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Ind. Eng. Chem. Res. 2008, 47, 2442-2448
RESEARCH NOTES Thermodynamics of an Aqueous-Alkaline/Carbonate Carbon Fuel Cell Michael Jerry Antal, Jr.* and Ge´ rard C. Nihous Hawaii Natural Energy Institute, School of Ocean and Earth Science and Technology, UniVersity of Hawaii at Manoa, Honolulu, Hawaii 96822
Thermodynamics permits the carbon fuel cell, which generates electrical power via the electrochemical combustion of its carbon fuel, to realize a theoretical efficiency of 100%. A recent paper [Nunoura et al. Ind. Eng. Chem. Res. 2007, 46, 734-744] reported promising results that were obtained from a moderatetemperature, aqueous-alkaline biocarbon fuel cell. In view of the fact that aqueous-alkaline hydrogen fuel cells have been used to power an Austin car and a commercial Black Cab in London, these recent results suggest the potential use of aqueous-alkaline carbon fuel cells for vehicular transportation. Usually, the practicality of an aqueous-alkaline carbon fuel cell is discounted, because the carbon dioxide product of carbon oxidation reacts with and consumes hydroxyl ions in the aqueous-alkaline electrolyte, thereby forming carbonate ions. As a result of this reaction, the performance of an aqueous-alkaline carbon fuel cell is expected to deteriorate over time. Contrary to this expectation, in this paper, we show that the aqueous-carbonate ion can be as effective as the hydroxyl ion as a charge carrier when the temperature of the cell approaches 300 °C. Thermodynamic estimates of the Gibbs free energy of formation (∆fG°) of the aqueous-carbonate ion indicate that the change in Gibbs free energy of the relevant anodic carbon oxidation reaction by carbonate ion equals that of carbon oxidation by hydroxyl ion at temperatures that approach 300 °C. Also, consideration of the temperature dependence of the standard hydrogen electrode reveals that aqueous-hydroxyl ion production on the cathode should be favored at temperatures as high as 300 °C. These findings are a cause for optimism, concerning the performance of an aqueous alkaline/carbonate biocarbon fuel cell designed to operate at 300 °C, and they should encourage further work at temperatures that approach 300 °C. Introduction The reaction enthalpy (∆rH°) of carbon combustion (C + O2 ) CO2) is -393.5 kJ/mol, and the Gibbs free energy of reaction (∆rG°) for this reaction is -394.4 kJ/mol with the reactants and products in their standard states at 298.15 K; consequently, the theoretical thermodynamic efficiency for a fuel cell that “burns” carbon is1,2
ηth )
∆rG° ) 100% ∆rH°
This surprising result is an outcome of the negligible value of the change in entropy ∆rS° (∆rS° ) 2.86 J/(K mol)) for the reaction at normal temperature and pressure (NTP; 298.15 K, 0.1 MPa). Because ∆rS° is so small, the limiting thermodynamic efficiency of a carbon fuel cell is not significantly affected by increasing temperature. Similarly, the standard potential (i.e., theoretical open circuit voltage) of the carbon fuel cell: E° ) -∆rG°/(nF) (where n is the number of electrons involved in the half-cell reactions and F is the Faraday constant) is virtually independent of temperature (e.g., E° ) 1.02 V at 298 K, E° ) 1.02 V at 600 K, and E° ) 1.02 V at 1100 K). Furthermore, both the carbon fuel and the product gas exist as pure substances in separate phases; consequently, their free energies are independent of the extent of conversion. Hence, it is possible to completely convert the carbon in a single pass through the cell. The overall efficiency of a carbon fuel cell is
η ) ηth × ηV × ηI
where ηth is the thermodynamic efficiency (as previously defined); ηV is the voltage efficiency (ηV ) Vact/Vth, where Vact is the actual voltage delivered by the cell in operation and Vth is the thermodynamic potential or open circuit voltage (OCV) value, including the Nernst correction, which accounts for the actual conditions within the cell); and ηI is the current efficiency, which represents the ratio of the actual current generated by the cell to its theoretical value based on the assumed electrochemical combustion chemistry.2 For example, in the case of the carbon fuel cell, the consumption of one mole of carbon should release 4 mol of electrons as current (see below). The release of fewer electrons as current is a signal of a loss of fuel to parasitic reactions. Thus, ηI is a representation of the efficiency of fuel utilization. A recent EPRI study3 indicates that carbon fuel cells have the potential to convert coal or charcoal to electrical power at an overall system level efficiency of ∼60%, which is more than 20% higher than the efficiencies realized by current state-of-the-art integrated gasification combined cycle or advanced pulverized coal power generation systems. Almost all carbon fuel cell researchers have emphasized consumable anodes1,2,4 made of fossil carbons with a variety of electrolytes as the charge carrier. Early workers emphasized aqueous-alkaline,16-19 molten potassium hydroxide,4-11 solid zirconia stabilized with magnesia or yttria,12,13 and molten lead14,15 electrolytes; however, the focus of current work is the molten carbonate carbon fuel cell.16-21 For example, Cooper and his co-workers20,21 at the Lawrence Livermore National Laboratory (LLNL) described the performance of a molten
10.1021/ie070819m CCC: $40.75 © 2008 American Chemical Society Published on Web 02/28/2008
Ind. Eng. Chem. Res., Vol. 47, No. 7, 2008 2443
carbonate carbon fuel cell that used nine different carbons and a porous nickel cathode. Operating at 800 °C, their cell delivered 50-125 mA/cm2 at 0.8 V. Provocatively, the LLNL researchers20 noted that their highest discharge rates (100-125 mA/ cm2 at 0.8 V) were obtained with biocarbon (peach pit and coconut shell activated carbon) anodes. Very large quantities of lignocellulosic residues (e.g., corncobs, coconut shells, and other biomass) accompany the production of bioethanol and biodiesel fuels. These residues can be quickly converted to biocarbons with yields that approach the theoretical limit set by thermodynamics.22-28 When biocarbon is produced efficiently from biomass that is harvested in a sustainable way, the electrochemical combustion of biocarbon in a fuel cell does not add to the CO2 burden of the atmosphere; consequently, it does not contribute to climate change. Thus, biocarbons can be a sustainable, environmentally friendly fuel for carbon fuel cell applications, whose production complements the production of bioethanol and biodiesel fuels in a biomass refinery. Our interest in the aqueous-alkaline biocarbon fuel cell is stimulated by the fact that aqueous-alkaline hydrogen fuel cells have been used to power an Austin car and a commercial London Black Cab.29-31 Thus, the development of a functional aqueous-alkaline carbon fuel cell could facilitate the replacement of non-renewable, liquid hydrocarbon transportation fuels by renewable, solid biocarbons. In a recent paper, Nunoura et al.32 detailed the performance of a moderate-temperature, aqueousalkaline biocarbon fuel cell. Operating at 245 °C and 35.8 bar with 0.5 g of corncob charcoal, this cell realized an open circuit voltage (OCV) of 0.57 V and a short circuit current density of 43.6 mA/cm2. The OCV was significantly less than the expected 1 V. A comparison of temperature-programmed desorption (TPD) data for the oxidized anode biocarbon with prior work indicated that the temperature of the anode was too low: carbon oxides accumulated on the biocarbon without the steady release of CO2 and active sites needed to sustain combustion.32 For this reason, our current work emphasizes the development of an aqueous-alkaline carbon fuel cell that will operate at temperatures approaching 300 °C. Much evidence exists to support our hypothesis that the biocarbon anode will sustain steady electrochemical combustion at temperatures approaching 300 °C.32-35 Unfortunately, the aqueous-alkaline carbon fuel cell has an Achilles’ heal. The exposure of the alkaline electrolyte to CO2 results in the consumption of hydroxyl ion and the formation of carbonate ion. The Bacon fuel cells used on the Apollo missions employed pure oxygen to ensure that the electrolyte was not compromised by the formation of carbonate ions.36-38 Of course, the electrolyte can be regenerated,29 but this additional step is viewed to be costly and complicated.38 Given the carbonate problem, it is not surprising that aqueous-alkaline carbon fuel cells have received little attention, because the loss of electrolyte would be greatly exacerbated by the evolution of CO2 at the anode of the carbon fuel cell. Liebhafsky and Cairns2 give special emphasis to “the problem of an invariant electrolyte” in their discussion of problems associated with the development of carbon fuel cells. The chief focus of this article is a thermodynamic inquiry into the effects of carbonate formation on the performance of a carbon fuel cell that operates with anode temperatures approaching 300 °C. We show that, under these conditions, the formation of carbonate ion should have no detrimental effect on the performance of the cell and may actually augment its power density.
Table 1. Aqueous-Alkaline/Carbonate Carbon Fuel Cell Reactions and Thermodynamic Data at 298.15 K with E°, Relative to the Standard Hydrogen Electrodea No.
reaction
1 2 3 4 5
C + 4OH- ) CO2(g) + 2H2O + 4eO2(g) + 2H2O + 4e- ) 4 OHC + O2(g) ) CO2(g) CO2(g) + 2OH- ) H2O + CO32C + 2CO32- ) 3CO2(g) + 4ea
E° [V]
∆rG° [kJ/mol]
∆rH° [kJ/mol]
0.621 0.401 1.02
-240. -155. -394.4 -56.3 -127.
-45.2 -348. -393.5 -110. 174.
0.329
Data taken from refs 39-43 and ref 45.
Aqueous-Alkaline/Carbonate Carbon Fuel-Cell Thermodynamics The aqueous-alkaline anode half-cell reaction is reaction 1 in Table 1, and the cathode half-cell reaction (identical to that used in Bacon’s hydrogen fuel cell) is reaction 2. The overall reaction is given as reaction 3. Considering the large negative values of ∆rG° for these reactions, it is clear that the equilibrium strongly favors their products at NTP. However, note that the cathode reaction is strongly exothermic. Consequently, the reduction of oxygen on the cathode is not favored by increasing temperature (LeChatelier’s Principle). The standard reference state (designated by the symbol “°”) of an element is the state that is thermodynamically stable at the given temperature and a fugacity (i.e., pressure) of 1 bar. For a pure gaseous substance, the standard state is the hypothetical ideal gas at the given temperature and a pressure of 1 bar. For a pure liquid substance, the standard state is that of the pure liquid at the given temperature under a pressure of 1 bar, whereas, for a pure solid substance, the standard state is that of the pure crystalline substance at the given temperature under a pressure of 1 bar. The standard state of a solute in water is the hypothetical ideal solution with a molality of 1.0 at the given temperature.39 Because all the gaseous and the liquid reactants and products of the aqueous-alkaline carbon fuel cell are far from their standard states, the reader may question the utility of the standard voltage (E°) as a representation of the expected OCV of a practical carbon fuel cell. The Nernst equation accounts for the effects of non-standard-state conditions on the expected potential E for each of the half-cells that comprise the carbon fuel cell. For example, the Nernst equation for the aqueousalkaline biocarbon fuel cell cathode is
E ) E° -
()( ) aOH-4 RT ln nF aH2O2fO2
where R is the universal gas constant, T the temperature, aOHthe activity of the aqueous OH- ion, aH2O the activity of water, and fO2 the fugacity of oxygen in the cell at the pressure and temperature of interest. In the case of the carbon fuel cell, it has been known for more than a half century that the Nernst correction to the standard potential is small.4 For example, Nunoura et al.32 estimated the Nernst correction for the cathode of -0.025 V with a standard potential of -0.043 V (relative to a standard hydrogen electrode; see below) operating at 500 K and 28.6 bar total pressure. In this case, the Nernst correction is significant relative to the magnitude of the standard potential of the cathode, but it is small relative to the overall standard potential of the carbon fuel cell (i.e., 1 V). The paucity of thermodynamic data for ions in hydrothermal solutions may explain why Bacon offered no discussion36-38 of the temperature dependence of the equilibrium constants for
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work of Criss41 and that of Criss and Cobble.42,43 Finally, we remark that the data of Barner and Scheuerman also enjoys good agreement with values calculated by the SUPCRT92 software of Johnson et al.46 and by the Geoscience Australia thermodynamic calculator of Bastrakov et al.47 It is well-known that the potential of a single half-cell reaction cannot be measured: only the potential of a half-cell relative to another half-cell can be measured. In most cases, the reference half-cell is the standard hydrogen electrode (SHE):
H+ + e- ) 0.5H2 For this reaction, we have
E°SHE ) Figure 1. Values of the Gibbs free energy of formation (∆fG°) of aqueous ions CO32- and OH-, as a function of temperature (0, 9) calculated using Geoscience Australia data,47 (], [) calculated using SUPCRT92,46 and (O, b) as tabulated by Barner and Scheuerman.40 Also shown is data for (2) OH-, as calculated from measurements of the ion constant Kw of water,32,44 and for (4) CO32-, as calculated using the methodology of Criss41 and Criss and Cobble.42,43
the two aqueous-alkaline half-cell reactions that were responsible for power production by his cell. The values of these equilibrium constants establish limits for the operation of the fuel cell and are particularly relevant to the design of an aqueous-alkaline biocarbon fuel cell. In their handbook, Barner and Scheuerman40 used the “entropy correspondence principle” of Criss,41 and that of Criss and Cobble,42,43 to estimate the thermodynamicproperties of many ions in hydrothermal solutions. Criss,41 as well as Criss and Cobble,42,43 observed that the “absolute” entropies of many aqueous ions at elevated temperatures could be correlated with their “absolute” entropies at 25 °C, provided that the entropy of H+ (aq) could be assigned a temperaturedependent, nonzero “absolute” reference value. Having established an approximate value via this correlation for the “absolute” entropy of an ion at an elevated temperature, Criss,41 and Criss and Cobble,42,43 used a thermodynamic relationship to estimate the ion’s average partial molal heat capacity over the temperature range. Barner and Scheuerman40 used these values of the ion’s average partial molal heat capacity over specific temperature ranges, together with the thermodynamic relationship representing the change in Gibbs free energy when the ion is formed from its elements, to estimate the Gibbs free energy of formation of the ion in hydrothermal solutions at specific elevated temperatures. The keystones of these estimates were the assumptions that ∆fH°H+ ) ∆fG°H+ ) 0 at all temperatures, combined with the conventional assumptions that ∆fH° and ∆fG° of all elements (except sulfur and phosphorus) are zero at all temperatures.40 To gain confidence in the tabulated data of Barner and Scheuerman,40 and to ensure that their data is compatible with that of NIST-JANAF,39 we compared values of ∆fG° taken from Barner and Scheuerman for the hydroxyl ion OH- with values deduced from accepted measurements of the equilibrium constant Kw for water at elevated temperatures32,44 (see Figure 1). The agreement of these values is quite satisfying. Figure 1 also compares values of ∆fG° taken from Barner and Scheuerman for the carbonate ion CO32- with values that we calculated independently, using the original work of Criss,41 Criss and Cobble,42,43 Laidler,45 and Excel spreadsheets. The agreement of these values shows that, in their handbook, Barner and Scheuerman40 offered a faithful representation of the original
- (∆rG°SHE) nF
and
∆fG°SHE ) 0.5∆fG°H2 - ∆fG°H+ - ∆fG°eConsider the anode reaction 1 displayed in Table 1. The potential E°A-SHE associated with this anode half-cell, relative to SHE, is given by
E°A-SHE )
- (∆rG°anode + 4∆rG°SHE) nF
) - (∆fG°CO2 + 2∆fG°H2O + 2∆fG°H2 - ∆fG°C 4∆fG°OH- - 4∆fG°H+)/(nF) Similarly, the potential E°SHE-C (that associated with the cathode half-cell (i.e., reaction 2 in Table 1), relative to SHE, where, in this case, SHE behaves as an anode and the SHE reaction proceeds to the left) is given by
E°SHE-C ) )
- (∆rG°cathode - 4∆rG°SHE) nF
- (4∆fG°H+ + 4∆fG°OH- - ∆fG°O2 - 2∆fG°H2O - 2∆fG°H2) nF
Finally, the potential E°overall associated with reaction 3 in Table 1 is given by
E°overall ) E°A-SHE + E°SHE-C ) )
-(∆rG°anode + 4∆rG°SHE) (∆rG°cathode - 4∆rG°SHE) nF nF -(∆fG°CO2 - ∆fG°C - ∆fG°O2) nF
We may now employ the baseline assumptions ∆fG°C ) ∆fG°O2 ) ∆fG°H2 ) ∆fG°H+ ) 0 at all temperatures to simplify the aforementioned equations. For the anode half-cell potential, relative to SHE, we have
E°A-SHE )
-(∆fG°CO2 + 2∆fG°H2O - 4∆fG°OH-) nF
and for the cathode half-cell potential, relative to SHE, we have
E°SHE-C )
-(4∆fG°OH- - 2∆fG°H2O) nF
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Values of E°SHE-C, as a function of temperature, calculated using the data of Barner and Scheuerman,40 were displayed in Figure 1 of Nunoura et al.32 Finally, the overall potential of the cell is given by
E°overall )
E°SHE,298-SHE,T ) -
) - (∆fG°H+,298+ ∆fG°e-,298 - 0.5∆fG°H2,298 + 0.5∆fG°H2,T - ∆fG°H+,T - ∆fG°e-,T)/(nF)
-∆fG°CO2 nF
)
as expected. The equilibrium constant of a chemical reaction is an important measure of the influence of temperature on the consumption of reactants and the production of products by the reaction. Fuel scientists often use the “turning temperature” of a chemical reaction, which is the temperature at which the reaction’s equilibrium constant is unity, to determine if the reaction will proceed to the right as written. In the case of exothermic reactions (such as reactions 1, 2, and 3 in Table 1), temperatures below the turning temperature favor the formation of products, whereas temperatures above the turning temperature favor the formation of reactants (i.e., LeChatelier’s Principle). Thus, thermodynamics permits the effective consumption of reactants on the anode and cathode of the carbon fuel cell when their temperatures are less than their respective turning temperatures. The equilibrium constant of a chemical reaction is given by
Keq ) exp
(
(-∆rG°SHE,298 + ∆rG°SHE,T) nF
)
- ∆rG° RT
Consequently, the turning temperature is the temperature at which ∆rG° ) 0. For the anode (reaction 1 displayed in Table 1), we have
∆rG°anode ) ∆fG°CO2 + 2∆fG°H2O + 4∆fG°e- ∆fG°C - 4∆fG°OHSimilarly, for the cathode (reaction 2 displayed in Table 1), we have
∆rG°cathode ) 4∆fG°OH- - ∆fG°O2 - 2∆fG°H2O - 4∆fG°eBoth of these expressions contain ∆fG°e-. Consequently, we must know the values of ∆fG°e-, as a function of temperature, to estimate the turning temperatures of the anode and cathode of the carbon fuel cell. Recall that the following definitions are the baseline for all electrochemical studies: ∆fG°H2 ) ∆fG°H+ ) 0 at all temperatures, and ∆fG°e- ) 0 at 298.15 K. Given the negligible mass of the electron, it is tempting to define ∆fG°e- ) 0 at all temperatures, in which case ∆fG°SHE ) 0 at all temperatures. Nunoura et al.32 applied the assumption of ∆fG°e- ) 0 in their evaluation of the temperature dependence of the equilibrium constant of reaction 2. The outcome of this assumption was an estimated turning temperature of ∼230 °C for the cathode reaction. This result caused Nunoura et al.32 to emphasize temperatures of
