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Aqueous Potassium Bicarbonate–Carbonate Ionic Equilibria at Elevated Pressures and Temperatures Maider Legarra, Ashley Blitz, Zsuzsanna Czegeny, and Michael Jerry Antal Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/ie400736u • Publication Date (Web): 28 Aug 2013 Downloaded from http://pubs.acs.org on September 7, 2013

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Industrial & Engineering Chemistry Research

Aqueous Potassium Bicarbonate–Carbonate Ionic Equilibria at Elevated Pressures and Temperatures

Maider Legarra,a Ashley Blitz,a Zsuzsanna Czégény,b and Michael Jerry Antal, Jr.a,*

a

Hawaii Natural Energy Institute, School of Ocean and Earth Science and Technology,

University of Hawaii at Manoa, Honolulu, Hawaii 96822 b

Institute of Materials and Environmental Chemistry, Research Centre for Natural Sciences,

Hungarian Academy of Sciences, P.O. Box 17, Budapest 1525, Hungary

*phone: 808-956-7267; fax: 808-956-2336; email: [email protected]

ACS Paragon Plus Environment

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Abstract Aqueous bicarbonate-carbonate ionic equilibria play an important role in determining the practicality of various aqueous-alkaline fuel cells, and the hot carbonate process for removing carbon dioxide from synthesis gas streams. These equilibria are also of interest to scientists concerned with climate change. In this paper we report measurements of aqueous bicarbonatecarbonate ionic equilibria between 150 and 320 °C at the solutions’ respective saturation pressures. The aqueous bicarbonate ions are not stable at temperatures above 150 °C: the bicarbonate decomposes into carbonate and aqueous CO2. The dissolved CO2 is released from the solution when the reaction vessel is quickly cooled and depressurized, leaving behind stable carbonate ions in a solution with increased pH. A thermodynamic analysis of these findings indicates that the spontaneous and endothermic bicarbonate decomposition reaction proceeds with a positive change in entropy.


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1. INTRODUCTION Among the many competing sources of sustainable power for the 21st century, direct carbon fuel cells (DCFC) possess numerous advantages: an efficiency close to unity, a familiar, safe, and economical fuel (biocarbon), operation as a source of baseload (not intermittent) power, and a pure CO2 effluent that can be captured and sequestered. These advantages, as well as the current state-of-the-art of these cells, are well described in three recent reviews.1-3 High temperature cells (e.g. molten carbonate, and a hybrid combination that also incorporates a solid oxide fuel cell electrolyte) have shown promising performance,4-9 but nonetheless are challenged by corrosion and unfavorable chemistry (i.e. the Boudouard reaction) that reduces their efficiency.10, 11 As foreseen by an early publication in this journal,12 biocarbons—which are highly reactive due to their porosity, disorder at the atomic level, and dangling bonds13-16— perform well in these high temperature cells. Moreover, the high reactivity of biocarbons obviates the high temperature constraint that exists when coke or graphite is used as a fuel.17-20 Aqueous-alkaline batteries (e.g. zinc/air) and fuel cells (e.g. the Bacon cell) perform well at much lower temperatures, where the Boudouard reaction is inactive but biocarbon oxidation can be vigorous; consequently there is interest in the development of aqueous-alkaline DCFC.21, 22 Unfortunately, the aqueous-alkaline cell has its own problems, of which the most famous is the instability of its electrolyte in the presence of CO2.23 The Apollo spacecraft delivered pure oxygen instead of air to its Bacon (hydrogen) fuel cell chiefly to ensure that no carbonate formed in its electrolyte.24-26 Obviously, the problem is greatly exacerbated when carbon is used as a fuel in the cell.23 Nevertheless, thermodynamic predictions indicate that at temperatures approaching 300 °C, the carbonate ion can be as effective an oxidant as the electrolyte’s


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hydroxyl ion, leading to the conclusion that an aqueous-alkaline-carbonate DCFC should function well at such relatively low temperatures.21 This conclusion overlooked the subsequent reaction of the carbonate ion with plentiful CO2 that forms bicarbonate, which – combined with the low solubility of bicarbonate salts – leads to heavy precipitation and plugging of the cell. The classic text by Liebhafsky and Cairns emphasizes “the problem of an invariant electrolyte” relative to alkaline DCFC technology,23 but makes no mention of bicarbonate precipitation. The equilibria of aqueous bicarbonate/carbonate solutions at elevated temperatures and pressures, together with solubility issues, is a familiar topic to chemical engineers, who developed the hot carbonate process for removing CO2 and H2S from synthesis gas streams in the late 50’s.27 Their research showed that the aqueous bicarbonate ion is unstable at sufficiently high temperatures: it decomposes into carbonate ion and CO2 (aq), but their findings did not extend into the temperature range of interest for aqueousalkaline-carbonate DCFC.27 Also, we remark that the buffer system equilibria between CO2 in the atmosphere and ocean water (including the bicarbonate and carbonate ions) together with minerals (chiefly limestone) is a determinant of climate change,28 and has been the subject of much research at relatively low temperatures.29-32 In light of the importance of CO2–carbonate– bicarbonate ion equilibria to the development of an aqueous-alkaline-carbonate DCFC, and its relevance to other fields, we undertook the work described in this paper. We emphasize equilibria between 150 and 320 °C at pressures as high as 11.28 MPa (1636 psi). Our findings show that the decomposition of the bicarbonate ion is strongly favored at temperatures above 200 °C, but the CO2 product remains in solution and is not released to the gas phase. Precipitation of bicarbonate salts occur as the cell is cooled to low temperatures, which favor the reformation of bicarbonate from dissolved CO2 and the carbonate ion.


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2. MATHEMATICS GOVERNING AQUEOUS CARBONATE EQUILIBRIA The chemistry of the bicarbonate-carbonate aqueous system at standard conditions is well understood.29-31 However, as far as we know, little is known of the chemistry at moderate temperatures (T > 150 °C) and pressures (P ≥ Psat). In water, when a bicarbonate concentration is below saturation, the bicarbonate salt dissociates into its cation/s and the carbonate anion/s. A bicarbonate from group 1 (a bicarbonate whose cation belongs to group 1 of the periodic table) dissociates into one cation and one bicarbonate anion, and a bicarbonate from group 2 gives one cation ion and two bicarbonate anions as specified by reactions (1a) and (1b) respectively. (

(1a) (1b)

)

Following dissolution, the bicarbonate anion reacts with water and equilibrates with the carbonate anion and carbonic acid. The distribution of dissolved carbonate species is governed by the charge balance, the mass balances of the carbon and cation; and the equilibrium equations tabulated in Table 1, where CHCO3 designates the initial bicarbonate concentration prior to equilibration. CHCO3 as well as the terms between brackets [] in eqs (2a-b) – 7 have units of molality (mol/ kg solvent). [

Eq (5) in Table 1 could be written as

][

]⁄[

]. However, the carbonic

acid (H2CO3) is in equilibrium with dissolved CO2 (CO2, aq) and water according to the reaction (

)

(

)

At equilibrium, the ratio of [H2CO3] to [CO2(aq)] is close to 10-3 at room conditions. Also, both species are uncharged; consequently they have no special significance in the acid–base equilibria. For these reasons, the hydrated and non-hydrated forms of CO2 are considered as a single entity that is designated by [CO2].29


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Our nomenclature for the dissociation constants of eqs (5) – (12) follows that of Butler.30 The equilibrium constants (Kj) of reactions j at finite ionic strength — which are functions of temperature, pressure and ionic medium — combine the extrapolated zero-ionic strength constants (

) and the activity coefficients of the species present in the reaction ( ) as shown in

eqs (10) – (12) of Table 1.

,

and

represent the activity coefficients of ions with a single

negative charge, a double negative charge and a single positive charge calculated using the Davies equation. The Davies equation is an empirical extension of Debye–Hückel theory that can be used to estimate the activity coefficients of electrolyte solutions at concentrations with ionic strengths as high as 0.5 molal.30 The final form of the equation gives the activity coefficient for an ion with charge z as a function of ionic strength (I) as in eq (9) where the function f(I) of eq (9) applies only to the temperature range 0–50 °C. Values of zero-ionic strength constants, unless indicated, are given by Li and Duan33 for eqs (10) and (11), and Bandura and Lvov34 for eq (12). The equilibrium pH can then be solved by combining eqs (2)–(12) into the following equations

[

[

] [

[ ]

] [

] [ [

]

] ] [

[ ]

]

(

[

]

) (

(

)

)(

)

Notice that the ionic effect of bicarbonate groups 1 and 2 are different, consequently, the equilibrium constants of eqs (14a-b) are different. By specifying the value of the initial bicarbonate concentration (

), and the temperature,

the only unknown in eqs (14a-b) is the concentration of hydronium ion [H+] (i.e. the pH of the


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solution). We solve either of eqs (14a-b) in MatLab; thereby providing the value of [H+]. Thereafter, the carbonate species concentrations can be calculated by use of the equilibrium equations. Alternatively, by specifying the value of pH at a certain temperature, the initial bicarbonate concentration can be calculated with eqs (14a-b) and the bicarbonate, carbonate and CO2 concentrations can be obtained by use of the equilibrium equations. Or by specifying the pH at a certain temperature, the bicarbonate/ CHCO3, carbonate/ CHCO3 and CO2/ CHCO3 ratios can be obtained by use of the equilibrium equations without eqs (14 a-b). We remark that Hunter and Savage also reported an expression for the H+ concentration related to the CO2 pressure for a CO2–H2O system at high temperatures.35 Their expression was solved using the dissociation constants and charge balance as well. However, they represented the solubility of CO2 in water with the Henry’s constant (i.e., they had no need of a carbon mass balance). Figure 1 displays the solutions of the carbonate ratios versus pH for a group 1 bicarbonate assuming activity coefficients of unity. The results of this pH model enjoy agreement with those of Butler displayed in his Figure 2.2.30 Figure 2 shows the concentrations of carbonic acid, sodium bicarbonate and sodium carbonate solutions obtained with this model assuming unity activity coefficients and compares these concentrations with those given by the model of Pourbaix.36 Results of the two models enjoy good agreement. In the case of carbonic acid and carbonate solutions, Pourbaix simplified both cases by considering only one relevant equilibrium reaction. Pourbaix considered the amount of carbonic acid in a carbonate solution and the amount of carbonate in a carbonic acid solution to be negligible. With that simplification, the algebra is considerably simplified (i.e. Pourbaix had no need for a charge balance in his model). Figure 1 corroborates Pourbaix’s assumption: both the concentrations of carbonic acid at high


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pH (carbonate solutions) and the concentration of carbonate at low pH (carbonic acid solutions) are small. In the case of bicarbonate solutions, Pourbaix considered both equilibrium reactions, as well as a mass balance of the hydroxide. As shown in Figure 2, this approximation agrees well with the exact solution in a pH range from 7 to 8.3. Figures 3a-b show the concentrations of the carbonate species after equilibration versus the initial concentrations of solutions composed of just potassium bicarbonate with different degrees of dilution (Figure 3a) and solutions composed of carbonate and bicarbonate with 1:1 mass ratios and different degrees of dilution (Figure 3b). Notice that the equilibrated concentrations are almost the same as the initial concentrations. Figure 4 displays the carbonate species’ concentrations versus temperature assuming an initial bicarbonate solution of 0.1 molal and unity activity coefficients including Ka values given by the Li and Duan equation 33 and those of Stumm and Morgan.29 Note that the activity coefficient approaches unity at low ionic strength (≤0.1 M). According to this acid–base equilibrium model, the bicarbonate ion is the main component of the solution (~95% to ~98.5%) from 0 to 250 °C (n.b. the Li and Duan model for

and

covers a temperature range from

0 to 250 °C) at the saturation pressure of water. These values are consistent with experimental observations at low temperatures, but they are not consistent with our experimental observations at high temperatures. Experimentally, we observed the decomposition reaction of bicarbonate into carbonate and CO2 (Eq 15 below) at temperatures from 150 to 320 °C. Hence, our findings indicate that the presence of carbonate at high temperatures is mainly governed by the decomposition reaction: 

(

)

and is not by the acid/base equilibria model.


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2.1. Consistency of the pH model with the experimental procedures. To check the consistency of the pH model with experiments, we prepared a 5 molal solution of potassium carbonate by dissolving 69.105 g of anhydrous potassium carbonate (Fisher Chemicals, Lot 105401A, 99.7% purity) in 0.1 L of deionized water. This stock solution was gradually diluted at room temperature, and experimental pH values of the diluted potassium carbonate solutions were measured (see Figure 5). Figure 5 also displays MatLab pH values (obtained from the solution of eq (14a) versus the initial molality of potassium carbonate solution. In Figure 5 two MatLab solutions are displayed. One employs the Davies equation to represent activity coefficients at finite ionic strength, while the other employs activity coefficients of unity. Recognizing the fact that our experimental pH measurements enjoy a precision (i.e. sample standard deviation) of 0.1, good agreement exists with the MatLab pH values that employed the Davies activity coefficients at potassium carbonate concentrations below 1 molal. However, a significant pH difference of 0.32 at concentration of 1 molal is observed, and the pH difference subsequently increases with increasing potassium carbonate concentration. This loss of accuracy is in agreement with the range of applicability of the Davies equation. At ionic strength above 0.5 molal, the experimentally determined activity coefficients for many salts differ significantly from those predicted by the Davies equation.30, 31 Ironically, the MatLab pH prediction, which assumes unity activity coefficients, shows better agreement with experimental measurements at concentrations above 1 molal. Nevertheless, the pH disagreement can exceed 0.6 and the pH– concentration trends are different. 3. APPARATUS AND EXPERIMENTAL PROCEDURES 3.1. Apparatus. Figure 6 shows a schematic diagram of the pressure-vessel reactor in use at the Hawaii Natural Energy Institute of the University of Hawaii in Honolulu. The reactor


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consisted of a 50.5 mL cylindrical stainless steel tube (2.0 cm I.D. x 16.1 cm) rated to 3100 psi at 25 °C and to 1700 psi at 300 °C. At the top of the reactor Swagelok fittings, a thin stainless steel tube (0.4 cm I.D. x 11.7 cm) and a Swagelok cross served as a 17.5 mL manifold resulting in a total reactor volume of 68 mL. A type K thermocouple, inserted through the top of the cross, measured the temperature of the solution. One side of the cross housed a pressure transducer (Omega model PX602-5KGV), which measured the pressure inside the vessel, and a safety burst diaphragm that prevented the pressure from exceeding the pressure limit of the vessel. The other side of the cross was connected to a manual pressure release valve that was used to depressurize the vessel at the end of an experiment. The vessel was submerged in a Techne Fluidized Sand Bath Model SBL-2D with four heaters. The sand bath had the desirable characteristics of accessibility, uniformity of temperature, small thermal capacity and good heat transfer. A Mettler Toledo SevenEasy pH meter and a Mettler Toledo InLab Routine Pro electrode, which were recommended by Mettler as their best choice for high pH measurements, were used to measure pH and quantify titrations. The pH meter was calibrated by a procedure that mimicked the protocol developed by the National Renewable Energy Laboratory (NREL) for calibrating HPLC determinations of carbohydrates, HMF, and furfural.37, 38 (see Supporting Information for details). This calibration procedure led to a measured value of 0.1 for the sample standard deviation of a pH measurement at high pH (See Supporting Information). TG/MS measurements were performed by the Institute of Materials and Environmental Chemistry of the Hungarian Academy of Sciences in Budapest using a modified Perkin-Elmer TGS-2 thermobalance and a HIDEN HAL 2/301 PIC quadrupole mass spectrometer. Typically a 2.5 mg electrolyte crystal sample was placed into the platinum sample pan and heated at 20 °C min-1 to 1000 °C in an argon atmosphere. Portions of the volatile products were introduced into


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the mass spectrometer through a glass-lined metal capillary transfer line heated to 300 °C. The quadrupole mass spectrometer operated at 70 eV. 3.2. Reagents and validation of their analyses. The potassium bicarbonate crystals (Fisher Scientific), which were used to prepare the potassium bicarbonate reactant solutions, were analyzed by Thermogravimetry Mass Spectrometry (TG/MS) to ensure their purity (see Figure 7). Both the decomposition temperature (near 216 °C) and the measured weight loss (69.07%) were consistent with that of dry 99.9% pure potassium bicarbonate. Titrations of the reaction products and the bicarbonate/carbonate controls employed either a hydrochloric acid 0.100 ± 0.001 N standard solution (Acculute Anachemia, Lot 90605), or nominal 0.1 N hydrochloric acid solutions that were prepared by diluting a concentrated 12.1 N hydrochloric acid solution (Fisher Scientific, CAS 7647-01-0, Lot 074064) with deionized HPLC grade water. The nominal 0.1 N acid was standardized with a standard 1.041 N sodium hydroxide solution from Aldrich (Aldrich, CAS 1310-73-2, Lot 319511). A bromocresol green pH indicator solution was prepared by dissolving 100 mg bromocresol green (Matheson Coleman and Bell, BX1155) sodium salt in 100 mL deionized HPLC grade water. The change in color from blue to yellow of the bromocresol green indicator occurs at pH around 4.5. A phenolphthalein indicator was prepared by mixing 0.5 g of phenolphthalein (Merck and Co., Inc., S 7458) with a 50% ethanol/50% deionized water solution. Its change in color from pink to colorless occurs at pH 8.2 approximately. 3.3. Experimental Procedure. 34 mL of a potassium bicarbonate solution (1 or 0.1 molal) was placed inside the 68 mL pressure vessel. To begin the experiment, air was supplied to the sand bath until the sand appeared to be boiling or fluidized. Once fluidization occurred, the four heaters were switched on and the sand bath was heated at a rate of 6 °C/min. In our earliest work,


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the pressure and temperature were recorded in increments of 10 °C from 150 °C until the desired temperature was obtained (150, 180, 200, 250, 300 or 320 °C). Later, a National Instruments Data Acquisition system was implemented and the pressure and temperature data were recorded every 10 seconds in LabView during the entire experiment. When the solution temperature reached the desired temperature, the temperature was held for reaction times of 2, 4 or 8 h; thereafter the pressure vessel was removed from the fluidized sand bath and cooled to room temperature. The remaining electrolyte, which consisted of a bicarbonate/carbonate mixture, was removed from the vessel and analyzed. Three different analyses of the final product solutions were employed: (1) pH measurement, (2) TG/MS of the dry crystals, and (3) titration. The titration procedure following the standard method reported by the American Public Health Association.39 (see Supporting Information) 4. RESULTS 4.1. Analysis to quantify conversion and equilibrium constant. As a first attempt to quantify conversion, pH measurements were related to conversion. Experimental pH–conversion values were obtained by preparing bicarbonate/carbonate solutions—whose concentrations corresponded to the products of experiments of initial experimental bicarbonate concentrations of 1 molal and 0.1 molal — that experienced reaction conversions (eq (16)) from 0 to 1:

(

where

is the bicarbonate conversion,

and

)

are the initial and final moles

of potassium bicarbonate respectively. Our use of these solutions to represent the calculated product composition assumed that all the CO2 formed by reaction escaped from the solution, and that the change in volume due to the formation of water was negligible. The pH values of these


12

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solutions were measured (see Figure 8). pH–conversion values for initial bicarbonate concentrations of 1, 0.1 and 0.01 M values were also calculated analytically in MatLab and plotted in Figure 8. Note the good agreement of the MatLab solution with the experimental pH measurements. However, a propagation of error analysis using the sample standard deviation of the pH meter (i.e. 0.l pH units) resulted in a predicted precision (i.e. sample standard deviation) of ±69.7 for the equilibrium constant Keq = 20.25 at pH = 10.52 , representing a conversion of 90%. (see Supporting Information for details) Because high conversions were emphasized in this work, this loss of precision was not acceptable and other means were sought to evaluate Keq. This approach was employed only to make a rapid estimate the impacts of cooling and reaction time on the values of the equilibrium constants.

TG/MS analyses were performed as a second effort to quantify the conversion of the reaction. One-third of the final experimental aqueous samples, as well as two solutions of known bicarbonate/carbonate concentration were dried at 90 °C under vacuum and sent to the Hungarian Academy of Science for TG/MS analysis. The aim of vacuum drying was to avoid atmospheric CO2 absorption by reactions: ( ) (

)

( (

)

) (

)

(

)

(

)

As shown in Figure 3, the expected values of the % KHCO3/% K2CO3 of the crystals obtained after drying the sample under vacuum would be approximately the initial % KHCO3/% K2CO3 values (see Table 2). However, due to vacuum drying the low partial pressure of CO2 above the solution promoted the reverse of reactions (17) and (18), thereby causing the carbon dioxide to enter the gas phase and shifting equilibrium towards the formation of CO32-. Table 2 shows the


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disagreement between the expected mass composition and the mass composition obtained by TG/MS analysis of the two bicarbonate/carbonate controls. These observations revealed the sensitivity of the bicarbonate solution equilibria to its surroundings, and indicated that TG/MS analysis could not be used to quantify the product composition of the reaction and its conversion.

Titration analyses were employed as our third and final attempt to quantify conversion. Eq (16) was rearranged so that the conversion was solved in terms of the carbonate mol percentage determined by titration as

(

)

( where

)

(

)

). The equilibrium conversion of

bicarbonate was related to the equilibrium constant,

[

][ [

where

(

] ]

, by eq (20)

(

(

)

)

depends on the temperature and ionic medium. Figure 9 displays

(

)

as a function of

the conversion of bicarbonate from 0 to 90%. Notice that the equilibrium constant is more sensitive to the conversion at high conversion values. A propagation of error analysis for this approach using the sample standard deviation of the titration measurements for a solution of an initial concentration of 1 M (see Supporting Information) resulted in a predicted precision of ±1.6 for the equilibrium constant Keq = 20.25, representing a conversion of 90%. (see Supporting Information for details)


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4.2 Absence of CO2(g). The equilibrium vapor pressure, or saturation pressure above the electrolyte, depends on the temperature and the molality of the bicarbonate solution as given by eq (21) |

where R is the gas constant,

(

)

is the molar fraction of the solution and L is the enthalpy increase

of the evaporation of 1 mol of water at temperature T.40 Figure 10 shows the increase of the boiling point with the potassium bicarbonate molality at pressures of 580 and 725 psi determined by eq (21). For instance, experimental 0.1 molal and 1 molal solutions have boiling points around 0.15 and 1.5 °C higher than pure water at 580 and 725 psi pressures. However, this slight change in the saturation conditions due to the molality could not be detected in our apparatus. Because the potential pressure increase in the vessel due to the decomposition of bicarbonate was a serious safety concern, our earliest efforts focused on predictions and measurements of the total pressure of 1 molal KHCO3 solutions at temperatures from 150 to 250 °C 41 (see Figure 11). Recognizing the fact (Figure 10) that the bicarbonate had little effect on the saturation temperature and pressure of pure water, the predicted, theoretical total pressure was estimated as the sum of the theoretical steam pressure given by the Steam Tables42 plus the rise in pressure due to CO2 formation. This rise in pressure was calculated assuming ideal gas behavior and a worst case scenario of 100% conversion of bicarbonate,

. As

displayed in Figure 11, no rise in pressure due to CO2 formation was detected. Experiments with 0.1 molal KHCO3 solutions also showed no pressure rise above that expected from pure water alone. Given the accuracy of the pressure transducer of 1%, the maximum amount of CO2 that could have been released into the gas phase ranged from 1 psi at 150 °C to 6 psi at 250 °C.


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However, our measured values of the saturation pressure of both pure water and the dilute carbonate solution enjoyed excellent agreement with the Steam Tables. In conclusion, the CO2 formed as a result of the decomposition of the KHCO3 remains dissolved in the electrolyte and is not released to the gas phase until the reactor is cooled and depressurized. We note that recently Professor Jerry King and his co-workers reviewed prior work on this topic.43, 44 Several studies of the dissolution of high pressure CO2 in hot water over a range of temperatures and pressures showed that its solubility decreases up to 100 °C,45-48 but Sabirzyanov et al.47 observed a subsequent increase in solubility from 100 to 150 °C. 4.3 Effect of cooling and reaction time to reach equilibrium. In order to study the effect of cooling as a means of quenching the reaction, a series of experiments were executed with initial 1 molal potassium bicarbonate solutions exposed to temperatures of 300 and 320 °C for 2 or 4 h. Three different methods of cooling the reactor vessel at the end of the experiment were tested: (1) cooling in the open air (about 1 hour to reach room temperature), (2) cooling using a fan (5 to 10 min to reach room temperature) and (3) submerging the vessel in cold water (about 30 s to reach room temperature). In all cases, the pressure in the vessel was released when the liquid temperature fell below 100 °C. The pH value of the remaining electrolyte was used as the indicator to determine the final experimental conversions. Table 3 shows the final experimental pH values for the first cooling method. The pH results indicated that the CO2 could back react to form bicarbonate while the vessel was cooled. Cooling the vessel quickly by submerging it in cold water prevented the CO2 back-reaction. Some of the subsequent experiments (experiments at 320 °C when working with 1 molal bicarbonate and at temperatures above 150 °C when working with 0.1 molal bicarbonate), which were quenched by submerging the reactor in water, gave 100% conversions indicating that the back-reaction had been completely prevented.


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In order to estimate the time to reach equilibrium, two series of experiments at different temperatures were performed (see Tables 3 and 4). In this series, initial 1 and 0.1 molal potassium bicarbonate solutions were exposed to temperatures from 150 to 320 °C for reaction times of 2, 4 or 8 h followed by a cold water quench. In our early work, the pH value of the final solution was used to determine the final experimental conversions for the 1 molal experiments (see Tables 3 and 4). Subsequently, titrations were performed to determine the final conversions (see Tables 5 and 6). Our observations indicated that equilibrium of the decomposition reaction of 1 molal bicarbonate solution was reached within 4 h when held at 150 °C and 200 °C, and by 8 h at 150 °C for an initial 0.1 molal bicarbonate solution. At 250 °C, equilibrium was achieved by 2 h with a 1 molal initial bicarbonate solution and by 4 h with a 0.1 molal initial bicarbonate solution. 4.4 Dependence of equilibrium conversion on temperature. Table 5 shows that 0.1 molal initial potassium bicarbonate solutions exposed to temperatures from 150 to 320 °C gave equilibrium conversions of 100%. However, the equilibrium conversions of the 1 molal potassium bicarbonate solutions were dependent upon temperature at 150 °C and above.

A final series of experiments with 1 molal initial potassium bicarbonate solutions exposed to temperatures from 150 to 320 °C for 4 h (to assure equilibrium was reached) were conducted. The bicarbonate/carbonate final solutions were titrated twice and the final equilibrium conversion and equilibrium constant (see Table 6) were determined by use of eqs (19) and (20) (respectively). Figure 12 shows the experimental conversion versus temperature for the potassium bicarbonate solutions of 0.1 molal and 1 molal experiments. While the 0.1 molal potassium bicarbonate experiments gave reproducible results, the 1 molal potassium bicarbonate experiments presented some reproducibility problems.


17


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Page 18 of 43

Tosh et al.49 studied bicarbonate/carbonate mixtures of 20, 30, 40 percent-equivalent concentrations of potassium carbonate (percent-equivalent concentrations of potassium carbonate refers to a solution in which only potassium carbonate and water are present) at temperatures from 70 to 130 °C at their saturation pressures. They, therefore, used 1.8, 3.1 and 3.6 molalequivalent concentrations of potassium carbonate (concentration in molality if all the bicarbonate in the system were converted back to carbonate). Their experimental bicarbonate/carbonate solutions, whose carbonate ion concentrations exceeded ours by a factor of 3.6 or more, released (unlike our experiments) gaseous CO2 .Tosh et al.49 calculated the equilibrium constants under the assumption that all CO2 was released as a gas. No analyses were performed of the final aqueous solutions, and the possible formation of aqueous CO2 was ignored. Their solutions may have become oversaturated with aqueous CO2, resulting in a misleading value of the conversion of the reaction. Also, their use of such high concentrations may have incurred bicarbonate solubility problems (the bicarbonate solubility is 3.37 molal at 20 °C and 6.56 molal at 60 °C.49 Tosh et al. reported reproducible equilibrium conversions with 1.8, 3.1 molal-equivalent concentrations of potassium carbonate. However, they encountered reproducibility problems at 3.6 molal-equivalent concentration of potassium carbonate and did not plot these results due to “the variation (of the equilibrium constants) from the individual tests” because of “a greater deviation from ideality of the ionization constants of carbonic acid”.49 All our experimental results confirm the reversible nature of reaction 2 (

)

(

)

(

)

. While low temperatures favor a shift of equilibrium to the left,

temperatures from 70 to 320 °C at or above the saturation pressure shifts the equilibrium in the opposite direction. This behavior was also observed by other researchers. Butler,30 for example, stated that the reaction Na2CO3+CO2+H2O

2NaHCO3 (as well as K2CO3+CO2+H2O


18

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2KHCO3) is reversible, where lower temperatures and higher CO2 pressures favor the right side, and higher temperatures and lower CO2 pressures favor the left side. Field et al.27 found that temperatures of about 38 °C favor nearly complete conversion of carbonate to bicarbonate in reaction K2CO3+CO2+H2O

2KHCO3 reaction, while boiling temperatures shift the equilibrium

to the left. All these experimental results are consistent with a reaction involving positive enthalpy and entropy changes (i.e. a switch in the direction of the reaction with temperature occurs when ΔrH and ΔrS present the same sign).50 However, these findings conflict with thermodynamic values calculated from thermodynamic databases. In their handbook, Barner and Scheuerman51 estimated the thermodynamic properties of many ions in hydrothermal solutions by means of the “entropy correspondence principle” of Criss,52 and that of Criss and Cobble.53, 54 Both Criss, and Criss and Cobble related the “absolute” entropies of many aqueous ions at elevated temperatures to their “absolute” entropies at 25 °C using the average partial molal heat capacity. Barner and Scheuerman calculated the change in Gibbs free energy of aqueous ions formed from their elements in hydrothermal solutions at specific elevated temperatures under the assumptions that ΔfH°H+ = ΔfG°H+= 0 at all temperatures and that ΔfH°and ΔfG°of all elements (except sulfur and phosphorus) are zero at all temperatures. Using the thermodynamic data given by Barner and Scheuerman,51 we estimated the thermodynamic values (enthalpy, entropy and Gibbs free energy) of the reaction (

)

(

)

(

)

from room temperature to 300°C.55 This

estimate required thermodynamic data of aqueous gaseous

that we calculated using the data for

given by Barner and Scheuerman together with Henry’s constant calculated from

the work of Versteeg and Van Swaaij.56 Surprisingly, a positive enthalpy and a negative entropy were obtained throughout the temperature range. Therefore, no switch of direction in the reaction


19


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Page 20 of 43

could be expected from these results. We also employed Craig’s thermodynamic database of species50 to calculate the thermodynamic properties of the reaction at room temperature. It also led to a positive enthalpy and negative entropy change for the reaction. Finally, the SUPCRT92 software of Johnson et al.57 also exhibited a positive enthalpy and a negative entropy in the specified range of temperature from room temperature to 275 °C at its saturation pressure (in this case the temperature range of validity did not quite extend to 300 °C). From a molecular point of view, a negative value of the ΔrS arises from the “freezing” of water molecules around the ions due to ion-dipole attractions.50 The dipolar water molecules orient themselves in an energetically favorable way around the positive and negative ions. The decreased mobility of these water molecules lowers their entropy because vibrational degrees of freedom take the place of translational and rotational degrees of freedom. But in the reaction (

)

(

)

(

)

two singly charged ions become one double

charged ion. According to the previous reasoning, the degrees of freedom of the water molecules would seem to increase, resulting a positive value of the entropy change. Also the number of molecules increase in the reaction. This behavior is usually associated with an increase in the entropy of the reaction. If CO2 were gaseous, then the increase in entropy would be very large. This reasoning is consistent with all experimental observations concerning the shift of reaction equilibrium towards the formation of carbonate ion from bicarbonate with increasing temperature. Finally, we note that the elevated temperature behavior of the equilibrium constants given by the Li and Duan equation33 are unable to represent the experimental findings discussed above. Returning to Fig. 4 we see that bicarbonate ion is the main component of the 0.1 M bicarbonate solution (~95% to ~98.5%) from 0 to 250 °C when the acid-base equilibrium model is solved


20

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using the Li and Duan equation,33 but in fact the bicarbonate ion decomposes irreversibly at temperatures above 150 °C. As noted previously, the relative concentrations of the bicarbonate and carbonate ions in water are governed by decarboxylation chemistry as well as acid-base chemistry. 5. CONCLUSION 1) The aqueous bicarbonate ion is not stable at elevated temperatures (i.e. ≥ 150 °C with P ≥ Psat): it decomposes into an aqueous carbonate ion together with aqueous (not gaseous) CO2. 2) The aqueous, dissolved CO2 can escape from the solution when the system is depressurized, leaving behind stable carbonate ions. But on the other hand, the CO2(aq) can also back-react with the carbonate ion and re-form bicarbonate while the vessel is cooled. 3) The CO2(aq) back-reaction can be prevented by quickly submerging the reaction vessel in cold water and releasing pressure immediately after the temperature of the aqueous system falls below 100 °C. 4) A thermodynamic analysis of the experimental behavior of the spontaneous bicarbonate decomposition reaction indicates that it is endothermic and proceeds with a positive change in entropy. 5) These experimental findings are not consistent with the thermodynamic tables of Barner and Scheuerman.51 Likewise, these findings are not consistent with an acid-base model for the equilibria that employs the equilibrium constants given by the Li and Duan equation.33


21


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Page 22 of 43

ACKNOWLEDGMENT We thank the following sponsors for their support: the National Science Foundation (Award No. CBET08-28006), the Office of Naval Research under the Hawaii Energy and Environmental Technologies (HEET) initiative, and the Coral Industries Endowment of the University of Hawaii. We thank Dr. Maria Burka (NSF) for her continuing interest in carbon fuel cell research, Dr. Gérard C. Nihous for his comments and advice, and Dr. Douglas Wheeler (DJW Technology) for encouraging us to examine the impacts of carbonate formation on the performance of aqueous-alkaline fuel cells. We also thank four reviewers for their helpful comments. Supporting Information.

pH meter calibration and precision; Titration procedure and

precision; Propagation of error in the equilibrium constant calculation. This information is available free of charge via the Internet at http://pubs.acs.org/.


22

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List of Figures and Tables

Figure 1. Logarithmic ratios of concentration of carbonate species as a function of pH at 25 °C assuming unity activity coefficients and a group 1 bicarbonate (values of Ka given by Li and Duan equation). Figure 2. Comparison of our acid–base equilibria model (values of Ka given by Li and Duan equation): o with the Pourbaix model (values of Ka given by Pourbaix): — for carbonic acid, sodium bicarbonate and sodium carbonate solutions. Figure 3. Mol percentages of carbonate species (%) vs (a) Initial potassium bicarbonate concentration (molal) and vs (b) mixtures of initial potassium bicarbonate and potassium carbonate concentrations (molal/molal) at 25 °C assuming unity activity coefficients (values of Ka given by Li and Duan equation). Figure 4. Equilibrium concentrations of H2CO3, HCO3-, CO32- (molal) and pH vs temperature (°C) for an initial 0.1molal potassium bicarbonate solution assuming unity activity coefficients with values of Ka given by Li and Duan equation: — and by Stumm and Morgan: x. Figure 5. pH vs initial potassium carbonate concentration in molality at 25 °C. We display experimental pH values: x, o; as well as pH MatLab solutions using Davies activity coefficients: --- and using unity activity coefficients: — (values of Ka given by Li and Duan equation). Figure 6. Schematic diagram of the pressure vessel in the sand bath. TC is the thermocouple, TR is the temperature regulator, HSL is the low heater switch, HSM is the medium heater switch, HSH is the high heater switch, HSB is the boost heater switch and AIR is the clean air supply. Figure 7. TG/MS analyses of potassium bicarbonate crystals. Potassium bicarbonate mass loss: —, mass loss rate (DTG): —, molecule ion curve of water (m/z 18): -●- and molecule ion curve of CO2 (m/z 44): -▼-. Figure 8. pH vs potassium bicarbonate conversion of reaction 2HCO3-

CO32-+ CO2(aq)+H2O

at 25°C. We display pH MatLab solution using Davies activity coefficients for initial bicarbonate concentrations of 1 molal: —, 0.1 molal: ·-·-· and 0.01 molal: --- ; and measured pH values for a 0.1 molal solution: x, and for a 1 molal solution: +.


23


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Figure 9. Equilibrium constant of reaction 2HCO3-

CO3

Page 24 of 43

2-

+ CO2 (aq)+H2O vs potassium

bicarbonate conversion. Figure 10. Boiling point (°C) of potassium bicarbonate solutions vs molality at 725 psig: -♦- and at 580 psig: -●-. Figure 11. Measured values of the pressure generated during experiments using 1M KHCO3 electrolyte heated to 250 ° C: -Δ-,-o-; theoretical steam pressure: -x- and theoretical total pressure:-■- that assumes a rise in pressure due to CO2 produced in the total decomposition of 1M potassium bicarbonate into carbonate and CO2. Figure 12. Equilibrium conversion (%) vs temperature (°C) of 1 molal potassium bicarbonate solution: ♦ and 0.1 molal potassium bicarbonate solution: ▲. Table 1. Model equations Table 2 Bicarbonate and carbonate concentrations, mass percentage composition of the crystals expected and mass percentage composition obtained by TG-MS of two known controls. Table 3. Set of experiments #1. Determination of the effects of different cooling methods. Experimental conditions and final pH and conversion. Table 4 Set of experiments #2. Determination of the time to reach equilibrium at 1.0 molal initial concentration of bicarbonate solution. Experimental conditions and final pH and conversion. All experiments employed a cold water quench. Table 5. Set of experiments #3. Determination of the time to reach equilibrium at 0.1 molal initial concentration of bicarbonate solution. All experiments employed a cold water quench. Table 6 Set of experiments #4. Determination of equilibrium conversion and equilibrium constant. Conditions and results for an initial 1.0 molal solution of potassium bicarbonate exposed to different temperatures and reaction times. All experiments employed a cold water quench.


24

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References (1) Giddey, S.; Badwal, S. P. S.; Kulkarni, A. A Comprehensive Review of Direct Carbon Fuel Cell Technology. Prog. Energy Combust. Sci. 2012, 38, 360-399. (2) Cooper, J. F.; Selman, J. R. Electrochemical oxidation of carbon for electric power generation: a review. ECS Trans. 2009, 19, 15-25. (3) Cooper, J. F.; Selman, J. R. Analysis of the carbon anode in direct carbon anode conversion fuel cells. Int. J. Hydrogen Energy 2012, 37, 1-10. (4) King, J. M.; Reiser, C. A.; Schroll, C. R. Molten-Carbonate Fuel-Cell System Verification and Scale-Up; United Technologies Corp: Palo Alto, CA: 1976. (5) Cherepy, N. J.; Krueger, R.; Fiet, K. J.; Jankowski, A. F.; Cooper, J. F. Direct Conversion of Carbon Fuels in a Molten Carbonate Fuel Cell. J. Electrochem. Soc. 2005, 152, A80-A87. (6) Cooper, J. F., Direct Conversion of Coal Derived Carbon in Fuel Cells. In Recent Trends in Fuel Cell Science and Technology, Babu, S., Ed. Anamaya Publishers: New Delhi, 2006; pp 246264. (7) Jiang, C.; Irvine, J. T. S. Catalysis and oxidation of carbon in a hybrid direct carbon fuel cell. J. Power Sources 2011, 196, 7318-7322. (8) Jiang, C.; Ma, J.; Bonaccorso, A. D.; Irvine, J. T. S. Demonstration of high power, direct conversion of waste-derived carbon in a hybrid direct carbon fuel cell. Energy. Environ. Sci. 2012, 5, 6973-6980. (9) Li, C.; Shi, Y.; Cai, N. Effect of contact type between anode and carbonaceous fuels on direct carbon fuel cell charateristics. J. Power Sources 2011, 196, 4588-4593.


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(10) Desclaux, P.; Nuernberger, S.; Rzepka, M.; Stimming, U. Investigation of direct carbon conversion at the surface of a YSZ electrolyte in a SOFC. Int. J. Hydrogen Energy 2011, 36, 10278-10281. (11) Kulkarni, A.; Giddey, S.; Badwal, S. P. S. Electrochemical performance of ceria gadilinia electrolyte based direct carbon fuel cells. Solid State Ionics 2011, 194, 46-52. (12) Mochidzuki, K.; Soutric, F.; Tadokoro, K.; Antal, M. J. Electrical and physical properties of carbonized charcoals. Ind. Eng, Chem. Res 2003, 42, 5140-5151. (13) Antal, M. J.; Gronli, M. G. The Art, Science, and Technology of Charcoal Production. Ind. Eng. Chem. Res. 2003, 42, 1619-1640. (14) Bourke, J. P.; Manley-Harris, M.; Fushimi, C.; Dowaki, K.; Nunoura, T.; Antal, M. J. Do All Carbonized Charcoals Have the Same Chemical Structure? 2. A Model of the Chemical Structure of Carbonized Charcoal. Ind. Eng. Chem. Res. 2007, 46, 5954-5967. (15) Meszaros, E.; Jakab, E.; Varhegyi, G.; Bourke, J. P.; Manley-Harris, M.; Nunoura, T.; Antal, M. J. Do All Carbonized Charcoals Have the Same Chemical Structure? 1. Implications of Thermogravimetry-Mass Spectrometry Measurements. Ind. Eng. Chem. Res. 2007, 46, 59435953. (16) Varhegyi, G.; Meszaros, E.; Antal, M. J.; Bourke, J. P.; Jakab, E. Combustion Kinetics of Corncob Charcoal and Partially Demineralized Corncob Charcoal in the Kinetic Regime. Ind. Eng. Chem. 2006, 45, 4962. (17) Jacques, W. W. Method of Converting Potential Energy of Carbon into Electrical Energy. U.S.A. Patent, 555,511, March 3, 1896, 1896. (18) Jacques, W. W. Harper's Magazine 1896, 94, 144-150.


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(19) Haber, F.; Bruner, L. Das Kohlenelement, Eine Knalgaskette. Zeit. Elektrochem. 1904, 10, 697-713. (20) Howard, H. C., Direct Generation of Electricity from Coal and Gas (Fuel Cells). In Chemistry of Coal Utilization, Lowry, H. H., Ed. J. Wiley: New York, 1945; Vol. 2, pp 15681585. (21) Antal, M. J.; Nihous, G. C. Thermodynamics of an Aqueous-Alkaline/Carbonate Carbon Fuel Cell. Ind. Eng. Chem. Res. 2008, 47, 2442-2448. (22) Nunoura, T.; Dowaki, K.; Fushimi, C.; Allen, S.; Meszaros, E.; Antal, M. J. Performance of a First-Generation, Aqueous-Alkaline Biocarbon Fuel Cell. Ind. Eng. Chem. Res. 2007, 46, 734744. (23) Liebhafsky, H. A.; Cairns, E. J. Fuel Cells and Fuel Batteries. J. Wiley & Sons: New York, 1968. (24) Bacon, F. T., The High-Pressure Hydrogen-Oxygen Fuel Cell. In Fuel Cells, Young, G. J., Ed. Rheinhold Publishing Co.: New York, 1960; Vol. 1, pp 51-77. (25) Bacon, F. T. Fuel Cells, Past, Present, and Future. Electrochim. Acta 1969, 14, 569-585. (26) Bacon, F. T.; Fry, T. M. The development and practical application of fuel cells. Proc. Roy. Soc. Lond. A. 1973, 334, 427-452. (27) Field, J. H.; Benson, H. E.; Johnson, G. E.; Tosh, J. S.; Forney, A. J. Pilot-Plant Studies of the Hot-Carbonate Process for removing Carbon Dioxide and Hydrogen Sulfide. ; Bulletin 597,U.S. Bureau of Mines, 1962. (28) Millero, F. J. Thermodynamics of the carbon dioxide system in the oceans. Geochim. Cosmochim. Acta 1995, 59, 661-677.


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(29) Stumm, W.; Morgan, J. J. Aquatic Chemistry. 2nd ed.; J. Wiley & Sons: New York, 1981; p 780. (30) Butler, J. N. Carbon dioxide equilibria and their applications. Lewis Publishers Inc.: Chelsea, MA, 1992; p 259. (31) Butler, J. N. Ionic Equilibrium. J. Wiley & Sons: New York, 1998; p 559. (32) Karberg, N. J.; Pregitzer, K. S.; King, J. S.; Friend, A. L.; Wood, J. R. Soil carbon dioxide partial pressure and dissolved inorganic carbonate chemistry under elevated carbon dioxide and ozone. Oceologia 2004, 142, 296-306. (33) Li, D.; Duan, Z. The speciation equilibrium coupling with phase equilibrium in the H2O– CO2–NaCl system from 0 to 250 °C, from 0 to 1000 bar, and from 0 to 5 molality of NaCl. Chem. Geol. 2007, 244 730–751. (34) Bandura, A. V.; Lvov, S. N. The Ionization Constant of Water over Wide Ranges of Temperature and Density. J. Phys. Chem. Ref. Data 2006, 35. (35) Hunter, S. E.; Savage, P. E. Acid-Catalyzed Reactions in Carbon Dioxide-Enriched HighTemperature Water. Ind. Eng. Chem. Res. 2003, 42, 290-294. (36) Pourbaix, M. Lectures on Electrochemical Corrosion. Plenum Publishing Corp.: New YorkLondon, 1973; p 29-59. (37) Ruiz, R.; Ehrman, T. Determination of carbohydrates in Biomass by High Performance Liquid Chromatography; Ethanol Project Laboratory Analytical Procedure #002. National Renewable Energy Laboratory: 1996. (38) Ruiz, R.; Ehrman, T. HPLC Analysis of Liquid Fractions of Process Samples for Organic Acids, Glycerol, HMF and furfural; Ethanol Project Laboratory Analytical Procedure #015. National Renewable Energy Laboratory: 1996.


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(39) Eaton, A. D.; Clescer, L. S.; Greenberg, A. E. Standard Methods for the Examination of Water and Wastewater; American Public Health Association; American Water Works; Water Environment Federation: Hanover, Maryland, 1995. (40) Denbigh, K. The Principles of Chemical Equilibrium. 4 ed.; Cambridge University Press: Cambridge, 1981. (41) Blitz, A. Experimental Analysis Of An Undesirable Crystal Precipitate In A Developmental Carbon Fuel Cell. B.S. Thesis, University of Hawaii at Manoa, Honolulu, 2011. (42) Ulrich Grigull, J. S.; Schiebener, P. Steam Tables in SI-Units Wasserdampftafeln. SpringerVerlag Berlin 1984. (43) King, J. W.; Srinivas, K. Multiple unit processing using sub- and supercritical fluids. J. Supercrit. Fluids 2009, 47, 598-610. (44) King, J. W.; Srinivas, K.; Guevara, O.; Lu, Y. W.; Zhang, D.; Wang, Y. J. Reactive highpressure carbonated water pretreatment prior to enzymatic saccharification of biomass substrates. J. Supercrit. Fluids 2012, 66, 221-231. (45) Teng, H.; Yamasaki, A. Solubility of liquid CO2 in synthetic sea water at temperatures from 278 K to 293 K and pressures from 6.44 MPa to 29.49 MPa, and densities of the corresponding aqueous solutions. J. Chem. Eng. Data 1998, 43, 2-5. (46) Weibe, R.; Gaddy, V. L. The solubility of carbon dioxide in water at various temperatures from 12 to 40o and at pressures to 500 atmospheres. J. Am. Chem. Soc. 1934, 62, 815-817. (47) Sabiryanov, A. N.; Ii'in, A. P.; Akhunov, A. R.; Gumerov, F. M. Solubility of water in supercritical carbon dioxide. High Temp. 2002, 40, 203-206.


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(48) Stewart, P. B.; Munjal, P. Solubility of carbon dioxide in pure water, synthetic sea water, and synthetic sea water concentrates at -5 to 25 oC and 10- to 45-atm Pressure. J. Chem. Eng. Data 1970, 15, 67-71. (49) Tosh, J. S.; Field, J. H.; Benson, H. E.; Haynes, W. P. Equilibrium study of the system potassium carbonate, potassium bicarbonate, carbon dioxide, and water.; U.S. Bureau of Mines 1959. (50) Craig, N. C. Entropy Analysis. Wiley-VCH: New York, 1992; p 208. (51) Barner, H. E.; Scheuerman, R. V. Handbook of Thermochemical Data for Compounds and Aqueous Species. Wiley-Interscience: New York, 1973. (52) Criss, C. M. Thermodynamic Properties of High Temperature Aqueous Solutions. Ph.D. Thesis, Purdue University, Lafayette, Indiana, 1961. (53) Criss, C. M.; Cobble, J. W. The Thermodynamic Properties of High Temperature Aqueous Solutions. IV. Entropies of the Ions up to 200 C and the Correspondence Principle. J. Am. Chem. Soc. 1964, 86, 5385-5390. (54) Criss, C. M.; Cobble, J. W. The Thermodynamic Properties of High Temperature Aqueous Solutions. V. The Calculation of Ionic Heat Capacities up to 200 C. Entropies and Heat Capacities above 200 C. J. Am. Chem. Soc. 1964, 86, 5390-5393. (55) Legarra, M. Study of the Chemistry of the Carbon Fuel Cell Electrolyte at Near Critical Conditions. M.S. Thesis, University of Hawaii at Manoa, Honolulu, 2012. (56) Versteeg, G. F.; van Swaaij, W. P. M. Solubility and Diffusivity of Acid Gases (CO2, N2O) in Aqueous Alkanolamine Solutions. Chem. Eng. Data 1988, 33, 29–34.


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(57) Johnson, J. W.; Oelkers, E. H.; Helgeson, H. C. SUPCRT92: a software package for calculating the standard molal thermodynamic properties of minerals, gases, aqueous species, and reactions from 1 to 5000 bar and 0 to 1000 ° C. Comput. Geosci. 1992, 18, 899-947. (58) Davies, C. W. Ion Association. Butterworths: London, 1962; p 37–53.


31


Figure 1 0

log of concentration ratio

-1 -2 -3 -4 -5 -6

[CO2]/C HCO3 3

-7

[HCO-3]/C HCO3

-8

[H 2CO3]/C HCO3

-9

2

4

6

8

10

12

14

pH

Figure 1. Logarithmic ratios of concentration of carbonate species as a function of pH at 25 °C assuming unity activity coefficients and a group 1 bicarbonate (values of Ka given by Li and Duan equation).

Figure 2 0 [CO2] 3 [H 2CO3]

-2

log C

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 43

Sodium bicarbonate solutions

[HCO-3]

[HCO-3]

-4

[HCO-3] Carbonic acid solutions

-6

Sodium carbonate solutions

-8 0

2

4

6

8

10

12

14

pH

Figure 2. Comparison of our acid–base equilibria model (values of Ka given by Li and Duan equation): o with the Pourbaix model (values of Ka given by Pourbaix): — for carbonic acid, sodium bicarbonate and sodium carbonate solutions.


32

Page 33 of 43

Figure 3 100

100 %H2CO3

%H2CO3 (a)

%HCO-3

80

Mol percentage (%)

80

Mol percentage(%)

%CO23

60

40

20

%HCO-3

(b)

%CO23

60

40

20

0 0.5/0

1/0 1.5/0 [KHCO3]o(molal)

2/0

0 0.5/0.36

1/0.72 1.5/1.09 [KHCO3]o/[K2CO3]o (molal/molal)

2/1.45

Figure 3. Mol percentages of carbonate species (%) vs (a) Initial potassium bicarbonate concentration (molal) and vs (b) mixtures of initial potassium bicarbonate and potassium carbonate concentrations (molal/molal) at 25 °C assuming unity activity coefficients (values of Ka given by Li and Duan equation).

Figure 4 -3

-3

x 10

0.099

1.5

x 10

9

4 3.5

0.098 8.8 0.097

1

pH

2.5

[CO32- ]

3

[HCO3-]

[H2CO3]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


8.6

2 1.5

0.096

8.4

1 0.5

0 100 200 Temperature (ºC)

0.095


0.5


8.2


Figure 4. Equilibrium concentrations of H2CO3, HCO3-, CO32- (molal) and pH vs temperature (°C) for an initial 0.1molal potassium bicarbonate solution assuming unity activity coefficients with values of Ka given by Li and Duan equation: — and by Stumm and Morgan: x.


33


Figure 5 14 13.5 13

pH

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 43

12.5 12 MatLab pH (Davies activity coefficients) MatLab pH (Unity activity coefficients) Experimental pH (experiment 1) Experimental pH (experiment 2)

11.5 11

0

1

2 3 [K2CO3]o (molal)

4

5

Figure 5. pH vs initial potassium carbonate concentration in molality at 25 °C. We display experimental pH values: x, o; as well as pH MatLab solutions using Davies activity coefficients: --- and using unity activity coefficients: — (values of Ka given by Li and Duan equation).


34

Page 35 of 43

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 6

Figure 6. Schematic diagram of the pressure vessel in the sand bath. TC is the thermocouple, TR is the temperature regulator, HSL is the low heater switch, HSM is the medium heater switch, HSH is the high heater switch, HSB is the boost heater switch and AIR is the clean air supply.


35


Figure 7 0.40

100

0.35

90 80

mass loss rate (%/s)

0.30

70

0.25

60

G (%) 0.20

50

DTG (%/s)

0.15

40

m/z: 18

30

m/z: 44

0.10

mass (%)

20

0.05

10

0.00

0 100 200 300 400 500 600 700 800 900 Temperature (°C)

Figure 7. TG/MS analyses of potassium bicarbonate crystals. Potassium bicarbonate mass loss: —, mass loss rate (DTG): —, molecule ion curve of water (m/z 18): -●- and molecule ion curve of CO2 (m/z 44): -▼-. Figure 8 12

11

pH

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 43

10

1M MatLab pH

9

0.1M MatLab pH 0.01M MatLab pH 0.1M experimental pH

8

1M experimental pH

0

20

40 60 Conversion KHCO3

80

100

Figure 8. pH vs potassium bicarbonate conversion of reaction 2HCO3- CO32-+ CO2(aq)+H2O at 25°C. We display pH MatLab solution using Davies activity coefficients for initial


36

Page 37 of 43

bicarbonate concentrations of 1 molal: —, 0.1 molal: ·-·-· and 0.01 molal: --- ; and measured pH values for a 0.1 molal solution: x, and for a 1 molal solution: +. Figure 9 25

20

Keq

15

10

5

0

0

0.2

0.4 0.6 Conversion KHCO3

0.8

Figure 9. Equilibrium constant of reaction 2HCO3bicarbonate conversion.

CO3

2-

+ CO2 (aq)+H2O vs potassium

Figure 10 270 Boiling point (°C)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


265

P=725 psi

260 255

P=580 psi

250 245 0

0.5

1

1.5

2

molality

Figure 10. Boiling point (°C) of potassium bicarbonate solutions vs molality at 725 psig: -♦and at 580 psig: -●-.


37


Figure 11

Figure 11. Measured values of the pressure generated during experiments using 1M KHCO3 electrolyte heated to 250 ° C: -Δ-,-o-; theoretical steam pressure: -x- and theoretical total pressure:-■- that assumes a rise in pressure due to CO2 produced in the total decomposition of 1M potassium bicarbonate into carbonate and CO2.

Figure 12 100.0 80.0 Conversion (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 38 of 43

60.0 40.0

1 molal 0.1 molal

20.0 0.0 150

200

250

300

Temperature (°C)

Figure 12. Equilibrium conversion (%) vs temperature (°C) of 1 molal potassium bicarbonate solution: ♦ and 0.1 molal potassium bicarbonate solution: ▲.


38

Page 39 of 43

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 1. Model equations Description Mass balance on carbon

[ (

]

[ (

]

Equation [ ]

[

[

]

[

[ [

[

[ ]

(

)

(

)

(

)

(

)

] (

)

] )

[ ] [ ] [ (Bicarbonate group 1)

] [

]

)

( ]

)

]

(

[

(

)

Mass balance on cation

Charge balance

] )

]

[ ] [ ] (Bicarbonate group 2) [ ][ [ ( [ ][ [ [ ][

Equilibrium equation of reaction Equilibrium equation of reaction Equilibrium equation of water Ionic strength of a solution of ions with charge

] [

] )] ] ] ]

( ) ( ) ( )

∑[ ]

( ) ()

Activity coefficient of an ion with charge Debye–Hückel theory and Davies equation58 ()

(

)(

)

( )

Dissociation constant of reaction

(

)

Dissociation constant of reaction

(

)

Dissociation constant of water

(

)


39


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 40 of 43

Table 2 Bicarbonate and carbonate concentrations, mass percentage composition of the crystals expected and mass percentage composition obtained by TG-MS of two known controls.

a

Control #

[KHCO3]o/[K2CO3]o /

% KHCO3 /%K2CO3 Expected

% KHCO3 /%K2CO3a Results TG/MS

1

0.1/0

100/0

45.8/54.2

2

0.05/0.05

50/50

35.2/64.8

%K2CO3 calculated by difference.

Table 3. Set of experiments #1. Determination of the effects of different cooling methods. Experimental conditions and final pH and conversion. Temperature

[KHCO3]o

t Cooling method

Results pH pH initial final

Run

(°C)

(molal)

(h)

Conversion (%)

1

300

1

2

Without a fan,1h

8.06

9.73

55.93

2

300

1

2

Fan,5min; T vessel open=100 °C

8.15

9.93

65.36

3

320

1

4

Fan,5min; T vessel open=100 °C

8.25

10.16

76.21

4

320

1

4

cold water; T vessel open=100 °C

8.05

12.42

>100


40

Page 41 of 43

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 4 Set of experiments #2. Determination of the time to reach equilibrium at 1.0 molal initial concentration of bicarbonate solution. Experimental conditions and final pH and conversion. All experiments employed a cold water quench.

Results Run 2

Temperature (°C) 320

t (h) 4

pH initial 8.02

pH final 12.42

Conversion (%) >100

3

320

4

8.1

13.40

>100

4

250

4

8.05

10.01

69.14

5

250

4

8.24

10.06

71.50

6

250

2

10.09

72.91

7

200

2

8.17

9.92

64.89

8

200

4

8.12

10.15

75.74

9

150

2

8.07

9.03

22.91

10

150

4

8.08

9.99

68.19

11

150

8

8.11

9.90

63.95

Table 5. Set of experiments #3. Determination of the time to reach equilibrium at 0.1 molal initial concentration of bicarbonate solution. All experiments employed a cold water quench.

mol % Carbonate

mol % Bicarbonate

4

100

0

100

200

6

88.1

11.9

93.7

3

200

4

64.9

35.1

79

4

200

4

62.2

37.8

76.7

5

180

6

101.15

-1.15

100

6

180

4

47.5

52.5

64.4

7

150

8

119

-19

100

8

150

4

46.4

53.6

63.4

9

150

4

47.2

52.8

64.15

Run

Temperature (°C)

t (h)

1

250

2


Conversion (%)

41


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 42 of 43

Table 6 Set of experiments #4. Determination of equilibrium conversion and equilibrium constant. Conditions and results for an initial 1.0 molal solution of potassium bicarbonate exposed to different temperatures and reaction times. All experiments employed a cold water quench.

mol % Carbonate

mol % Bicarbonate

4

100

280

4

3

250

4

200

5

Run

Temperature (°C)

t (h)

Conversion (%)

Keq

1

320

0

100

∞

2

93.2

6.8

96.5

190.0

4

64.15

35.85

78.1

3.2

4

69.45

30.55

81.95

5.2

200

4

48.1

51.9

64.95

0.86

6

200

4

54.5

45.5

70.55

1.4

7

180

4

35.1

64.9

52

0.29

8

150

8

14.5

85.5

25.3

0.03

9

150

4

26.8

73.2

42.3

0.13


42

Page 43 of 43

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“For Table of Contents Only”


43

Carbonate Ionic Equilibria at

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