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Principle of hydrogen production by electrocatalytic oxidation of organic compounds in a proton exchange membrane electrolysis cell
CHAPTER TWO
Principle of hydrogen production by electrocatalytic oxidation of organic compounds in a proton exchange membrane electrolysis cell Contents 2.1 Thermodynamic considerations 2.2 Kinetics limitations 2.3 Analysis of the cell voltage versus current characteristics 2.4 Estimation of the energy efficiency References
9 12 15 18 20
The electrochemical decomposition of an organic compound, CxHyOz, for producing clean hydrogen can be performed in a proton exchange membrane electrolysis cell (PEMEC) of configuration similar to that of a water electrolysis cell (Fig. 2.1). In the case of water electrolysis, the anodic compartment of the electrochemical cell is fed with water, under liquid or gaseous state, which is oxidized leading to the production of oxygen and protons, according to reaction (2.1): H2 O-1/2 O2 1 2 H1 1 2 e2
anodic reaction
(2.1)
Oxygen evolves in the gaseous phase, whereas the electrons circulate in the external circuit and protons cross-over the membrane, reaching the cathodic compartment where they are reduced by the electrons coming from the external circuit, thus producing hydrogen, as follows: 2 H1 1 2 e2 -H2
cathodic reaction
(2.2)
The electrical balance between reactions (2.1) and (2.2) corresponds to the electrochemical splitting of water into hydrogen and oxygen according to the overall reaction: Production of Clean Hydrogen by Electrochemical Reforming of Oxygenated Organic Compounds. DOI: https://doi.org/10.1016/B978-0-12-821500-5.00002-3
© 2020 Elsevier Inc. All rights reserved.
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8
Production of Clean Hydrogen
Figure 2.1 Principle of the electrochemical decomposition, in a proton exchange membrane electrolysis cell, of (A) water and (B) an organic compound CxHyOz.
H2 O-H2 1 1/2 O2
overall reaction
(2.3)
with the following data under standard conditions (T 5 25 C, p 5 1 bar, liquid water): ΔH 0 51 285:8 kJðmole H2 OÞ21 and ΔG 0 51 237:2 kJðmole H2 OÞ21 These electrochemical processes are exactly the reverse of those occurring in a fuel cell with an acid electrolyte, for example, phosphoric acid, or a proton exchange membrane (PEM). For a PEM device, such as an electrolyzer or a fuel cell, the electrocatalysts at the negative electrode for the hydrogen evolution reaction (HER) or hydrogen oxidation reaction (HOR) are similar, that is, Pt/C nanoparticles, since the HER/HOR is a quasi-reversible reaction. Conversely, the electrocatalysts at the positive electrode are different, that is, Pt-based nanoparticles dispersed on the large surface area carbon powder, for example, Vulcan XC72R, for the oxygen reduction reaction (ORR) and Ir-based oxides dispersed on a corrosion-proof support, for example, a Ti mesh or foam, for the oxygen evolution reaction (OER). In the case of an organic compound, CxHyOz, its complete electro-oxidation in the anodic compartment of the electrolysis cell is realized with a suitable electrocatalyst, which is specific for the
Principle of hydrogen production by electrocatalytic oxidation of organic compounds
9
considered compound, leading to carbon dioxide and protons, according to reaction (2.4): Cx Hy Oz 1 ð2x 2 zÞH2 O-x CO2 1 nðH1 1 e2 Þ
anodic reaction (2.4)
where n 5 4x 1 y 2 2z is the number of exchanged electrons. Then the protons produced cross-over the PEM and are reduced to molecular hydrogen by a convenient catalyst in the cathodic compartment by the electrons coming from the external circuit according to reaction (2.5): nðH1 1 e2 Þ-ðn=2ÞH2
cathodic reaction
(2.5)
The electrical balance between reactions (2.4) and (2.5) leads to the following overall reaction: Cx Hy Oz 1 ð2 x 2 zÞH2 O-x CO2 1 ðn=2ÞH2
overall reaction
(2.6)
Reaction (2.6) corresponds to the electrochemical reforming of CxHyOz producing hydrogen and carbon dioxide by its complete oxidation. The electrochemical decomposition of CxHyOz, according to the overall reaction (2.6), is thus similar to a steam reforming process, but this reaction can occur at relatively low temperatures (25 C 2 85 C) instead of the high temperatures (600 C 2 800 C) encountered in steam reforming [15].
2.1 Thermodynamic considerations Knowing the thermodynamic data of the formation of H2O, CO2, and CxHyOz under standard conditions, usually the liquid state at 25 C, that is, ΔHf0 and ΔGf0 , one may calculate the thermodynamic data ΔH1 and ΔG1 associated with reaction (2.4) or (2.6) under standard conditions: 0 ΔH 1 5 xΔHCO 2 ð2x 2 zÞΔHH0 2 O 2 ΔHf0 2 0 0 ΔG1 5 xΔGCO 2 ð2x 2 zÞΔGH 2 ΔGf0 2 2O
Since most of the electroreactive organic compounds can be used as fuels in a direct oxidation fuel cell (DOFC), the thermodynamic data of
10
Production of Clean Hydrogen
their complete oxidation corresponding to the overall reaction in the fuel cell device, that is, Cx Hy Oz 1 ðx 1 y=4 2 z=2ÞO2 -x CO2 1 y=2 H2 O overall reaction (2.7) 0 can be estimated from the combustion data of the compounds, ΔHFC and 0 ΔGFC , in the fuel cell. Thus, the thermodynamic data of the electrochemical reforming reaction can be related to those of the combustion reaction of H2 and CxHyOz as follows: ΔH 1 5 ΔHC0 x Hy Oz ;FC 2 n=2 ΔHH0 2 ;FC 0 ΔG1 5 ΔGC0 x Hy Oz ;FC 2 n=2 ΔGH 2 ;FC
For low-weight organic compounds, the knowledge of their thermodynamic data of formation allowed us to calculate Δh1 5 ΔH1/(2x 1 y/ 2 2 z) corresponding to the total external energy needed to produce one mole of hydrogen and Ea1 5 ΔG1 =ðð4x 1 y 2 2zÞFÞ, the minimum anode potential necessary to decompose the organic compound through its electrocatalytic oxidation. Since the cathode potential Ec2 associated with the HER (2.2) or (2.5) is close to 0 V versus the standard hydrogen electrode (SHE), using the Pt/C electrode in contact with the hydrogen contained in the cathodic compartment as a reference electrode, the minimum cell voltage to be applied to the electrolysis cell to decompose the organic compound will be given as follows: 0 Ucell 5 Ea1 2 Ec2 Ea1
For many organic compounds, this theoretical cell voltage (Table 2.1) is very small compared with that of the electrolytic decomposition of 0 water, that is, Ucell 1:23 V under standard conditions, so that the 0 theoretical electrical energy, proportional to Ucell , to be provided by the external power source, to produce one hydrogen mole by the electrooxidation of CxHyOz, is much smaller than that used in water electrolysis. Table 2.1 gives the values of the thermodynamic data under standard conditions calculated for the electrocatalytic oxidation of water and of several organic compounds with one to six carbon atoms. Table 2.1 shows clearly that for most of these organic compounds, the theoretical total energy Δh10 necessary to produce one mole of hydrogen by their electrochemical dissociation under standard conditions is at least
Table 2.1 Standard thermodynamic data, cell voltage, and number of hydrogen moles, NH2 , produced by the electrochemical reforming of different hydrogen containing compounds. 0 Compound NH2 =mole ΔH10/kJ mol21 Δh10/kJ mol H21 ΔG10 /kJ mol21 Ucell Ea1 51 ΔG10 =nF (V vs SHE) 2
H2O 1 HCOOH 1 3 CH3OH 6 C2H5OH 5 CH2OH-CH2OH 9 1-C3H7OH 8 DMMCH2(OCH3)2 CH2OH-CHOH-CH2OH 7 12 1-C4H9OH Glucose 12
1 286 1 32 1 131.2 1 348 1 240 1 545 1 340.6 1 350 1 754 627.1
1 286 1 32 1 44 1 58 1 48 1 61 1 42.6 1 50 1 63 1 52.3
1 237 2 33 1 9.3 1 97.3 1 17.2 1 170 2 5.6 21 1 205 2 27.4
1.23 2 0.17 0.016 0.084 0.018 0.098 2 0.004 2 0.001 0.177 2 0.012
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Production of Clean Hydrogen
five times lower than that for water electrolysis. Moreover, the theoretical electrical energy, which is proportional to the cell voltage—see Eq. (2.11) in Section 2.2—is at least several times lower than that for water dissociation, or even negative, for example, for HCOOH dissociation, which means that it is a spontaneous electrochemical process although the total energy ΔH10 is positive due to a larger positive reversible heat transfer TΔS associated with the entropy change.
2.2 Kinetics limitations However, the kinetics of the anodic reactions involved in both processes, that is, water oxidation in the water electrolysis process or the electrocatalytic oxidation of organic compounds in the electrochemical reforming process, is relatively slow leading to high anodic overpotentials and thus to higher cell voltages at the relatively high current density, over 1 A cm22, required for a high hydrogen production rate (Fig. 2.2).
Figure 2.2 Theoretical electrical characteristics j(E) for a reaction kinetics controlled by the Butler 2 Volmer law: CxHyOz oxidation, H2O oxidation, O2 reduction, and proton reduction. UCx Hy Oz ; UH2 O ; UDOFC ; and UH2 FC are the cell voltages for CxHyOz electrolysis, water electrolysis, direct oxidation fuel cell, and hydrogen/oxygen fuel cell at a given current density j, for example, 1 A cm22.
Principle of hydrogen production by electrocatalytic oxidation of organic compounds
13
This figure gives the current density j 5 I/S 5 nFv/S 5 nFvi, where I is the current intensity, S is the electrode surface area, v and vi are the reaction rate and the intrinsic rate, respectively, as a function of the electrode potential Ei( j) versus the SHE taken as reference, for the different electrochemical processes involved: • HOR and HER, which are described by a quasi-linear plot, assume that the hydrogen exchange current density joc (of the order of 1023 A cm22) is at least 103 times greater than the exchange current density joa of the anodic processes. These processes are associated, either to the electrocatalytic oxidation of the organic compound or to the OER in water electrolysis, with joa 1026 A cm22 , whereas the ORR has joc 1026 A cm22 . • In these latter cases, the current density j versus Ei(j) curves are exponential functions when assuming no mass transfer limitation according to the Butler 2 Volmer law: jðηÞ 5 jo ½expfα nF=RT ηg expf 2 ð1 2 αÞðnF=RT Þηg (2.8) where η 5 Ei 2 Eeq is the overpotential, jo is the exchange current density, and α is the anodic transfer coefficient. • For irreversible reactions such as the OER/ORR or the electrochemical oxidation of an organic compound, we can neglect the opposite reaction, and the j(E) characteristics become an exponential function, as plotted in Fig. 2.2, that is: j(η) 5 jo exp{α(nF/RT)η} for the oxidation of an organic compound or water in water electrolysis and jðηÞ 5 jo expf 2 ð1 2 aÞðnF=RT Þηg for the ORR When taking into account the charge transfer overpotentials ηact, the concentration overpotentials ηconc and the ohmic drop Re j associated with the cell resistance Re, the cell voltage versus current density curves, Ucell( j), of an electrolysis cell, can be expressed as follows: Ucell ð jÞ 5 Ea1 ð jÞ Ec2 ð jÞ 1 Re j 5 Ucell ð0Þ 1 ðjηact a ðj Þj (2.9) act conc conc 1 ηa ð jÞj 1 jηc ð jÞj 1 jηc ð jÞjÞ 1 Re j where Ucell(0) 5 Eeq is the equilibrium cell voltage, that is, the cell voltage at zero current, ηi is the overpotential defined as the deviation of the electrode potential Ei( j) under working conditions from its equilibrium value,
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Production of Clean Hydrogen
that is, ηi 5 Ei( j) Eieq(0), and the subscripts “a” and “c” refer to the anodic and cathodic reactions, respectively. For an electrochemical reaction not limited by mass transfer, that is, the corresponding concentration overpotentials ηconc-0, and assuming a high exchange current density j0c for HER, equation (2.9) can be expressed as follows: RT j RT j j 1 Ucell ð jÞ 5 Ucell ð0Þ 1 1 R ln e nF j0c αnF j0a (2.10) RT j ln 5 Ucell ð0Þ 1 Rexp j 1 αnF j0a so that Ucell( j) 2 Ucell(0) 2 Rexp | j| can be plotted as a logarithmic function of the current density j, where Rexp 5 Re 1 RT/(nFjoc) is the total contribution of the cell resistance, Re, and the hydrogen transfer resistance Rt 5 RT/(nFjoc) to the linear part of the semi-logarithmic plot [6]. A specific software developed in our laboratory allowed us to estimate the unknown Rexp. At a given current density, for example, j 5 1 A cm22 as in Fig. 2.2, the measured cell voltage, Ucell( j), corrected from the ohmic losses Rexp j, allows to evaluate the electrical energy consumed to produce 1 Nm3 of hydrogen, which is directly proportional to Ucell( j), according to equation (2.11) [7]: We in kWh=Nm3 5
nF ~ Ucell ð jÞ 2:191Ucell ð jÞ 2:2 Ucell ð jÞ 3600Vm 3 103 (2.11)
where ñ 5 2 is the number of Faraday per mole of hydrogen produced and Vm 5 24.465 1023 m3 mol21 is the molar volume of an ideal gas at a temperature of 25 C under a pressure of 1 atm., that is, 101.325 kPa, corresponding to normal conditions for gaseous species. Equation (2.11) shows that the electrical energy consumed to produce molecular hydrogen by the electro-oxidation of an organic compound is directly proportional to Ucell( j), which must be as small as possible to decrease significantly the energy consumed, for example, below 1.0 kWh (Nm3)21 for Ucell( j) # 0.45 V. In contrast, the rate of hydrogen produced can be evaluated by measuring the volume of evolved hydrogen, VH2, which is a linear function of time for several fixed current intensities I during the electrolysis of the
Principle of hydrogen production by electrocatalytic oxidation of organic compounds
15
organic compound. The volume of evolved hydrogen, at a given electrolysis time Δt, depends only on the current intensity I, since it is a linear function of the quantity of electricity involved Δq 5 I Δt. The linear function can be derived from Faraday’s law, equation (2.12a) or (2.12b), giving the rate of hydrogen evolution [7]: dVH2 =dt 5 Vmol ðdNH2 =dtÞ 5 Vmol I=˜n F (2.12a) dVH2 =dt 5 Vmol ðI=2FÞ 3 60 5 7:607 Iðin cm3 min21 Þ
(2.12b)
where NH2 is the number of hydrogen mole, F 5 96,485 C per mole of electron is the Faraday constant, I is the current intensity in Ampere, and ñ 5 2 is the average number of Faraday per mole of dihydrogen produced in the complete oxidation reaction of an organic molecule according to reaction (2.4) or (2.6). The volume of hydrogen produced after Δt 5 15 min of electrolysis at a given temperature, when a quasi-stationary state is reached, can be obtained by integration of equation (2.12a), that is: VH2 5 Vmol ðI Δt=2FÞ 5 24:465 1023 Ið60 3 15Þ=ð2 3 96485Þ 5 114:1 3 Iðin cm3 Þ
at 25 C
or VH2 5 119:8 3 I cm3 at 40 C and
VH2 5 131:3 3 I cm3
(2.13a) at 70 C (2.13b)
when taking into account the hydrogen molar volume at 40 C or 70 C, corresponding to the dilatation of an ideal gas. This confirms that VH2 is proportional to the current intensity I leading to linear plots VH2 ðIÞ.
2.3 Analysis of the cell voltage versus current characteristics When analyzing the cell voltage, Ucell( j), recorded at a given current density j under several experimental conditions of temperature T and pressure p, equation (2.10) can be written, after correction of ohmic drop Re | j|, as follows: RT j ln Ucell ð jÞ 2 Ucell ð0Þ 2 Rexp j 5 αnF j0a
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Production of Clean Hydrogen
where Rexp 5 Re 1 RT/(nFjoc) is the total contribution of the cell resistance, Re, and the hydrogen transfer resistance Rt 5 RT/(nFjoc) to the linear part of the semi-logarithmic plot. The effect of temperature T, at the standard pressure p0, is contained in Ucell(0) 5 Urev(0) 5 Eeq(0), that is, in the Gibbs energy change with T at j 5 0: Ucell ð0Þ 5 Ea1 2 Ec2 Ea1 5 ðΔG1 2 ΔG2 Þ=nF ΔG1 ðT Þ=nF since ΔG2 5 0 at any temperature for the hydrogen electrode, with n 5 (4x 1 y 2 2z) is the number of Faraday involved in the complete oxidation of CxHyOz, into H2 and CO2—see eq. (2.6). For a given organic compound, ΔG1(T) can be evaluated from the variation of ΔGH2 O , ΔGCO2 , and ΔGCx Hy Oz with T according to the following relation: ΔG1 ðT Þ 5 x ΔGCO2 ðT Þ 2 ð2x 2 zÞ ΔGH2 O ðT Þ 2 ΔGCx Hy Oz ðT Þ As an example, the complete calculation can be made for the generation of H2 from methanol electro-oxidation: CH3 OH 1 H2 O-CO2 1 3 H2 since the variations of ΔH and ΔG with T are available from 298.15 to 400 K (Table 2.2 and Fig. 2.3). The variation of Ucell(0) with T may be calculated from Utn by the following differential thermodynamic law: ! ! d ΔG ΔH d Ucell ð0Þ Utn 52 52 2 or 2 dT RT RT dT T T where Utn 5 ΔH/nF is the thermoneutral voltage with ΔH 5 130.58 1 0.0349 T0.0001 T 2 1 etc. 5 a 1 b T 1 c T 2 1 d T 3 1 e T 4 1 etc. One obtains ðT ΔG ΔG 0 ΔH ΔG0 1 1 5 2 2 dT 5 1a 2 T T T0 T0 T0 T0 T T 2 b Ln 2 c 2 dðT 2 T0 Þ 1 etc: T0 and
T T T 1a 12 2c T 2 b T Ln ΔG ðT Þ 5 ΔG T0 T0 T0 0
2 d T ðT 2 T0 Þ 1 etc:
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Principle of hydrogen production by electrocatalytic oxidation of organic compounds
Table 2.2 Thermodynamic data and open circuit cell voltage corresponding to the electrochemical reforming of methanol as a function of temperature between 298.15 and 400 K. T (K) ΔS (J mol K)21 ΔH (kJ mol21) ΔG (kJ mol21) Ucell(0) (mV)
298.15 300.00 305.00 310.00 315.00 320.00 325.00 330.00 335.00 340.00 345.00 350.00 355.00 360.00 365.00 370.00 375.00 380.00 385.00 390.00 395.00 400.00
408.252 408.048 407.495 406.940 406.381 405.818 405.250 404.676 404.097 403.512 402.920 402.321 401.715 401.100 400.477 399.846 399.206 398.557 397.898 397.231 396.554 395.868
131.16 131.10 130.93 130.76 130.58 130.40 130.22 130.03 129.84 129.64 129.44 129.23 129.02 128.80 128.57 128.34 128.10 127.86 127.61 127.35 127.08 126.81
9.44 8.68 6.64 4.61 2.57 0.54 2 1.49 2 3.51 2 5.53 2 7.55 2 9.57 2 11.58 2 13.59 2 15.60 2 17.60 2 19.60 2 21.60 2 23.59 2 25.59 2 27.57 2 29.56 2 31.54
16.30 14.99 11.47 7.96 4.44 0.94 2 2.57 2 6.06 2 9.55 2 13.04 2 16.52 2 20.00 2 23.47 2 26.94 2 30.40 2 33.86 2 37.31 2 40.75 2 44.19 2 47.62 2 51.05 2 54.47
Another way to get the temperature variation of Ucell(0) is to consider the entropic term, that is, ΔSr0 5 nF (dUcell(0)/dT), which is related to the temperature coefficient of the cell. Thus, knowing the variation of ΔH and ΔS with the temperature, one may calculate Ucell(0) as follows: Ucell ð0Þ 5 ΔG=nF 5 ðΔH T ΔSÞ=nF for water and methanol in the liquid state. The effect of pressure for gases or concentration for liquids can be evaluated with the Nenst’law giving the electrode potential for each compartment: Urev ðT0 ; pÞ 5 Eeq 5Eeq ðT0 ; p0 Þ " 3 # ½CH3 OH ½H2 O RT pCO2 pH2 ln = 1 ½CH3 OH0 ½H2 O0 nF p0 p0
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Production of Clean Hydrogen
140.00 120.00
ΔH
y = -0.0001x2 + 0.0349x +130.58 (R2 = 1)
ΔH, ΔG/kJ mol–1
100.00 80.00 60.00 40.00 20.00 y = 6E-05x2 - 0.4445x +136.59 (R2 = 1)
0.00 –20.00 –40.00 290.00
ΔG
310.00
330.00
350.00
370.00
390.00
Absolute temperature/K
Figure 2.3 Enthalpy change ΔH1 and Gibbs energy change ΔG1 for the electrochemical reforming of methanol as a function of temperature between 298.15 and 400 K.
where Urev (T0, p0) 5 Eeq (T0, p0) 5 ΔG0/nF is the equilibrium cell voltage in the standard state and [species (i)] the concentration of species (i) in the liquid state.
2.4 Estimation of the energy efficiency [8] The energy efficiency εcell of an electrolysis cell can be defined as the ratio between the theoretical amount of total energy Wt ( J mol21) required to decompose the organic compound CxHyOz with the production of (2x 1 y/2 2 z) mole of hydrogen, according to the overall 0 0 equation (2.6), that is, the reaction enthalpy ΔHrev 5 x ΔHCO2 2 ΔHf0 2 0 0 ð2x 2 zÞΔHH2O , where ΔHf are the formation enthalpy, under standard state, of the species involved and the real amount of energy Wr (J mol21) used in the process: Wt J mol21 energy requirement under reversible conditions εcell 5 5 energy requirement under irreversible conditions Wr J mol21 (2.14)
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Principle of hydrogen production by electrocatalytic oxidation of organic compounds
When taking into account all the energies involved, that is, electrical and thermal energies, the numerator of Eq. (2.14), that is, the energy requirement under reversible conditions ( j 5 0), is defined as the necessary electrical work 1 the necessary heat flow ΔQrev 5 T ΔS (in J mol21), associated with the entropy change. Therefore: Wt 5 ΔGrev 1 ΔQrev 5 ΔHrev 5 nF Urev (electrical work) 1 nF (Utn 2 Urev) (reversible Q) Wt 5 nF Utn (J mol21) (total energy) with Utn the thermoneutral cell voltage (Utn 5 ΔHrev/nF). The denominator of Eq. (2.14), that is, the energy requirement under irreversible conditions ( j6¼0), is defined as the real electrical energy consumption, that is, the necessary electrical work 1 the extra amount of electrical work, which is dissipated internally into heat 1 the necessary heat associated with the entropy increase. Therefore: Wr 5 ΔGrev 1 nF ηloss 1 ΔQrev 5 ΔHrev 1 nF ηloss 5 nF Urev (electrical work) 1 nF (Ucell 2 Urev) (irreversible Q) 1 nF (Utn 2 Urev) (reversible Q), where the irreversible heat, defined as: X 21 Qirrev ðin J mol Þ 5 nFðUcell 2 Urev Þ 5 nF ηloss 5 nF jηi j 1 Re I represents the energy loss due to internal dissipation via the charge transfer overpotentials (Σ|ηi|) and the ohmic dissipation (Re I). Thus Wr 5 nF (Utn 1 Ucell 2 Urev) (total energy in J mol1), and the “energy efficiency” is given by: ΔHrev ð j 5 0Þ ΔHrev ΔGrev 1 ΔQrev 5 5 ΔHð j 6¼ 0Þ ΔHrev 1 nFηloss nF Ucell 1 ΔQrev Utn 5 Utn 1Ucell 2 Urev
εcell 5
(2.15a)
If the reversible heat, ΔQrev 5 T ΔS, is small compared to ΔGrev, that is, ΔQrev/ΔGrev ,, 1, this expression can be simplified as follows: εcell Urev =Ucell ; which represents the voltage efficiency
(2.15b)
However, for most decomposition reactions of organic compounds, the reversible heat, ΔQrev, is much greater than ΔGrev so that only the full equation (2.15a) does apply.
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Production of Clean Hydrogen
As an example [7], the energy efficiency of an electrolysis cell fed with methanol at 70 C working at I 5 500 mA and at a corrected cell voltage Ucell 5 0.488 V leading to an energy loss is as follows: nF ηloss 5 nFðUcell 2 Urev Þ 5 6 3 96:485ð0:488 2 ð2 0:015ÞÞ 5 291:2 kJ and a decomposition reaction enthalpy ΔHrev 5 129.5 kJ (see Table 2.2) would be: εcell 5 129:5=ð129:5 1 291:2Þ 5 0:308 31% If instead of using the complete formula (2.15a), the simplified expression (2.15b) would give: εcell 5 0:015=0:488 5 0:0307 3:1%; which is completely wrong
References [1] Y.H. Hu, E. Ruckenstein, Binary MgO-based solid solution catalysts for methane conversion to syngas, Catal. Rev. Sci. Eng. 44 (2002) 423453. Available from: https://doi.org/10.1081/CR-120005742. [2] F. Auprêtre, C. Delorme, D. Duprez, Bio-ethanol catalytic steam reforming over supported metal catalysts, Catal. Commun. 3 (2002) 263267. Available from: https:// doi.org/10.1016/S1566-7367(02)00118-8. [3] G.A. Deluga, J.R. Salge, L.D. Schmidt, X.E. Verykios, Renewable hydrogen from ethanol by autothermal reforming, Science 303 (2004) 993997. Available from: https://doi.org/10.1126/science.1093045. [4] D.K. Liguras, K. Goundani, X.E. Verykios, Production of hydrogen for fuel cells by catalytic partial oxidation of ethanol over structured Ru catalysts, Int. J. Hydrogen Energy 29 (2004) 419427. Available from: https://doi.org/10.1016/S0360-3199(03) 00210-6. [5] C. Lamy, Operation of fuel cells with biomass resources (hydrogen and alcohols), in: P. Lens, C. Kennes, P. Le Cloirec, M. Deshusses (Eds.), Waste gas treatment for resource recovery, IWA Publishing, London, 2006, pp. 360384. ISBN13: 9781843391272. [6] C. Lamy, B. Guenot, M. Cretin, G. Pourcelly, Kinetics analysis of the electrocatalytic oxidation of methanol inside a DMFC working as a PEM electrolysis cell (PEMEC) to generate clean hydrogen, Electrochim. Acta 177 (2015) 352358. Available from: https://doi.org/10.1016/j.electacta.2015.02.069. [7] B. Guenot, M. Cretin, C. Lamy, Clean hydrogen generation from the electrocatalytic oxidation of methanol inside a proton exchange membrane electrolysis cell (PEMEC): effect of methanol concentration and working temperature, J. Appl. Electrochem. 45 (2015) 973981. Available from: https://doi.org/10.1007/s10800-015-0867-3. [8] C. Lamy, From hydrogen production by water electrolysis to its utilization in a PEM fuel cell or in a solid oxide fuel cell: some considerations on the energy efficiencies, Int. J. Hydrogen Energy 41 (2016) 1541515425. Available from: https://doi.org/ 10.1016/j.ijhydene.2016.04.173.
Principle of hydrogen production by electrocatalytic oxidation of organic compounds in a proton exchange membrane electrolysis cell Contents 2.1 Thermodynamic considerations 2.2 Kinetics limitations 2.3 Analysis of the cell voltage versus current characteristics 2.4 Estimation of the energy efficiency References
9 12 15 18 20
The electrochemical decomposition of an organic compound, CxHyOz, for producing clean hydrogen can be performed in a proton exchange membrane electrolysis cell (PEMEC) of configuration similar to that of a water electrolysis cell (Fig. 2.1). In the case of water electrolysis, the anodic compartment of the electrochemical cell is fed with water, under liquid or gaseous state, which is oxidized leading to the production of oxygen and protons, according to reaction (2.1): H2 O-1/2 O2 1 2 H1 1 2 e2
anodic reaction
(2.1)
Oxygen evolves in the gaseous phase, whereas the electrons circulate in the external circuit and protons cross-over the membrane, reaching the cathodic compartment where they are reduced by the electrons coming from the external circuit, thus producing hydrogen, as follows: 2 H1 1 2 e2 -H2
cathodic reaction
(2.2)
The electrical balance between reactions (2.1) and (2.2) corresponds to the electrochemical splitting of water into hydrogen and oxygen according to the overall reaction: Production of Clean Hydrogen by Electrochemical Reforming of Oxygenated Organic Compounds. DOI: https://doi.org/10.1016/B978-0-12-821500-5.00002-3
© 2020 Elsevier Inc. All rights reserved.
7
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Production of Clean Hydrogen
Figure 2.1 Principle of the electrochemical decomposition, in a proton exchange membrane electrolysis cell, of (A) water and (B) an organic compound CxHyOz.
H2 O-H2 1 1/2 O2
overall reaction
(2.3)
with the following data under standard conditions (T 5 25 C, p 5 1 bar, liquid water): ΔH 0 51 285:8 kJðmole H2 OÞ21 and ΔG 0 51 237:2 kJðmole H2 OÞ21 These electrochemical processes are exactly the reverse of those occurring in a fuel cell with an acid electrolyte, for example, phosphoric acid, or a proton exchange membrane (PEM). For a PEM device, such as an electrolyzer or a fuel cell, the electrocatalysts at the negative electrode for the hydrogen evolution reaction (HER) or hydrogen oxidation reaction (HOR) are similar, that is, Pt/C nanoparticles, since the HER/HOR is a quasi-reversible reaction. Conversely, the electrocatalysts at the positive electrode are different, that is, Pt-based nanoparticles dispersed on the large surface area carbon powder, for example, Vulcan XC72R, for the oxygen reduction reaction (ORR) and Ir-based oxides dispersed on a corrosion-proof support, for example, a Ti mesh or foam, for the oxygen evolution reaction (OER). In the case of an organic compound, CxHyOz, its complete electro-oxidation in the anodic compartment of the electrolysis cell is realized with a suitable electrocatalyst, which is specific for the
Principle of hydrogen production by electrocatalytic oxidation of organic compounds
9
considered compound, leading to carbon dioxide and protons, according to reaction (2.4): Cx Hy Oz 1 ð2x 2 zÞH2 O-x CO2 1 nðH1 1 e2 Þ
anodic reaction (2.4)
where n 5 4x 1 y 2 2z is the number of exchanged electrons. Then the protons produced cross-over the PEM and are reduced to molecular hydrogen by a convenient catalyst in the cathodic compartment by the electrons coming from the external circuit according to reaction (2.5): nðH1 1 e2 Þ-ðn=2ÞH2
cathodic reaction
(2.5)
The electrical balance between reactions (2.4) and (2.5) leads to the following overall reaction: Cx Hy Oz 1 ð2 x 2 zÞH2 O-x CO2 1 ðn=2ÞH2
overall reaction
(2.6)
Reaction (2.6) corresponds to the electrochemical reforming of CxHyOz producing hydrogen and carbon dioxide by its complete oxidation. The electrochemical decomposition of CxHyOz, according to the overall reaction (2.6), is thus similar to a steam reforming process, but this reaction can occur at relatively low temperatures (25 C 2 85 C) instead of the high temperatures (600 C 2 800 C) encountered in steam reforming [15].
2.1 Thermodynamic considerations Knowing the thermodynamic data of the formation of H2O, CO2, and CxHyOz under standard conditions, usually the liquid state at 25 C, that is, ΔHf0 and ΔGf0 , one may calculate the thermodynamic data ΔH1 and ΔG1 associated with reaction (2.4) or (2.6) under standard conditions: 0 ΔH 1 5 xΔHCO 2 ð2x 2 zÞΔHH0 2 O 2 ΔHf0 2 0 0 ΔG1 5 xΔGCO 2 ð2x 2 zÞΔGH 2 ΔGf0 2 2O
Since most of the electroreactive organic compounds can be used as fuels in a direct oxidation fuel cell (DOFC), the thermodynamic data of
10
Production of Clean Hydrogen
their complete oxidation corresponding to the overall reaction in the fuel cell device, that is, Cx Hy Oz 1 ðx 1 y=4 2 z=2ÞO2 -x CO2 1 y=2 H2 O overall reaction (2.7) 0 can be estimated from the combustion data of the compounds, ΔHFC and 0 ΔGFC , in the fuel cell. Thus, the thermodynamic data of the electrochemical reforming reaction can be related to those of the combustion reaction of H2 and CxHyOz as follows: ΔH 1 5 ΔHC0 x Hy Oz ;FC 2 n=2 ΔHH0 2 ;FC 0 ΔG1 5 ΔGC0 x Hy Oz ;FC 2 n=2 ΔGH 2 ;FC
For low-weight organic compounds, the knowledge of their thermodynamic data of formation allowed us to calculate Δh1 5 ΔH1/(2x 1 y/ 2 2 z) corresponding to the total external energy needed to produce one mole of hydrogen and Ea1 5 ΔG1 =ðð4x 1 y 2 2zÞFÞ, the minimum anode potential necessary to decompose the organic compound through its electrocatalytic oxidation. Since the cathode potential Ec2 associated with the HER (2.2) or (2.5) is close to 0 V versus the standard hydrogen electrode (SHE), using the Pt/C electrode in contact with the hydrogen contained in the cathodic compartment as a reference electrode, the minimum cell voltage to be applied to the electrolysis cell to decompose the organic compound will be given as follows: 0 Ucell 5 Ea1 2 Ec2 Ea1
For many organic compounds, this theoretical cell voltage (Table 2.1) is very small compared with that of the electrolytic decomposition of 0 water, that is, Ucell 1:23 V under standard conditions, so that the 0 theoretical electrical energy, proportional to Ucell , to be provided by the external power source, to produce one hydrogen mole by the electrooxidation of CxHyOz, is much smaller than that used in water electrolysis. Table 2.1 gives the values of the thermodynamic data under standard conditions calculated for the electrocatalytic oxidation of water and of several organic compounds with one to six carbon atoms. Table 2.1 shows clearly that for most of these organic compounds, the theoretical total energy Δh10 necessary to produce one mole of hydrogen by their electrochemical dissociation under standard conditions is at least
Table 2.1 Standard thermodynamic data, cell voltage, and number of hydrogen moles, NH2 , produced by the electrochemical reforming of different hydrogen containing compounds. 0 Compound NH2 =mole ΔH10/kJ mol21 Δh10/kJ mol H21 ΔG10 /kJ mol21 Ucell Ea1 51 ΔG10 =nF (V vs SHE) 2
H2O 1 HCOOH 1 3 CH3OH 6 C2H5OH 5 CH2OH-CH2OH 9 1-C3H7OH 8 DMMCH2(OCH3)2 CH2OH-CHOH-CH2OH 7 12 1-C4H9OH Glucose 12
1 286 1 32 1 131.2 1 348 1 240 1 545 1 340.6 1 350 1 754 627.1
1 286 1 32 1 44 1 58 1 48 1 61 1 42.6 1 50 1 63 1 52.3
1 237 2 33 1 9.3 1 97.3 1 17.2 1 170 2 5.6 21 1 205 2 27.4
1.23 2 0.17 0.016 0.084 0.018 0.098 2 0.004 2 0.001 0.177 2 0.012
12
Production of Clean Hydrogen
five times lower than that for water electrolysis. Moreover, the theoretical electrical energy, which is proportional to the cell voltage—see Eq. (2.11) in Section 2.2—is at least several times lower than that for water dissociation, or even negative, for example, for HCOOH dissociation, which means that it is a spontaneous electrochemical process although the total energy ΔH10 is positive due to a larger positive reversible heat transfer TΔS associated with the entropy change.
2.2 Kinetics limitations However, the kinetics of the anodic reactions involved in both processes, that is, water oxidation in the water electrolysis process or the electrocatalytic oxidation of organic compounds in the electrochemical reforming process, is relatively slow leading to high anodic overpotentials and thus to higher cell voltages at the relatively high current density, over 1 A cm22, required for a high hydrogen production rate (Fig. 2.2).
Figure 2.2 Theoretical electrical characteristics j(E) for a reaction kinetics controlled by the Butler 2 Volmer law: CxHyOz oxidation, H2O oxidation, O2 reduction, and proton reduction. UCx Hy Oz ; UH2 O ; UDOFC ; and UH2 FC are the cell voltages for CxHyOz electrolysis, water electrolysis, direct oxidation fuel cell, and hydrogen/oxygen fuel cell at a given current density j, for example, 1 A cm22.
Principle of hydrogen production by electrocatalytic oxidation of organic compounds
13
This figure gives the current density j 5 I/S 5 nFv/S 5 nFvi, where I is the current intensity, S is the electrode surface area, v and vi are the reaction rate and the intrinsic rate, respectively, as a function of the electrode potential Ei( j) versus the SHE taken as reference, for the different electrochemical processes involved: • HOR and HER, which are described by a quasi-linear plot, assume that the hydrogen exchange current density joc (of the order of 1023 A cm22) is at least 103 times greater than the exchange current density joa of the anodic processes. These processes are associated, either to the electrocatalytic oxidation of the organic compound or to the OER in water electrolysis, with joa 1026 A cm22 , whereas the ORR has joc 1026 A cm22 . • In these latter cases, the current density j versus Ei(j) curves are exponential functions when assuming no mass transfer limitation according to the Butler 2 Volmer law: jðηÞ 5 jo ½expfα nF=RT ηg expf 2 ð1 2 αÞðnF=RT Þηg (2.8) where η 5 Ei 2 Eeq is the overpotential, jo is the exchange current density, and α is the anodic transfer coefficient. • For irreversible reactions such as the OER/ORR or the electrochemical oxidation of an organic compound, we can neglect the opposite reaction, and the j(E) characteristics become an exponential function, as plotted in Fig. 2.2, that is: j(η) 5 jo exp{α(nF/RT)η} for the oxidation of an organic compound or water in water electrolysis and jðηÞ 5 jo expf 2 ð1 2 aÞðnF=RT Þηg for the ORR When taking into account the charge transfer overpotentials ηact, the concentration overpotentials ηconc and the ohmic drop Re j associated with the cell resistance Re, the cell voltage versus current density curves, Ucell( j), of an electrolysis cell, can be expressed as follows: Ucell ð jÞ 5 Ea1 ð jÞ Ec2 ð jÞ 1 Re j 5 Ucell ð0Þ 1 ðjηact a ðj Þj (2.9) act conc conc 1 ηa ð jÞj 1 jηc ð jÞj 1 jηc ð jÞjÞ 1 Re j where Ucell(0) 5 Eeq is the equilibrium cell voltage, that is, the cell voltage at zero current, ηi is the overpotential defined as the deviation of the electrode potential Ei( j) under working conditions from its equilibrium value,
14
Production of Clean Hydrogen
that is, ηi 5 Ei( j) Eieq(0), and the subscripts “a” and “c” refer to the anodic and cathodic reactions, respectively. For an electrochemical reaction not limited by mass transfer, that is, the corresponding concentration overpotentials ηconc-0, and assuming a high exchange current density j0c for HER, equation (2.9) can be expressed as follows: RT j RT j j 1 Ucell ð jÞ 5 Ucell ð0Þ 1 1 R ln e nF j0c αnF j0a (2.10) RT j ln 5 Ucell ð0Þ 1 Rexp j 1 αnF j0a so that Ucell( j) 2 Ucell(0) 2 Rexp | j| can be plotted as a logarithmic function of the current density j, where Rexp 5 Re 1 RT/(nFjoc) is the total contribution of the cell resistance, Re, and the hydrogen transfer resistance Rt 5 RT/(nFjoc) to the linear part of the semi-logarithmic plot [6]. A specific software developed in our laboratory allowed us to estimate the unknown Rexp. At a given current density, for example, j 5 1 A cm22 as in Fig. 2.2, the measured cell voltage, Ucell( j), corrected from the ohmic losses Rexp j, allows to evaluate the electrical energy consumed to produce 1 Nm3 of hydrogen, which is directly proportional to Ucell( j), according to equation (2.11) [7]: We in kWh=Nm3 5
nF ~ Ucell ð jÞ 2:191Ucell ð jÞ 2:2 Ucell ð jÞ 3600Vm 3 103 (2.11)
where ñ 5 2 is the number of Faraday per mole of hydrogen produced and Vm 5 24.465 1023 m3 mol21 is the molar volume of an ideal gas at a temperature of 25 C under a pressure of 1 atm., that is, 101.325 kPa, corresponding to normal conditions for gaseous species. Equation (2.11) shows that the electrical energy consumed to produce molecular hydrogen by the electro-oxidation of an organic compound is directly proportional to Ucell( j), which must be as small as possible to decrease significantly the energy consumed, for example, below 1.0 kWh (Nm3)21 for Ucell( j) # 0.45 V. In contrast, the rate of hydrogen produced can be evaluated by measuring the volume of evolved hydrogen, VH2, which is a linear function of time for several fixed current intensities I during the electrolysis of the
Principle of hydrogen production by electrocatalytic oxidation of organic compounds
15
organic compound. The volume of evolved hydrogen, at a given electrolysis time Δt, depends only on the current intensity I, since it is a linear function of the quantity of electricity involved Δq 5 I Δt. The linear function can be derived from Faraday’s law, equation (2.12a) or (2.12b), giving the rate of hydrogen evolution [7]: dVH2 =dt 5 Vmol ðdNH2 =dtÞ 5 Vmol I=˜n F (2.12a) dVH2 =dt 5 Vmol ðI=2FÞ 3 60 5 7:607 Iðin cm3 min21 Þ
(2.12b)
where NH2 is the number of hydrogen mole, F 5 96,485 C per mole of electron is the Faraday constant, I is the current intensity in Ampere, and ñ 5 2 is the average number of Faraday per mole of dihydrogen produced in the complete oxidation reaction of an organic molecule according to reaction (2.4) or (2.6). The volume of hydrogen produced after Δt 5 15 min of electrolysis at a given temperature, when a quasi-stationary state is reached, can be obtained by integration of equation (2.12a), that is: VH2 5 Vmol ðI Δt=2FÞ 5 24:465 1023 Ið60 3 15Þ=ð2 3 96485Þ 5 114:1 3 Iðin cm3 Þ
at 25 C
or VH2 5 119:8 3 I cm3 at 40 C and
VH2 5 131:3 3 I cm3
(2.13a) at 70 C (2.13b)
when taking into account the hydrogen molar volume at 40 C or 70 C, corresponding to the dilatation of an ideal gas. This confirms that VH2 is proportional to the current intensity I leading to linear plots VH2 ðIÞ.
2.3 Analysis of the cell voltage versus current characteristics When analyzing the cell voltage, Ucell( j), recorded at a given current density j under several experimental conditions of temperature T and pressure p, equation (2.10) can be written, after correction of ohmic drop Re | j|, as follows: RT j ln Ucell ð jÞ 2 Ucell ð0Þ 2 Rexp j 5 αnF j0a
16
Production of Clean Hydrogen
where Rexp 5 Re 1 RT/(nFjoc) is the total contribution of the cell resistance, Re, and the hydrogen transfer resistance Rt 5 RT/(nFjoc) to the linear part of the semi-logarithmic plot. The effect of temperature T, at the standard pressure p0, is contained in Ucell(0) 5 Urev(0) 5 Eeq(0), that is, in the Gibbs energy change with T at j 5 0: Ucell ð0Þ 5 Ea1 2 Ec2 Ea1 5 ðΔG1 2 ΔG2 Þ=nF ΔG1 ðT Þ=nF since ΔG2 5 0 at any temperature for the hydrogen electrode, with n 5 (4x 1 y 2 2z) is the number of Faraday involved in the complete oxidation of CxHyOz, into H2 and CO2—see eq. (2.6). For a given organic compound, ΔG1(T) can be evaluated from the variation of ΔGH2 O , ΔGCO2 , and ΔGCx Hy Oz with T according to the following relation: ΔG1 ðT Þ 5 x ΔGCO2 ðT Þ 2 ð2x 2 zÞ ΔGH2 O ðT Þ 2 ΔGCx Hy Oz ðT Þ As an example, the complete calculation can be made for the generation of H2 from methanol electro-oxidation: CH3 OH 1 H2 O-CO2 1 3 H2 since the variations of ΔH and ΔG with T are available from 298.15 to 400 K (Table 2.2 and Fig. 2.3). The variation of Ucell(0) with T may be calculated from Utn by the following differential thermodynamic law: ! ! d ΔG ΔH d Ucell ð0Þ Utn 52 52 2 or 2 dT RT RT dT T T where Utn 5 ΔH/nF is the thermoneutral voltage with ΔH 5 130.58 1 0.0349 T0.0001 T 2 1 etc. 5 a 1 b T 1 c T 2 1 d T 3 1 e T 4 1 etc. One obtains ðT ΔG ΔG 0 ΔH ΔG0 1 1 5 2 2 dT 5 1a 2 T T T0 T0 T0 T0 T T 2 b Ln 2 c 2 dðT 2 T0 Þ 1 etc: T0 and
T T T 1a 12 2c T 2 b T Ln ΔG ðT Þ 5 ΔG T0 T0 T0 0
2 d T ðT 2 T0 Þ 1 etc:
17
Principle of hydrogen production by electrocatalytic oxidation of organic compounds
Table 2.2 Thermodynamic data and open circuit cell voltage corresponding to the electrochemical reforming of methanol as a function of temperature between 298.15 and 400 K. T (K) ΔS (J mol K)21 ΔH (kJ mol21) ΔG (kJ mol21) Ucell(0) (mV)
298.15 300.00 305.00 310.00 315.00 320.00 325.00 330.00 335.00 340.00 345.00 350.00 355.00 360.00 365.00 370.00 375.00 380.00 385.00 390.00 395.00 400.00
408.252 408.048 407.495 406.940 406.381 405.818 405.250 404.676 404.097 403.512 402.920 402.321 401.715 401.100 400.477 399.846 399.206 398.557 397.898 397.231 396.554 395.868
131.16 131.10 130.93 130.76 130.58 130.40 130.22 130.03 129.84 129.64 129.44 129.23 129.02 128.80 128.57 128.34 128.10 127.86 127.61 127.35 127.08 126.81
9.44 8.68 6.64 4.61 2.57 0.54 2 1.49 2 3.51 2 5.53 2 7.55 2 9.57 2 11.58 2 13.59 2 15.60 2 17.60 2 19.60 2 21.60 2 23.59 2 25.59 2 27.57 2 29.56 2 31.54
16.30 14.99 11.47 7.96 4.44 0.94 2 2.57 2 6.06 2 9.55 2 13.04 2 16.52 2 20.00 2 23.47 2 26.94 2 30.40 2 33.86 2 37.31 2 40.75 2 44.19 2 47.62 2 51.05 2 54.47
Another way to get the temperature variation of Ucell(0) is to consider the entropic term, that is, ΔSr0 5 nF (dUcell(0)/dT), which is related to the temperature coefficient of the cell. Thus, knowing the variation of ΔH and ΔS with the temperature, one may calculate Ucell(0) as follows: Ucell ð0Þ 5 ΔG=nF 5 ðΔH T ΔSÞ=nF for water and methanol in the liquid state. The effect of pressure for gases or concentration for liquids can be evaluated with the Nenst’law giving the electrode potential for each compartment: Urev ðT0 ; pÞ 5 Eeq 5Eeq ðT0 ; p0 Þ " 3 # ½CH3 OH ½H2 O RT pCO2 pH2 ln = 1 ½CH3 OH0 ½H2 O0 nF p0 p0
18
Production of Clean Hydrogen
140.00 120.00
ΔH
y = -0.0001x2 + 0.0349x +130.58 (R2 = 1)
ΔH, ΔG/kJ mol–1
100.00 80.00 60.00 40.00 20.00 y = 6E-05x2 - 0.4445x +136.59 (R2 = 1)
0.00 –20.00 –40.00 290.00
ΔG
310.00
330.00
350.00
370.00
390.00
Absolute temperature/K
Figure 2.3 Enthalpy change ΔH1 and Gibbs energy change ΔG1 for the electrochemical reforming of methanol as a function of temperature between 298.15 and 400 K.
where Urev (T0, p0) 5 Eeq (T0, p0) 5 ΔG0/nF is the equilibrium cell voltage in the standard state and [species (i)] the concentration of species (i) in the liquid state.
2.4 Estimation of the energy efficiency [8] The energy efficiency εcell of an electrolysis cell can be defined as the ratio between the theoretical amount of total energy Wt ( J mol21) required to decompose the organic compound CxHyOz with the production of (2x 1 y/2 2 z) mole of hydrogen, according to the overall 0 0 equation (2.6), that is, the reaction enthalpy ΔHrev 5 x ΔHCO2 2 ΔHf0 2 0 0 ð2x 2 zÞΔHH2O , where ΔHf are the formation enthalpy, under standard state, of the species involved and the real amount of energy Wr (J mol21) used in the process: Wt J mol21 energy requirement under reversible conditions εcell 5 5 energy requirement under irreversible conditions Wr J mol21 (2.14)
19
Principle of hydrogen production by electrocatalytic oxidation of organic compounds
When taking into account all the energies involved, that is, electrical and thermal energies, the numerator of Eq. (2.14), that is, the energy requirement under reversible conditions ( j 5 0), is defined as the necessary electrical work 1 the necessary heat flow ΔQrev 5 T ΔS (in J mol21), associated with the entropy change. Therefore: Wt 5 ΔGrev 1 ΔQrev 5 ΔHrev 5 nF Urev (electrical work) 1 nF (Utn 2 Urev) (reversible Q) Wt 5 nF Utn (J mol21) (total energy) with Utn the thermoneutral cell voltage (Utn 5 ΔHrev/nF). The denominator of Eq. (2.14), that is, the energy requirement under irreversible conditions ( j6¼0), is defined as the real electrical energy consumption, that is, the necessary electrical work 1 the extra amount of electrical work, which is dissipated internally into heat 1 the necessary heat associated with the entropy increase. Therefore: Wr 5 ΔGrev 1 nF ηloss 1 ΔQrev 5 ΔHrev 1 nF ηloss 5 nF Urev (electrical work) 1 nF (Ucell 2 Urev) (irreversible Q) 1 nF (Utn 2 Urev) (reversible Q), where the irreversible heat, defined as: X 21 Qirrev ðin J mol Þ 5 nFðUcell 2 Urev Þ 5 nF ηloss 5 nF jηi j 1 Re I represents the energy loss due to internal dissipation via the charge transfer overpotentials (Σ|ηi|) and the ohmic dissipation (Re I). Thus Wr 5 nF (Utn 1 Ucell 2 Urev) (total energy in J mol1), and the “energy efficiency” is given by: ΔHrev ð j 5 0Þ ΔHrev ΔGrev 1 ΔQrev 5 5 ΔHð j 6¼ 0Þ ΔHrev 1 nFηloss nF Ucell 1 ΔQrev Utn 5 Utn 1Ucell 2 Urev
εcell 5
(2.15a)
If the reversible heat, ΔQrev 5 T ΔS, is small compared to ΔGrev, that is, ΔQrev/ΔGrev ,, 1, this expression can be simplified as follows: εcell Urev =Ucell ; which represents the voltage efficiency
(2.15b)
However, for most decomposition reactions of organic compounds, the reversible heat, ΔQrev, is much greater than ΔGrev so that only the full equation (2.15a) does apply.
20
Production of Clean Hydrogen
As an example [7], the energy efficiency of an electrolysis cell fed with methanol at 70 C working at I 5 500 mA and at a corrected cell voltage Ucell 5 0.488 V leading to an energy loss is as follows: nF ηloss 5 nFðUcell 2 Urev Þ 5 6 3 96:485ð0:488 2 ð2 0:015ÞÞ 5 291:2 kJ and a decomposition reaction enthalpy ΔHrev 5 129.5 kJ (see Table 2.2) would be: εcell 5 129:5=ð129:5 1 291:2Þ 5 0:308 31% If instead of using the complete formula (2.15a), the simplified expression (2.15b) would give: εcell 5 0:015=0:488 5 0:0307 3:1%; which is completely wrong
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