well as sintering of the solids constitute inseparable part of the overall transformation of precursor.

where p is given in kPa. The decomposition temperature, Td, at which the dissociation pressure is just equal to an external pressure of 101.325 kPa and estimated by eq 3, amounts to Td = 405.98 K (132.83 °C). This value is noticeably lower than that deduced from somewhat oldish experimental measurements of Caven and Sand22,23 which is as large as 430.11 K (156.96 °C). The predictions of eq 3 are visualized and compared to experiment in Figure 1. As can be seen in this figure, the thermodynamic straight line 2 is shifted from the experimental line 1 to lower temperatures by about 20−25 deg. A moderately smaller shift, but in the opposite direction, is also visible in Figure 1 for the analogous system with NaHCO3. As has been shown, both thermodynamics and experiment indicate/confirm that potassium hydrogen carbonate is significantly more stable than its sodium analog. However, a quantitative measure of the difference in thermal stability remains to be the subject to discussion. Detailed computations indicate that the shifts between the experimental lines 1 (KHCO3) and 4 (NaHCO3) are as large 51−56 deg; those between the theoretical lines 2 (KHCO3) and 3 (NaHCO3) are considerably smaller and amount to 16−19 deg. The reaction equilibria of the two analogous systems are further documented and compared in terms of the enthalpy, the Gibbs energy, and the decomposition temperatures in Tables S1 and S2 in Supporting Information. It can be of interest to note that in the course of reaction 1, the solid phase remains crystalline (predominantly monoclinic) and its true density increases slightly from 2.17 g/cm3 (KHCO 3 ) to 2.29 g/cm 3 (K 2 CO 3 ). These handbook values14,15 provide the respective molar volumes as large as 46.136 cm3/mol (KHCO3) and 60.352 cm3/mol (K2CO3). Simple considerations indicate that the original dense (nonporous) crystal KHCO3 can be made quite porous by decomposing it. Experimental findings on the practical onset of reaction 1 differ markedly. While Duval24 and Hisatsune and Adl25 concluded that KHCO3 is stable below 398 and 413 K (125 °C) and (140 °C), respectively, Lee and Kim21 observed

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DISSOCIATION EQUILIBRIUM While in the structure of NaHCO3 each CO32− group is bound by hydrogen bonds to form the infinite ion chain (HCO3)nn−, in the monoclinic crystal of KHCO3 the CO32− groups are linked only in pairs to form dimer ions (CO3·H2·CO3)22− (ref 20). The differential scanning calorimetry indicates that the first phase transition occurs already at 317−318 K (44−45 °C) when other monoclinic phase and a triclinic form occur.20,21 These transformations appear to be driven by the order− disorder process of the above-mentioned dimers rather than by chemical reaction(s). The overall decomposition reaction of potassium hydrogen carbonate at elevated temperature can be written as 2KHCO3(s) = K 2CO3(s) + H 2O(g) + CO2 (g)

(1)

with ΔG°(298) = 40.568 kJ. Of course, some intermediate transitions cannot be ruled out, particularly at lower temperature. For instance, the transformation of the bicarbonate dimer into two monomer species seems to be quite likely. The thermodynamic data compiled by Wagman et al.13 indicate that reaction 1 is considerably endothermic, with ΔH°(298) = 140.052 kJ/mol of K2CO3. The equilibriumconstant of reaction 1, K, inferred from the same thermochemical data, can be expressed as a function of temperature by eq 2, log K = 21.43574 −

7315.313 T

(2)

The dissociation pressure of potassium hydrogen carbonate, p, is then given as log p = 11.01980 −

3657.656 T

(3) 2869

DOI: 10.1021/acs.iecr.8b06151 Ind. Eng. Chem. Res. 2019, 58, 2868−2881

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Figure 2. Fractional extent of the thermal decomposition of potassium hydrogen carbonate, X, in a linearly increasing-temperature experiment: initial mass of the sample, 6.99 mg; particle sieve size, 53−74 μm; heating rate, 1 deg/min; flow rate of entrainer nitrogen, 55 cm3/min. Symbols represent the experimental results; solid line shows the model predictions.

the first perceptible mass loss already in the vicinity of 373 K (100 °C). The formed potassium carbonate remains entirely stable at temperature below 1123 K (850 °C); it starts melting at approximately 1172 K (899 °C) and decomposes to K2O at higher temperature.

Apparatus and Procedure. The overall chemistry of the calcination transformation is unequivocally described by reaction 1. Since transient techniques approximate an isothermal condition in principle better than static ones, a dynamic approach is preferred. However, every effort was taken to eliminate potential temperature inhomogeneities within the solid, as well as differences between the temperature within the reacted particles and that in the gas flowing around them. Experience indicates that slow rates of heating, small sample mass, and finely sized particles minimize or virtually eliminate unwanted heat and mass transfer intrusions into the course of reaction. It also follows from the authors’ practice that the reproducibility of experimental measurements is better when the particle size distribution is as narrow as possible/ practical. On preliminary runs, the following operating conditions were chosen: the heating rate as slow as 1 deg/ min, the sample mass as small as ∼7 mg of 53−74 μm solids, and a dry nitrogen flow of 55 cm3/min was maintained around the sample to ward off the gaseous products of reaction and to supply needed heat. In light of commonly accepted practice,26−37 it is believed that such operating conditions ensure that relevant, unbiased experimental kinetic data can be amassed. Also, invariant-temperature measurements were carried out under such conditions. The experimental apparatus employed was a commercial instrument Setsys Evolution, Simultaneous TGA/DTA analyzer (Setaram. Corp.) equipped with Omni Star mass spectrometer (Pfeiffer Vacuum Corp.). The bead of the thermocouple was positioned in or very near the sample. The progress of decomposition of potassium bicarbonate was determined as mass loss, w0 − w(τ), and calculated from eq 4:

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EXPERIMENTAL SECTION The experimental study consists of several basic parts: precursor characteristics, its treatment, and processing into samples, replicated TGA experiments at linearly and slowly increasing temperature under carefully maintained conditions, TGA measurements at constant temperature, experimental determination of the pore size distribution, and the porosity of the decomposing particles. Material and Particles. The experimental measurements were carried out with the potassium hydrogen carbonate secured from a commercial network (Reagent grade) with a guaranteed purity of ≥99.8% by weight. The content of sodium in the precursor was less than 0.005 wt %; the weight loss on ignition at 773 K (500 °C) amounted to 30.92 wt %. Xray powdered-diffraction analysis confirmed the presence of a single, well-crystalline compound (KHCO3) occurring in the monoclinic crystal system. For the TGA experiments, small crystals of bicarbonate were manually crushed and ground with an agate mortar and pestle. With the use of two adjacent sieves 53 and 74 μm (270 and 200 mesh by Tyler), a very fine and narrow fraction of precursor was collected by hand sieving for the kinetic experiments. It is believed that potential temperature and concentration gradients within such small reacted particles are minimized, if not practically eliminated. The arithmetic average of these sieve apertures can be viewed as the mean (sieve) particle size. Microscopic examinations revealed that both the crushed and ground particles were of irregular shape and predominantly isometric. To remove adsorbed aerial water vapor, the prepared reactant was dried at 343 K (70 °C) for 2 h and transferred into an airtight container. Larger solids (210−250 μm) and samples were prepared for the textural measurements. All the bottled reactant and product samples were maintained in desiccators.

X (τ ) =

M KHCO3 w0 − w(τ ) 2 z M H2O + MCO2 w0

(4)

where z (>0) is the mass fraction of potassium bicarbonate in the precursor and Mi is the relative molar mass of species. As is evident, complete conversion of pure KHCO3 to K2CO3 corresponds to a relative decrease in mass of 0.309 76. Pore volume within (partially) reacted particles was measured by mercury and helium displacement with the aid 2870


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Industrial & Engineering Chemistry Research Table 1. Effective Kinetic Parameters for Thermal Decomposition of Potassium Hydrogen Carbonate in Nitrogen Atmospherea kinetic parameter

value

95% confidence interval

variance

pre-exponential factor, A, 1/s activation energy, E, kJ/mol ratio A/E, mol/(J s) order of reaction, n

4.9992 × 1014 141.34 3.5370 × 109 1.145

±4.930 × 1011 ±0.5321

2.171 × 1011 0.1688

±0.0362

0.01483

Inferred from experiments performed with narrow-sized, finely powdered (53−74 μm) 7 mg samples in a nitrogen flow of 55 cm3/min at a heating rate of 1 deg/min, temperature range from 372 to 445 K (99−172 °C), fractional conversion from 0.04 to 0.95. The data employed originate from three independent runs replicated under the same conditions. Schlömilch’s approximation38 to the temperature integral was used.

a

used Coats and Redfern expression,39 ICR(T). These two approximations can be written down as follows

of Accu Pyc 1330 and Autopore III instruments (Micromeritics Instrument Corp.). Pore volume distribution with the pore diameter was obtained by measuring the volume of mercury penetrating the pores under pressure increasing up to 690 MPa (∼105 psi).

Is = (E /R )u−1(2 + u)−1 exp( −u)

for u > 15

(4a)

and

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ICR = (E /R )u−2(1 − 2u−1) exp( −u)

RESULTS AND DISCUSSION Decomposition at a Constant Rate of Temperature Increase. First experiments revealed that potassium hydrogen carbonate tends to start decomposing at about 363−365 K (90−92 °C). The equilibrium dissociation pressure estimated for 364 K (91 °C) by means of thermodynamics (eq 3) is as large as 9.45 kPa. The correlation inferred from the experimental data measured by Caven and Sand22,23 and shown in Figure 1 predicts that the corresponding decomposition pressure is quite lower and amounts to 3.53 kPa. Experimental results of Lee and Kim21 collected at a heating rate of 2 deg/min indicate the commencement of dissociating at approximately 373 K (100 °C). Duval’s findings24 that potassium hydrogen carbonate is entirely stable up to 398 K (125 °C) and can be used as an analytical standard/etalon at such temperatures do not seem to be convincing. This work indicates that appreciable decomposition of KHCO3 is not likely below about 353 K (80 °C). Preliminary runs were also made with an atmosphere of pure carbon dioxide at a temperature of 453 K (180 °C). The measured conversion− time curves were compared to those collected with pure nitrogen at the same temperature. The curves were measured up to complete conversion, and it was very difficult to discern any difference between them. Thus, there were not any relevant equilibrium constraints in the system and no significant mass transfer intrusions occurred within solid nor at its surface. Experiments were carried out at a heating rate of 1 deg/min which makes it possible to virtually eliminate or minimize unwanted heat transfer effects. As can be seen in Figure 2, the decomposition becomes quite rapid at about 410 K (137 °C) and slows down extensively above approximately 430 K (157 °C). The final temperature was as high as 450 K (177 °C) at which decomposition was complete. As can be noted, the sigmoid curve is not entirely symmetrical. In an effort to eliminate unwanted and hardly avoidable random inaccuracies, the experimental measurements were repeated. The plotted and further-treated data form a single curve that represents the means of three times repeated runs carefully replicated under the same experimental conditions. As is established, an nth order, Arrhenius type reaction rate expression constitutes a solid basis for interpreting the collected data.26,29,35 Furthermore, it follows from the authors’ experience that the Schlömilch approximation,38 Is(T), to the transcendental temperature integral is more accurate than the commonly

for u > 25

(4b)

For instance, computations for u ∈ ⟨15,40⟩ indicate that the deviations of Is(T) from the true values amount to ⟨1.3,0.1⟩%; those of ICR(T) are greater and occur in the interval ⟨6.0,0.4⟩%. However, the Schlömilch formula38 loses its accuracy with u < ∼15. A more fitting expression can be employed instead in such situations: log p(u) = 0.003693u 2 − 0.59283u − 0.85329 for u ∈ ⟨5, 15⟩ (5)

Thirty-five experimental data points at equal temperature/ time intervals were taken to fit an appropriate form of the integral conversion function, Y(X), iAy Y (X ) = Y (T ) ≅ jjjj zzzz I(T ) kβ{

(6)

In terms of the integral temperature function, Y(T), the expressions for the rate of reaction, dX/dT, and the overall conversion, X, take the forms dX = [k(T )/β ][1 + (n − 1)Y (T )]n /(1 − n) dT

(6a)

and X = 1 − [1 + (n − 1)Y (T )]1/(1 − n)

(6b)

for n ≠ 1. Having used the Schlömilch approximation,38 the values of effective kinetic parameters were estimated by means of the flexible polyhedron search (the simplex procedure). Statistical evaluations of the confidence intervals were performed on the basis of the Student “t” distribution. Computational results for the nonlinear regression fitting are presented in Table 1. As can be read, the estimated effective activation energy, E, amounts to 141.34 kJ/mol. This value is slightly larger than the enthalpy of reaction given above. Thus, there may be some room to speculate about possible minor effects of structural and textural changes, occurring in the solid phase (e.g., the nucleation of a new solid phase and the growth of nuclei), on the overall rate of reaction. The apparent order of reaction was estimated to be slightly above unity and is as large as n = 1.145. The authors’ results seem to be in reasonable agreement with those of Tanaka.40 For instance, the characteristic (peak) temperatures, Tp, amounts to 422 K (the authors) and 409 K (Tanaka; determined by means of DSC method). 2871


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Figure 3. Rate of reaction, dX/dT, in the course of a linearly increasing-temperature experimental. Curve represents the model predictions for the operating conditions enumerated in the caption of Figure 2.

Figure 4. Comparison of reaction rate constants, k[≡(dX/dτ)X →0], for the decomposition of potassium hydrogen carbonate and sodium hydrogen carbonate at different temperature, T. Kinetic triplets are given in Table 1 (KHCO3) and in the note below Table 2 (NaHCO3).

For the sake of comparison, the effective kinetic triplets (the pre-exponential factor, A, the activation energy, E, and the order of reaction, n) were also deduced with the use of the expression introduced by Coats and Redfern.39 The results obtained are not radically different from those based upon the Schlö milch integral approximation. 38 For example, the estimated activation energy amounts to 137.89 kJ/mol (Coats and Redfern39) that corresponds to a difference of 2.44%, which is a satisfactory agreement. It can be of interest to note that for the pertinent values of u ∼ 40; the deviations of the two integral approximations amount to ∼0.1% (Schlömilch38) and ∼0.4% (Coats and Redfern39). Of course, some other approaches to the analyses of nonisothermal TGA data can be found in the literature.41−44 It may be worth mentioning that also Lee and Beck43 derived a suitable approximation formula. Yet their relationship can be rewritten into a form which is identical to the Schlömilch expression.38

The systematic computation makes it possible to outline general and compensation effects of the respective kinetic parameters (E, A, n, and β) upon the course/shape of integral sigmoid curves X, X(T). Increase in the activation energy, E, manifests itself in a shift of the X-curve toward higher temperatures. An effect of the pre-exponential factor, A, appears to be opposite that of E, and moreover, an augmentation of this parameter leads to larger slopes of the curves. While the initial sections of the curve remain practically unaffected by the (apparent) order of reaction, n, more advanced parts, corresponding to elevated and high conversions, are significantly prolonged with an increase in the reaction order. What is often neglected or overlooked is the fact that when the rate of heating, β, is augmented, the curves do not shift to higher temperatures just parallel to each other, but their slopes decrease concurrently. 2872


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Industrial & Engineering Chemistry Research Table 2. Comparison of Decomposition Kinetics of Potassium and Sodium Hydrogen Carbonatesa quantity

KHCO3

NaHCO3

maximum (peak) rate of reaction, (dX/dτ)p, 1/s temperature of maximum rate of reaction, Tp, K conversion at maximum rate of reaction, Xp difference between temperatures at which dX/dτ = 0.5(dX/dτ)p, deg difference between conversions at which dX/dτ = 0.5(dX/dτ)p, deg integral temperature function at maximum rate of reaction, Y(Tp)

5.7283 × 10−4 421.87 (148.72 °C) 0.58780 26.71 0.73680 0.94572

4.7448 × 10−4 407.05 (133.90 °C) 0.60404 32.57 0.74067 0.93901

a Kinetic triplet for sodium hydrogen carbonate is as follows: A = 1.158 × 1010 1/s, E = 101.1 kJ/mol, and n = 1.029 (ref 35). Kinetic parameters for potassium hydrogen carbonate are given in Table 1.

Figure 5. Progress in the isothermal decomposition of potassium hydrogen carbonate, [(1 − X)−0.145 − 1]/0.145, at 383 K (110 °C) and 393 K (120 °C). Initial mass of the samples was 8.11 and 8.26 mg, respectively; flow rate of entrainer nitrogen was 55 cm3/min.

Figure 6. Progress in the isothermal decomposition of potassium hydrogen carbonate, [(1 − X)−0.145 − 1]/0.145, at 403 K (130 °C), 413 K (140 °C), and 423 K (150 °C). Initial mass of the samples was in the range from 8.05 to 8.25 mg; flow rate of entrainer nitrogen was 55 cm3/min.

[(dX/dT)p, (dX/dτ)p] is attained at about 422 K (149 °C) and its value is as large as 0.0344 1/deg (5.73 × 10−4 1/s). In ref 35 the maximum rate of decomposition for NaHCO3

The course of the rate of reaction, dX/dT, dependent on the slowly increasing temperature (β, 1 deg/min), is visualized in Figure 3. As is shown, the maximum (peak) rate of reaction, 2873


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Figure 7. Comparison of reaction rate constants, k, inferred from the data measured by the increasing-temperature experiments and those deduced from the constant-temperature runs. Kinetic triad provided by the nonisothermal method is given in Table 1; that determined by the isothermal method is as follows: A = 6.8067 × 1012 1/s, E = 129.426 kJ/mol, with n = 1.145.

Figure 8. Rate of reaction, dX/dτ, as a function of the fractional conversion of solid, X, for different temperatures, T, (383−423 K; 110−150 °C). The kinetic triad determined by the isothermal method is given in the caption of Figure 7.

already reached at 407 K (134 °C) is approximately 20% smaller and amounts to 0.0285 1/deg (4.74 × 10−4 1/s). As is visualized in Figure 4, to ensure equal reaction rate constants, k, for both hydrogen carbonates, temperature must be significantly higher at KHCO3. Understandably, such shifts decrease nonlinearly with temperature: from about 17 deg at 401 K (128 °C) to approximately 8 deg at 432 K (159 °C). To obtain closer insights into the course of reaction, the numerical values of the kinetic triad can also be accompanied by several more instructive and demonstrative quantities. Aside from the position of the point of inflection on the integral X − T(τ) curve, the spans of temperature and conversion between the two points at which the rate of reaction is raised/reduced to 0.5(dX/dτ)p should be considered as well. The aforesaid quantities are presented for both of these hydrogen carbonates in Table 2. As is shown, the temperature-based quantities are appreciably more compound-responsive than the conversion-

related ones. Moreover, it is seen that the integral temperature and conversion functions, Y, of the two hydrogen carbonates look very similar and are not far from unity (∼0.94) at (dX/ dτ)p. All the quantities given in Table 2 can be precisely pinpointed by means of appropriate relationships. For example, the temperature of the maximum rate of reaction, Tp, can be predicted by eq 7 3 2 β R iRy iRy 6njjj zzz T 4 − 2(n − 1)jjj zzz T 3 − T 2 + e u = 0 E A kE{ kE{

for n ≠ 1 (7)

which is based upon the Coats−Redfern approximation.39 The Schlömilch analogous expression38 is lengthy and rather cumbersome to use in this situation. Constant-Temperature Decomposition. The rate of the thermal decomposition of potassium hydrogen carbonate was also explored by experiment under the constant temperature conditions. These experiments were conducted at 383, 393, 2874


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Figure 9. Fractional conversion, X, and the dimensionless rate of reaction, [(dX/dτ)/k], as functions of the dimensionless reaction parameter, kτ. The marks are explained in Figure 8.

403, 413, and 423 K (110−150 °C). As can be seen, these temperatures cover the first half of the sigmoid decomposition curve in Figure 2. Thus, it seems feasible to assume that the measured results are less likely to be affected by heat transfer intrusions at these moderate temperatures and reaction rates. The other experimental conditions such as the initial mass of the samples and the flow rate of entrainer nitrogen were maintained as close as possible to those at work in the increasing-temperature mode. The concave shape of the original experimental curves X vs τ indicates a significant inhibiting effect of the progress of solid transformation on the rate of reaction. The measured data are presented in the linear form in Figures 5 and 6 for the five above-stated temperatures. As is seen, all of the data fit the straight lines quite well: the respective regression parameters occur in the range from r2 = 0.9945 to r2 = 0.9999. The kinetic triad deduced from the estimated effective rate constants determined by the isothermal method is as follows: A = 6.8067 × 1012 1/s, E = 129.426 kJ/ mol, and n = 1.145. The values of the corresponding confidence intervals and variances are similar to those given in Table 1. The reaction rate constants deduced from the constanttemperature data and those determined from the increasingtemperature measurements are compared in Figure 7. As can be seen, the constant-temperature method provides the rate constants which are moderately lower than those provided by the increasing-temperature procedure. The corresponding rate constants differ by a factor in the range from 0.40 (at 383 K/ 110 °C) to 0.57 (at 423 K/150 °C). Aside from differences in the basic methodology, the true temperature differences between the particles and the thermocouple would quite likely deserve closer examination. With respect to such experimental difficulties, it is believed that the findings provided by the two methods are in reasonable agreement. As is visualized in Figure 8, the initial rates of decomposition increase with temperature from 1.54 × 10−5 1/s at 383 K (110 °C) to 7.2 × 10−4 1/s at 423 K (150 °C). Furthermore, the presented curves show a monotonic decrease of the rate of reaction with the progress of reaction at different temperatures.

The multibranched family of curves shown in Figure 8 can easily be combined together into a single curve, when the relative rate of reaction, (dX/dτ)/k ∈ ⟨0,1⟩, is introduced and further employed. Due to the fact that the apparent order of reaction is slightly greater than unity (i.e., n = 1.145), the function plotted as (dX/dτ)/k vs X is a trifle curved. Alternative to Figures 5, 6, and 8, the attained fractional conversions (the proper concave function) and the corresponding relative rates of reaction (the proper convex dependence) are also shown as functions of the dimensionless reaction parameter, kτ, in Figure 9. As can be seen, the relative rate of reaction falls down quite rapidly in the course of decomposition and the reaction comes to a standstill at kτ ∼ 4−5. The experimental results presented in Figures 5, 6, and 8 indicate at which combinations (twos) of temperature and elapsed time of reaction, the desired conversions (and/or the rates of reaction) can be reached. As is known, the unwanted phenomenon of sintering the nascent product of reaction occurs already in the course of decomposition. Apart from a rather weak influence of the time of exposure, the physicochemical properties of reaction product are particularly affected by temperature. For example, it is known from the authors’ practical experience with the dry, CaO-based desulfurization of gas that the most reactive sorbent should still contain a small portion of the undecomposed precursor [Ca(OH)2] to avoid or minimize the adverse effects of sintering. A basic relation, among the conversion, X, and the operating conditions (the temperature, T, and the duration of reaction, τ), and the order of reaction, n, can be written as follows A(n − 1)τ + [1 − (1 − X )1 − n ] exp u = 0 for n ≠ 1 (8)

and Aτ + [ln(1 − X ]exp u = 0 for n = 1

(9)

Selected results of the systematic computation by means of eq 8 are presented in Figure 10 for the fractional conversions 2875


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Figure 10. Diagram depicting the relationship between the elapsed time of reaction, τ, and the temperature of reaction, T, for the attained elevated and high conversions, X. Curve 1: X = 0.80, kτ = 1.8127. Curve 2: X = 0.85, kτ = 2.1837. Curve 3: X = 0.90, kτ = 2.7336. Curve 4: X = 0.95, kτ = 3.7518. The curves show the predictions of eq 8.

Figure 11. Comparison of the porosity functions of reacted solids, (ex − ein)/(1 − ein), over the course of important calcination and sorption reactions for pure reactants. Line 1, 2NaHCO3 = Na2CO3 + H2O(g) + CO2, f = 0.5464, ein = 0; line 2, 2KHCO3 = K2CO3 + H2O(g) + CO2, f = 0.6541, ein = 0; line 3, K2CO3 + 2HCl(g) = 2KCl + H2O(g) + CO2, f = 1.2427, ein = 0.3459; line 4, Na2CO3 + 2HCl(g) = 2NaCl + H2O(g) + CO2, f = 1.2908, ein = 0.4536; ○, experimental data points measured for different conversions of KHCO3 at 473 K (200 °C) in a flow of nitrogen. e − ein = [1 − fC − (fCl − fC )XCl ]XC 1 − ein

in the range from 0.80 to 0.95. Thus, for instance, curve 4 indicates that a fractional conversion of 0.95 (kτ = 3.752) can be attained after decomposing for 136.9 min at 418 K (145 °C) or, for example, on a 37.68 min exposure to a temperature of 433 K (160 °C). Porous Structure of Decomposed Solids. It is feasible to assume that a reacted particle retains its original gross external volume and conditions are uniform throughout its interior. Then, a plain relationship between the fractional porosity, e, of the reacting particle and the progress of calcination, XC, and, for instance, that of successive/parallel chloridization, XCl, can be expressed as follows,

for z = 1 and XC ≥ XCl

(10)

On inserting the expansion/reduction factors f C = 0.6541, f Cl = 0.8128 and XC = XCl = 1 and ein = 0, it is evident that an original nonporous crystal of KHCO3 remains quite porous (e = 0.1872) after complete calcination and total conversion to KCl by chloridization. This prediction indicates that the pore volume generated by calcination is large enough to accumulate with a reserve all potassium chloride formed by HCl(g) sorption. However, when no chloridization occurs, i.e., XCl = 0, eq 10 simplifies accordingly and predicts that the completely calcined KHCO3 particles (XC = 1) attain a fractional porosity of 0.3459 and the pore volume amounts to 0.2309 cm3/g. In 2876


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and porous potassium carbonate is likely to take place. There is a general difference in structural transformations accompanying the calcination of KHCO3 and that of NaHCO3: while the monoclinic NaHCO3 is converted into the powdery carbonate, both the parent KHCO3 and the nascent K2CO3 are crystalline and exhibit the monoclinic (and possibly also the triclinic) crystal lattice. The experimental measurements were performed at 403− 503 K (130−230 °C) and are illustrated in Figure 12. The figure displays the distributive pore volume vs pore diameter data for K2CO3 particles prepared by the decomposition of KHCO3 solids at 403 K (130 °C) in a nitrogen atmosphere. The derivative curve in this figure shows that the calcined particles comprise the pores whose diameters are distributed over the broad range from 110 to 2000 nm. The curve exhibits a single peak at a diameter of 170 nm as the most probable pore size (by pore volume) in the calcined sample. In view of common practice, all such sized pores fall into a category of macropores. When the operating temperature was increased in additional experiments, the size of the most probable pores augmented. The derivative curves for the other temperatures exhibited very similar courses and, therefore, are not presented. All the curves show a significant shift toward greater pores with the increasing temperature. Such increase in the pore size can be correlated with temperature as follows,

Figure 11, there are shown the results of the decomposition experiments with nonporous crystals of KHCO3. The straight line 2 in this figure represents the porosities predicted by eq 10 for ein = XCl = 0. As can be seen, the calculated porosities are in fair agreement with the experimental measurements. Consequently, this finding indicates that possible shrinkage of the reacted particles is insignificant or never occurs at temperatures below 473 K (200 °C). As is also apparent from Figure 11, the porosity functions, embodied in eq 10, are for the analogous systems (i.e., for KHCO3−K2CO3−KCl and NaHCO3− Na2CO3−NaCl) fairly similar. Basic textural characteristics of the K2CO3 particles formed at 473 K (200 °C) in a flow of nitrogen are presented in Table 3. Microphotographs of the Table 3. Textural Features of Potassium Carbonate Formed by Thermal Decomposition of KHCO3 at 473 K (200 °C) in a Flow of Nitrogena parameter

value

true solid density, ρs, g/cm3 apparent particle density, ρp, g/cm3 pore volume, Vp, cm3/g fractional porosity mean pore radius (by pore volume), rp, nm surface (total pore) area, S, m2/g mean grain radius, dg, nm

2.290 1.498 0.2309 0.3459 96.54 4.784 273.8

a The mean Tammann temperature of K2CO3 amounts to 621.2 K (348.1 °C).

ln d p̅ = −10.13831 −

339.097 T

for τ = 120 min

(11)

where dp is given in cm. Predictions of this relationship are confronted by the measured data in Figure 13. As is seen, the predicted, most probable diameters of pores, dp, do not deviate from the experimental values more than by a few percent. Having assumed the porous texture as a system of parallel, open, and noninterconnected cylindrical pores, the specific surface area, S, can be estimated by means of the relationships

surfaces and the interiors of the particles show that the texture of these particles is dense and composed of approximately isometric subparticles. On decomposing to K2CO3, the solids became porous and the grain size was reduced; nonetheless the isometry was preserved. Pore-Size Distribution. Upon the release of water and carbon dioxide according to reaction 1, some pseudomorphs similar to the parent hydrogen carbonate can remain in the reacted particles particularly at lower temperatures. At higher temperatures, some restructuring or sintering of the nascent

339.097 yz i zz S = 4Vp expjjj10.13831 + T { k

(12)

Figure 12. Pore-size distribution within K2CO3 particles formed at 403 K (130 °C) in a flow of nitrogen. Time of exposure, 120 min; sieve particle size, 0.25−0.32 mm. 2877


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Figure 13. Effect of the temperature of calcination, T, on the most probable diameter of pores, d _“p”, within K2CO3 particles. Time of exposure, 120 min; sieve particle size, 0.25−0.32 mm. Symbols represent the experimental results; solid line shows the predictions of eq 11.

predicts that the very first traces of KHCO3 decomposing (∼pdiss = 1 kPa) are presumed to already occur at 331.9 K (58.8 °C). In comparison with the sodium analog, it appears that these values are about 18.5 and 14.0 deg, respectively, higher than the corresponding temperatures estimated for sodium hydrogen carbonate. In an atmosphere of dry nitrogen, the slowly heated KHCO3 (β = 1 deg/min) commences decomposing at approximately 364 K (91 °C). The highest rate of reaction, dX/dτ, determined by this increasing-temperature method as large as 5.73 × 10−4 1/s (0.0344 1/deg), was attained at 421.9 K (148.7 °C) and at a fractional conversion, X, of 0.588. There appears that the Schlömilch approximation38 to the exponential integral is significantly more accurate than the currently used expression developed by Coats and Redfern.39 However, both of these formulas lose their accuracy rapidly for u less than ∼15 or 25; therefore, proposed eq 5 should be employed instead in such situations. The course of the reaction explored under dynamic conditions is well described by means of the effective kinetic triplet A = 4.999 × 1014 1/s, E = 141.3 kJ/mol, and n = 1.145 estimated with the aid of the Schlömilch approximation.38 The apparent activation energy, deduced by the Coats and Redfern39 method, is 2.4% less for the pertinent interval of operation u ∈ ⟨38.9,42.5⟩. To get clearer insights into the kinetics of decomposition, the kinetic triad is further supplemented with additional characteristics of the derivative (somewhat asymmetrical) curve describing its height and breadth and given in Table 2. The reaction rate constants, k, deduced from the constanttemperature results are by a factor of 0.4−0.6 less than those inferred from the increasing-temperature data which occur in the range 1 × 10−5 to 6 × 10−4 1/s. The multibranched family of the separate isothermal rate curves are combined into a single line with the use of the relative reaction rate. Furthermore, it is shown that the decomposition reaction is nearing completion (i.e., X → 1) when the dimensionless reaction parameter, kτ, is close to 4−5. The relationships and the diagram are presented which makes it possible to

as a function of temperature. Illustrative calculations for 423 and 473 K (150 and 200 °C) provide for the specific surface area the values as large as 52 062 and 47 835 cm2/g, respectively. The surface area of the calcined particles was measured as well by means of nitrogen multilayer adsorption (BET). Such determined surface area was very near that deduced from the pore-size distribution. In general, the higher surface area of sorbent particles is a prerequisite to their greater activity for reacting with gases. In the case of spherical, nonoverlapped micrograins, their diameter can be predicted from the surface area. Estimates of the mean grain size, dg, for 423 and 473 K (150 and 200 °C) amount to 5.0326 × 10−5 and 5.4773 × 10−5 cm, respectively. As is evident, all the aforementioned textural features can readily be estimated and helpfully employed in different reaction or reactor models (e.g., ref 45). It should be reminded that all the correlation/regression equations presented above are of empirical nature and can be employed outside the conditions for which they have been deduced with due caution. The most important results of porosimetry are presented in Table 3. As is shown, the nascent potassium carbonate commences restructuring at very moderate temperature. Quite historically, the term Tammann temperature was originally employed as an index for the onset of significant lattice mobility of metal and oxide powders. Such temperature is usually conceived as 0.52− 0.54 times the melting point on the thermodynamic temperature scale. This definition leads to the Tammann temperature of the nascent potassium carbonate as high as 609−633 K (336−360 °C). However, the authors’ findings indicate that the nascent K2CO3 undergoes a significant process of sintering at considerably lower temperature.

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CONCLUSIONS Newer, critically evaluated, thermochemical data indicate that the explored decomposition reaction of KHCO3 is strongly endothermic with ΔH°(298), 140.05 kJ/mol of K2CO3. The decomposition temperature, at which pdiss = 101.325 kPa, amounts to 406 K (132.8 °C). The proposed equation also 2878


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(dX/dT)p = maximum (peak) rate of reaction corresponding to the inflection point on the sigmoid curve X vs T, 1/ deg (dX/dτ)T = rate of an nth order reaction in the constanttemperature regime, kT(1 − X)n = kT[1 + (n − 1)kTτ]n/(1−n), 1/s ec = fractional porosity of a calcine particle ecl = fractional porosity of a chlorinated particle ein = fractional porosity of solid prior to calcination/ sorption (reaction) e0 = initial fractional porosity of potassium carbonate before sorption reaction ex = fractional porosity of a reacted particle E = effective (apparent) activation energy, Arrhenius constant, fitted parameter, J/mol f = relative decrease/increase in the solid volume caused by calcination/sorption reaction fc = solid volume reduction factor in calcination, VK2CO3/ (2VKHCO3) = 0.6541 fcl = solid volume reduction factor in chloridization, VKCl/ VKHCO3 = 0.8128 I(T) = approximation to the exponential integral = (E/R) p(u), K ICR(T) = Coats−Redfern approximation function given by eq 4b, K IS(T) = Schlömilch approximation function given by eq 4a, K k = effective reaction rate constant = A·exp(−u), 1/s K = equilibrium constant for reaction 1 given by eq 2 ≡ Kp = pH2OpCO2, (kPa)2 Mi = molar (formula) mass of component i, g/mol n = effective (apparent) order of reaction, fitted parameter p = dissociation pressure of KHCO3 given by eq 3 = pH2O + pCO2 = 2K0.5, kPa p(u) = dimensionless approximation function = (R/E)I(T) r2 = regression parameter rg = mean micrograin radius, cm rp = most probable pore radius, cm R = ideal gas law constant = 8.31441 J/(mol K) S = specific surface area of K2CO3 particles, cm2/g t = Celsius temperature, °C T = thermodynamic temperature, K Td = temperature at which the pressure of gaseous reaction product(s) is equal to 101.325 kPa Tp = temperature corresponding to the inflection point of sigmoid curve X vs T, K u = dimensionless activation energy = E/(RT) Vi = molar volume of component i, cm3/mol VKCl = molar volume of potassium chloride = 37.501 cm3/ mol VKHCO3 = molar volume of potassium hydrogen carbonate = 46.136 cm3/mol VK2CO3 = molar volume of potassium carbonate = 60.352 cm3/mol Vp = pore volume in a particle = (1/ρHg) − (1/ρHe) = e/ ρHg, cm3/g w0 = initial mass of sample, g w(τ) = mass of sample at any moment of time τ, g X = extent of decomposition of KHCO3 as the fractional conversion of KHCO3 to K2CO3 given by eq 4 X(T) = fractional conversion in the increasing-temperature regime for an nth order reaction given by eq 6b

conveniently predict practical conditions needed to attain more or less complete conversion of the bicarbonate and minimize unwanted sintering of the nascent carbonate. An impervious crystal KHCO3 is made porous by calcining it (ec = 0.3459, Vp = 0.2309 cm3/g). Such a pore volume is capable of accommodating with reserve all the reaction product, e.g., in the case of chloridization (i.e., eKCl = 0.1872, Vp = 0.1159 cm3/g). Although its monoclinic lattice remains for the most part preserved, the nascent K2CO3 undergoes inherently a significant process of unwanted sintering. In light of the mean Tammann temperature, 621.2 K (348.1 °C), it appears that lattice diffusion can be the predominant mechanism of matter transport. Elevating the decomposition temperature from 403 K (130 °C) to 503 K (230 °C) increases the most probable pore diameter from 167 to 203 nm, and the mean grain diameter augments from 474 to 576 nm. Correspondingly, the specific surface area decreases over this temperature span from 5.53 to 4.55 m2/g. The well-produced K2CO3 has considerable potential for the rapid sorption of acidic gases such as hydrogen halogens or nitrogen oxides as well as malodorous components from the rarefied gas streams.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.8b06151.

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Thermochemical characteristics of reactions and coefficients of predictive relationships (PDF)

AUTHOR INFORMATION

Corresponding Author

*Tel.: +420 220 390 254. Fax: +420 220 661. E-mail: [email protected]. ORCID

Miloslav Hartman: 0000-0001-9189-1344 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Ministry of Education, Youth, and Sports of the Czech Republic under OP RDE Grant CZ.02.1.01/0.0/0.0/16_019/0000753 “Research Centre for Low-Carbon Energy Technologies” and the Technology Agency of the Czech Republic through Project TE02000236 “Waste-to-Energy Competence Centre”. The authors are grateful to Eva Fišerová for her assistance with the manuscript.

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NOMENCLATURE

Abbreviations

ppm(v) = parts per million by volume wt = weight Symbols

A = frequency/pre-exponential factor, Arrhenius constant, fitted parameter, 1/s dg = mean diameter of micrograins, cm dp = most probable diameter of pores, cm dX/dT = rate of an nth order reaction in the linearly increasing-temperature mode, (dX/dτ)/β, k(T)(1 − X)n/β given by eq 6a, 1/deg 2879


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X(τ) = fractional conversion in the constant-temperature regime for an nth order reaction = 1 − [1 + (n − 1) kTτ]1/(1−n) Xc = fractional conversion of bicarbonate to carbonate in eq 12 Xcl = fractional conversion of bicarbonate to chloride in eq 12 y = mole (volume) fraction of species Y(T) = dimensionless integral temperature function = (A/ β)∫ T0 [exp(−μ)] dT ≅ (A/β)I(T) Y(X) = dimensionless integral conversion function for an nth order reaction = ∫ X0 dX/(1 − X)n = [1 − (1 − X)1−n]/(1 − n) z = content of KHCO3 in sample, mass fraction Greek Letters

β = rate of heating, deg/s ΔH° = standard heat of reaction, J/mol of K2CO3 ρHe = true (helium) solid density, g/cm3 ρHg = apparent (mercury) density = (1 − e)ρHe, g/cm3 δ = elapsed time of reaction/exposure, s

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Decomposition of Potassium Hydrogen Carbonate: Thermochemistry

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