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Treatment of NOx using recyclable CO32--intercalated Mg–Al layered double hydroxide Tomohito Kameda∗, Masahito Tochinai, Shogo Kumagai, Toshiaki Yoshioka Graduate School of Environmental Studies, Tohoku University, 6−6−07 Aoba, Aramaki, Aoba−ku, Sendai, 980-8579, Japan
ARTICLE INFO
ABSTRACT
Keywords: NOx Treatment Recyclable CO32--intercalated Mg–Al layered double hydroxide Regeneration
We investigated NOx removal using a CO3·Mg–Al layered double hydroxide (CO3·Mg–Al LDH) and compared its NO2 removal performance against that of Mg(OH)2 and NO3·Mg–Al LDH to elucidate the nature of adsorption of NO2. The NO removal rate was lower than that for NO2 removal. The success of NO2 removal with CO3·Mg–Al LDH is attributed to the surface adsorption of NO2 on CO3·Mg–Al LDH in addition to the formation of NOx·Mg–Al LDH. We investigated its recycling in NO2 treatment by CO3·Mg–Al LDH. The results demonstrated the possibility of recycling through CO3·Mg–Al LDH generation using a Na2CO3 solution.
1. Introduction Acidic gas generated by waste incineration plants contains HCl, SOx, and NOx. HCl and SOx can typically be removed using highly reactive slaked lime, resulting in the formation of calcium chloride and calcium sulfate (Chu and Rochelle, 1989; Karlsson et al., 1981; Kim et al., 2017; Pozzo et al., 2018; Sakai et al., 2002). However, NOx cannot be removed using highly reactive slaked lime (Chu and Rochelle, 1989; Sakai et al., 2002), because calcium nitrate is not formed. NOx control technologies include combustion control, while NOx treatment technologies include non-catalytic and catalytic reduction (Bacher et al., 2015; Gao et al., 2017; Shi et al., 2013). Catalytic reduction, which is a dry process, is currently the most conventional technique and is typically employed. However, the use of this technique generates problems such as reduced power generation efficiency and deterioration of the catalyst; therefore, development of a new NOx treatment technology is required. We have already investigated NOx removal using an Mg–Al oxide slurry (Kameda et al., 2011, 2013a, 2013b, 2015). However, this is a wet process, and is difficult to apply as an alternative to the dry process. Therefore, in this study, we investigated NOx (NO or NO2) treatment using an Mg–Al layered double hydroxide intercalated with CO32− (CO3·Mg–Al LDH); this is a dry method and serves as an alternative to catalytic reduction. Our aim was to establish a recycling treatment process, as shown in Fig. 1. Mg–Al LDH facilitates anion exchange, and can intercalate various type of anions in the interlayer (Cavani et al., 1991; Miyata, 1983). Mg–Al LDH can be transformed into Mg–Al oxide by calcination at 450–800 °C, which in turn can
rehydrate and combine with anions to reconstruct the LDH structure. We have already clarified that CO3·Mg–Al LDH treatment removes gaseous HCl in the dry method (Kameda et al., 2010). Therefore, CO3·Mg–Al LDH is expected to treat NOx (NO or NO2) in the dry method. In this work, we investigated the effect of the Mg/Al molar ratio, stoichiometric quantity of CO3·Mg–Al LDH to the gases to be removed, temperature, and concentration on NOx (NO or NO2) treatment using the CO3·Mg–Al LDH. The chemicals used for treating acidic gas in incineration plants are not recycled, which puts pressure on final disposal sites. Here, it was assumed that the reaction between NOx and CO3·Mg–Al LDH could progress to yield NOx·Mg–Al LDH; therefore, we investigated methods to recover CO3·Mg–Al LDH via anion exchange reactions with NOx·Mg–Al LDH and CO32−. First, we synthesized NO3·Mg–Al LDH by coprecipitation. Next, we investigated the effect of the stoichiometric quantity of CO32− on the anion exchange reaction with NO3·Mg–Al LDH and CO32−, and the kinetics. We then discussed the CO32− adsorption and desorption processes of each anion using equilibrium and thermodynamic analyses. Furthermore, we investigated the recyclability of CO3·Mg–Al LDH for NO2 treatment. 2. Experimental 2.1. NOx treatment CO3·Mg–Al LDH (Mg/Al = 2.0 or 4.0) was synthesized by coprecipitation, according to our previous method (Kameda et al., 2016). Equations (1) and (2) show the theoretical reaction formulae for the
Peer review under responsibility of Turkish National Committee for Air Pollution Research and Control. ∗ Corresponding author. E-mail address:
[email protected] (T. Kameda). https://doi.org/10.1016/j.apr.2019.07.018 Received 24 February 2019; Received in revised form 23 June 2019; Accepted 10 July 2019 1309-1042/ © 2019 Turkish National Committee for Air Pollution Research and Control. Production and hosting by Elsevier B.V. All rights reserved.
Please cite this article as: Tomohito Kameda, et al., Atmospheric Pollution Research, https://doi.org/10.1016/j.apr.2019.07.018
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Fig. 1. Proposed treatment of NOx using CO3 Mg
A predetermined amount of NO3·Mg–Al LDH was injected into 20 mL Na2CO3 solution in a 50 mL screw-cap Erlenmeyer flask. To examine the effect of the stoichiometric quantity of CO32−, 0.2 g NO3·Mg–Al LDH was added to the Na2CO3 solution in 0.5–2.5 times the stoichiometric quantity according to Equation (3). For the kinetic study, NO3·Mg–Al LDH in 1.0 times the stoichiometric quantity was added to a 0.025 M Na2CO3 solution. For the equilibrium and thermodynamic studies, 0.2 g NO3·Mg–Al LDH was added to a 0.005–0.05 M Na2CO3 solution. The temperature was set at 10–60 °C, and the solution was shaken for 0.5–180 min. After measuring the pH of the post-reaction solution, the solids and liquid were separated with a 0.45 μm membrane filter; the NO3− volume in the filtrate was measured by ion chromatography, the C concentration was measured in terms of the total organic carbon (TOC). After the products were dried at 40 °C under reduced pressure, phase identification was performed by X-ray diffraction.
Al LDH.
removal of NO and NO2 using CO3·Mg–Al LDH (Mg/Al = 2.0 or 4.0). Mg1-xAlx(OH)2(CO3)x/2·mH2O + xNO → Mg1-xAlx(OH)2(NO2)x + x/ 2CO2 + mH2O (1)
2.3. Recycling Firstly, NO2 treatment using CO3·Mg–Al LDH was conducted according to “2.1 NOx treatment”. For this, 150 ppm NO2 was treated with 10.0 times the stoichiometric quantity of CO3·Mg–Al LDH (Mg/Al = 2.0 or 4.0) according to Equation (2) at 110 °C for 90 min. Next, the regeneration of CO3·Mg–Al LDH after NO2 treatment was conducted according to “2.2 Anion desorption”. A Na2CO3 solution (20 mL) in 2.0 times the stoichiometric quantity according to Equation (3) was added to CO3·Mg–Al LDH (Mg/Al = 2.0 or 4.0) after NO2 treatment, and was shaken at 30 °C for 180 min. This procedure was repeated 3 times.
2Mg1-xAlx(OH)2(CO3)x/2·mH2O + 2xNO2 → Mg1-xAlx(OH)2(NO2)x + Mg1-xAlx(OH)2(NO3)x + xCO2 + mH2O (however, x = 0.2, 0.33)
(2)
Fig. 2 shows the experimental apparatus for treating NOx with CO3·Mg–Al LDH. We filled CO3·Mg–Al LDH (Mg/Al = 2.0 or 4.0) to 5.0–30.0 times the stoichiometric quantity according to Equations (1) and (2), or 0.1–0.25 g CO3·Mg–Al LDH (Mg/Al = 2.0 or 4.0), Mg(OH)2, or NO3·Mg–Al LDH(Mg/Al = 2.0) within the fiberglass in a quartz tube (inner diameter: 16 mm). The temperature of the electric furnace was set at 110–200 °C under N2 (or O2) flow. Based on the assumed velocity of the actual waste incineration exhaust gas, 150 ppm NO or 100–200 ppm NO2 was introduced with the flow rate adjusted with a mass flow controller to generate a linear velocity of 1.0 m/min for 60 or 90 min. The evolved gas was continuously analyzed using a NOx analyzer. The products were analyzed by X-ray diffraction. In this case, a stoichiometric quantity of 1.0 for CO3·Mg–Al LDH according to Equations (1) and (2) implies that the mole ratio of Al in CO3·Mg–Al LDH and NO or NO2 is 1.0. The total quantity of NO or NO2 was calculated from the estimation that 150 ppm NO or 100–200 ppm NO2 was fed to the quartz tube at 1.0 m/min for 60 or 90 min.
3. Results and discussion 3.1. NOx treatment 3.1.1. Effect of Mg/Al molar ratio and stoichiometric quantity on NO removal Fig. 3 shows the effect of the Mg/Al molar ratio and stoichiometric quantity on NO removal. There was almost no NO removal when CO3·Mg–Al LDH was used at a stoichiometric quantity of 15.0 times; even at 30.0 times the stoichiometric quantity, the values were extremely low with Mg/Al = 2.0 and 4.0, at 10.5% and 9.8% respectively. CO3·Mg–Al LDH had almost no NO removal capacity under an N2 atmosphere.
2.2. Anion desorption
3.1.2. Effect of O2 on NO removal We investigated the removal of NO as NO2 by oxidizing NO to NO2 using O2. Figure S1 shows the effect of O2 on NO removal. While there was almost no NO removal in the presence of 0% O2, i.e., under an N2 atmosphere, the NO removal rate in the presence of 10% O2 increased to 5.5% and 6.2%, respectively, with Mg/Al = 2.0 and 4.0. These findings suggest that NO can be removed with CO3·Mg–Al LDH as NO2 after oxidization with O2. However, oxidation to NO2 with O2 would significantly lower the reaction rate. Therefore, based on the
We synthesize NO3·Mg–Al LDH by coprecipitation, and used a Mg/ Al molar ratio of 2.2 and NO3− content of 22.9 wt%. Equation (3) shows the theoretical reaction formula for anion exchange between NO3·Mg–Al LDH and CO32−. Mg0.67Al0.33(OH)2(NO3)0.33 + 0.17CO32− ⇌ Mg0.67Al0.33(OH)2(CO3)0.17 + 0.33NO3− (3)
Fig. 2. Experimental apparatus for treating NOx with CO3 Mg furnace; (6) Quartz tube; (7) Fiberglass; (8) NOx analyzer.
Al LDH. (1) NO or NO2 cylinder; (2) N2 cylinder; (3) Mass flow controller; (4) Gas mixer; (5) Electric
2
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Fig. 3. Effect of CO3 Mg Al LDH quantity on the removal of NO. NO concentration: 150 ppm; Temperature: 170 C; Linear velocity: 1.0 m/min; Time: 90 min.
Fig. 5. Effect of temperature on the removal of NO2. NO2 concentration: 150 ppm; CO3 Mg Al LDH quantity: 10.0-times the stoichiometric quantity; Linear velocity: 1.0 m/min; Time: 90 min.
oxidization of NO to NO2, investigations were conducted with the NO2–N2 system.
3.1.4. Effect of temperature on NO2 removal Fig. 5 shows the effect of temperature on the NO2 removal rate. We found that the NO2 removal rate tended to decrease as the temperature increased from 110 to 170 °C, irrespective of the Mg/Al molar ratio. In particular, at 110 °C and 200 °C, the removal rates with Mg/Al = 2.0 and 4.0 were 53.3% and 50.7%, respectively, which decreased to 15.0% and 31.3%, respectively, at 200 °C. In accordance with Equation (4), NO2 decomposes to NO and O2 at ≥140 °C.
3.1.3. Effect of Mg/Al molar ratio and stoichiometric quantity on NO2 removal Fig. 4 shows the effect of the Mg/Al molar ratio and stoichiometric quantity on NO2 removal. NO2 removal was possible with CO3·Mg–Al LDH, and the removal rate increased with increasing quantity of CO3·Mg–Al LDH. The removal rates were 48.1% and 54.4%, respectively for Mg/Al = 2.0 and 4.0 at 15.0 times the stoichiometric quantity. Figure S2 shows the post-reaction X-ray diffraction pattern. The Xray diffraction peak ascribed to NOx·Mg–Al LDH could not be confirmed. These results suggest that NO2 removal with CO3·Mg–Al LDH occurs due to the surface adsorption of NO2 on CO3·Mg–Al LDH in addition to the formation of NOx·Mg–Al LDH according to Equation (2).
2NO + O2 ⇌ 2NO2
(4)
In this experiment, therefore, NO2 progressively decomposed to NO as the temperature increased, generating NO. As mentioned earlier, there was almost no NO removal by CO3·Mg–Al LDH, which supports that high-temperature NO2 treatment is not possible. Low temperatures are advantageous for NO2 removal with CO3·Mg–Al LDH. 3.1.5. Effect of concentration on NO2 removal The effect of concentration on the NO2 removal rate are shown in Fig. 6. The NO2 removal rates at a NO2 concentration of 100 ppm were 16.0% and 18.1%, respectively, for Mg/Al = 2.0 and 4.0, but 39.4% and 49.4%, respectively, at 150 ppm. However, at 200 ppm, the NO2 removal rates decreased to 29.4% and 40.6%, respectively. Given that CO3·Mg–Al LDH was present in 10.0 times the stoichiometric quantity (that is, the CO3·Mg–Al LDH quantity is higher with increasing NO2 concentration), the increase in contact efficiency between NO2 and CO3·Mg–Al LDH was considered to be the reason; however, if there is excess CO3·Mg–Al LDH, the contact efficiency decreases due to channeling, which is thought to be responsible for the decrease in the removal rate. 3.1.6. Breakthrough curve Fig. 7 shows the NO2 breakthrough curve with CO3·Mg–Al LDH packed bed heights of 0.5 cm and 1.0 cm, respectively. The removal rate decreased immediately after the introduction of NO2 flow for both heights, and then slowly. The reason for this is now being investigated. The higher CO3·Mg–Al LDH packed bed results in higher NO2 removal.
Fig. 4. Effect of CO3 Mg Al LDH quantity on the removal of NO2. NO2 concentration: 150 ppm; Temperature: 170 C; Linear velocity: 1.0 m/min; Time: 90 min.
3.1.7. NO2 removal by CO3·Mg–Al LDH We compared NO2 removal with CO3·Mg–Al LDH, NO3·Mg–Al LDH, 3
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Fig. 8. Effect of (a) CO3 Mg Al LDH , (b) NO3 Mg Al LDH, and (c) Mg(OH)2 on the removal of NO2. NO2 concentration: 150 ppm; Temperature: 170 C; Linear velocity: 1.0 m/min; CO3 Mg Al LDH quantity: 15.0-times the stoichiometric quantity; NO3 Mg Al LDH and Mg(OH)2 quantity: same as CO3 Mg Al LDH quantity; Time: 60 min.
Fig. 6. Effect of NO2 concentration on the removal of NO2. Temperature: 170 C; CO3 Mg Al LDH quantity: 10.0-times the stoichiometric quantity; Linear velocity: 1.0 m/min; Time: 90 min.
3.2. Anion desorption
and Mg(OH)2 to analyze in detail the NO2 removal by CO3·Mg–Al LDH. If NO2 treatment with CO3·Mg–Al LDH progresses by the formation of NOx·Mg–Al LDH according to Equation (2), NO2 removal should not occur with NO3·Mg–Al LDH, where NO3− is already present in the interlayer, nor with Mg(OH)2. Moreover, if NO2 removal progresses through surface adsorption on CO3·Mg–Al LDH, adsorption should also occur with NO3·Mg–Al LDH and Mg(OH)2. Fig. 8 shows the effect of adsorbents on the NO2 removal rate. NO2 removal is possible using all the adsorbents. The reactivity order was CO3·Mg–Al LDH > NO3·Mg–Al LDH ≒ Mg(OH)2. All adsorbents have surface hydroxyl groups; therefore, it is considered that NO2 adsorption occurs via weak interaction with the surface hydroxyl groups. The NO2 removal rates with all adsorbents indicated that CO3·Mg–Al LDH performed better than NO3·Mg–Al LDH and Mg(OH)2; this difference is possibly attributed to NO2 reacting with CO3·Mg–Al LDH and generating NOx·Mg–Al LDH. Therefore, in NO2 removal with CO3·Mg–Al LDH, both, removal by surface adsorption and generation of NOx·Mg–Al LDH, occurred. That is, this reaction certainly involves physical and chemical adsorption.
3.2.1. Effect of CO32− stoichiometric quantity on NO3− desorption Fig. 9 shows the effect of the CO32− stoichiometric quantity on the NO3− desorption rate. An NO3− desorption of 59.0% was confirmed even with the addition of CO32− at 0.5 times the stoichiometric quantity. This is thought to be due to the simultaneous intercalation of OH−. The NO3− desorption rate increased as the CO32− stoichiometric quantity increased, and a desorption rate of almost 100% was obtained with a stoichiometric quantity of ≥1.0 times. Figure S3 shows the postreaction X-ray diffraction pattern, and indicates the formation of CO3·Mg–Al LDH after NO3− desorption. It is assumed that desorption occurred through an anion exchange reaction between NO3− in the interlayer of NO3·Mg–Al LDH and CO32−. It is also thought that the NO2 adsorbed on the surface dissolved into the Na2CO3 solution and was desorbed as NO3− and NO2−. 3.2.2. Kinetic study Fig. 10 and S4 show the changes in the NO3− desorption rate and pH at each temperature over time. There was no significant difference in the NO3− desorption rates at 10, 30, and 60 °C. The pH declined significantly at higher temperatures. We analyzed the desorption
Fig. 7. Variation in the removal of NO2 by CO3 Mg Al LDH (Mg/Al = 2.0, 4.0) with time. NO2 concentration: 150 ppm; Temperature: 170 C; Linear velocity: 1.0 m/min; CO3 Mg Al LDH quantity: (a) 0.25 g and (b) 0.50 g (bed height: (a) 0.5 cm and (b) 1.0 cm). 4
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and qe and qt[mmol/g] are the adsorption amounts for the equilibrium desorption amount and time t[min]. When Equation (7) is integrated, it can be expressed by Equation (8).
t 1 1 = + t qt qe kqe2
(8)
The result of plotting t/qt against the reaction time at the initial stage of the reaction in the results of Fig. 10 is shown in Figure S5(b). Comparing the pseudo-first-order and pseudo-second-order plots in Figure S5, the correlation coefficients of the latter were higher than those of the former at all temperatures, and very close to 1.0. This suggests that NO3− desorption from NO3·Mg–Al LDH with CO32− conforms to the pseudo-second-order rate equation. 3.2.3. CO32− and HCO3− adsorption/NO3− desorption isotherm Figure S6 shows the absorption/desorption isotherms observed in CO32− and HCO3− adsorption and NO3− desorption in the NO3·Mg–Al LDH and CO32− reaction. Fitting was conducted using the Langmuir equation and Freundlich equation. The Langmuir equation is expressed by Equation (9). Fig. 9. Effect of CO3 2- stoichiometric quantity on the NO3 Temperature: 30 C; Time: 60 min.
qe =
desorption.
(5)
Ce 1 1 = + Ce qe KL qm qm
Here, t is the reaction time [min] and k is the apparent reaction rate constant [min−1]. Equation (5) is integrated and expressed as Equation (6) when expressed using the NO3− desorption rate x. Considering the pseudo-first-order rate equation at the initial stage of the reaction for the result shown in Fig. 10, leads to the result shown by plotting -ln(1-x) against the reaction time in Figure S5(a). The pseudo-second-order rate equation is expressed by (7).
dqt dt
= k (qe
qt ) 2
(7) −1
Here, k is the apparent reaction rate constant [(min・mmol・g)
(10)
Figure S7(a) shows the Ce/qe vs Ce plot. A good linear relationship is obtained between Ce/qe vs Ce in all adsorption and desorption processes, which matches the Langmuir equation. This implies chemical adsorption, and confirms that this reaction involves anion exchange between NO3− in the interlayer of NO3·Mg–Al LDH and CO32− in the aqueous solution. The maximum adsorption amount qm and the adsorption equilibrium constant KL determined from the slope and intercept of the straight line were 1.47 mmol/g and 8.75 × 10−1 L/mmol, respectively. The maximum desorption amount qm and the desorption equilibrium constant KL were 3.77 mmol/L and 8.96 × 10−2 L/mmol, respectively. Here, the relationship of Equation (11) holds for the equilibrium adsorption and desorption constant KL and the standard Gibbs energy ΔG0[kJ/mol].
(6)
ln(1 x) = kt
(9)
Here, qe is the equilibrium adsorption and desorption amount [mmol/g], Ce is the carbon C(CO32− and HCO3−) equilibrium concentration [mmol/L], qm is the maximum adsorption and desorption volume [mmol/g], and KL is the adsorption and desorption equilibrium constant [L/mmol]. Equation (10) is obtained from Equation (9).
reaction rates using these results. The pseudo-first-order rate equation is expressed by the following equation.
d [Cl ] = k [Cl ] dt
KL qm Ce 1 + KL Ce
],
G0 =
(11)
RTlnKL
The standard Gibbs energy ΔG0 at 30 °C became −17.1 kJ/mol in the adsorption process and −11.3 kJ/mol in the desorption process. As ΔG0 had a negative value, the CO32− and HCO3− adsorption processes and the simultaneous NO3− desorption process were spontaneous reactions. The Freundlich equation is an empirical formula found experimentally, and is expressed by Equation (12). 1
(12)
q e = KF Cen
Here, KF is the adsorption equilibrium and desorption constant [L/ mol], and n is a constant. Taking the log of both sides of Equation (12) results in Equation (13).
logq e = logKF +
1 logCe n
(13)
Figure S7(b) shows the plot of logqe vs logCe. A good correlation was not established between logCe and logqe, and it was concluded that approximation using the Freundlich equation could not be performed. Fig. 10. Change over time in NO3 desorption rate at each temperature. Na2CO3 concentration: 0.025 M; CO32- stoichiometric quantity: 1.0.
3.2.4. Thermodynamic analysis Fig. 11 and S8(a) show the desorption isotherm at 10, 30, and 60 °C 5
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Figure S8(b) shows the lnKL vs T−1 plot. A good linear relationship was obtained between lnKL and T−1, and the standard enthalpy ΔH0 and standard entropy ΔS0 were calculated as −13.5 kJ/mol and −8.06 × 10−3 kJ/(mol・K), respectively. The standard enthalpy ΔH0 had a negative value, which makes NO3− desorption an exothermic reaction. 3.3. Recycling Fig. 12 shows the effect of the number of recycling treatments on the NO2 removal rate. The NO2 removal rates in the first treatment were 46.8% and 53.6% for Mg/Al = 2.0 and 4.0, and 52.6% and 45.4% in the third treatment, respectively. The ability of CO3·Mg–Al LDH for NO2 removal was nearly maintained for three recycling experiments. This demonstrates that it may be possible to apply recycled CO3·Mg–Al LDH for NO2 removal. 4. Conclusion CO3·Mg–Al LDH could remove NO2, but not NO. While the NO removal rate was low, NO2 removal was possible with removal rates of 48.1% and 54.4%, respectively, for Mg/Al = 2.0 and 4.0 using a 15.0 times stoichiometric quantity. NO2 adsorption by CO3·Mg–Al LDH occurs by surface adsorption as well as the formation of NO3·Mg–Al LDH. CO3·Mg–Al LDH could be regenerated from CO3·Mg–Al LDH after NO2 adsorption using a Na2CO3 solution. The ability of CO3·Mg–Al LDH for NO2 removal was nearly maintained for three recycling experiments, suggesting that it may be possible to use recycled CO3·Mg–Al LDH for NO2 removal. To increase the efficiency of NO2 removal, CO3·Mg–Al LDH in more than 15.0 times the stoichiometric quantity is required. That is, an appropriate amount of CO3·Mg–Al LDH leads to increased efficiency of NO2 removal. For NO removal, NO needs to be oxidized to NO2 using an oxidation catalyst before treatment by CO3·Mg–Al LDH; this will constitute future work.
Fig. 11. Desorption isotherms on the NO3 desorption. Na2CO3 concentration: 0.005–0.5 M; Time: 180 min.
Acknowledgments This research was supported by the Environment Research and Technology Development Fund (3K163007) of the Ministry of the Environment, Japan. Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.apr.2019.07.018 References Fig. 12. Effect of the number of recycling cycles on the NO2 removal. NO2 concentration: 150 ppm; CO3 Mg Al LDH quantity: 10.0-times the stoichiometric quantity; Temperature: 110 C.
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and the Ce/qe vs Ce plot. A good linear relationship was obtained for Ce/ qe and Ce at all temperatures. The desorption equilibrium constants KL obtained from the slope and intercept of the straight line were 1.16 × 10−1, 8.96 × 10−2, and 4.94 × 10−2 L/mmol at 10, 30, and 60 °C, respectively. The standard Gibbs energies ΔG0 were −11.2, −11.3, and −10.8 kJ/mol at 10, 30, and 60 °C, respectively. Here, the relationship of Equation (14) holds for the desorption equilibrium constant KL, standard enthalpy ΔH0, and standard entropy ΔS0.
G0 =
RTlnKL = H0
T S0
(14)
Equation (15) is obtained through further transformation.
lnKL =
S0 R
H0 RT
(15) 6
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