Article pubs.acs.org/JPCC
Cu2+/Cu+ Redox Battery Utilizing Low-Potential External Heat for Recharge Sergey S. Lemishko* and Alexander S. Lemishko Department of Physical and Analytical Chemistry, Volgograd State Technical University, 28, Lenin Avenue, Volgograd, 400005, Russian Federation S Supporting Information *
ABSTRACT: We viewed a redox galvanic cell with copper and platinum electrodes in an electrolyte of copper(II) sulfate and studied the chemical equilibrium between the Cu1+ and Cu2+. The basis of the work of the cell is the ability to continuously generate electromotive force (EMF) by absorbing external heat. The cell is charged by an endothermic reaction, accumulating the reduced form of copper (Cu1+), the number of which is limited thermodynamically, and is discharged by oxidation of Cu1+ to Cu2+ on the surface of copper electrode. In this work we investigated the dependence of the electromotive force of the temperature and a long continuous operation with a voltage of 1.5 mV and thermodynamic efficiency of 45%.
anode (Cu): 3Cu+ − e− → Cu 0 + 2Cu 2 +, E 0 = +0.207 V
1. INTRODUCTION
(2)
Rechargeable batteries are an alternative energy source designed to maintain a constant current in the network for a certain period time.1−7 In everyday life, the batteries are found in cell phones, under the hood of the car, but the batteries are used much more widely.8−10 Batteries are the most widely used in electrical installations of telecommunications companies, primarily for the implementation of systems of uninterrupted electric power supply (UPS) ac and dc to the equipment. Thus, they not only largely determine the cost of the equipment and reliability of the power supply but also tend to determine the level of the output voltage direct current power supply in all modes of its operation.11−13 During the past decade significant amount of research has been devoted to alternative energy sources such as wind energy, solar energy, and hydroelectric energy.14−17 However, most of the current sources of “clean energy” suffer from drawbacks. Its energy is supplied independently of our desires and often not when it is necessary. A notable exception is the fuel cell technology where the fuel (typically methanol or hydrogen) is transformed into electrical energy by redox reactions.18−20 We have investigated the possibility of producing electrical energy from the electrochemical cell consisting of two metal electrodes, an active (copper) and inert (platinum), and the electrolyte, which contains an oxidized form of the active electrode metal (Cu2+). Copper is an inert to water metal, so in solution side reactions are excluded. Electrode reactions in the assembled electrochemical cell are the following: cathode (Pt): Cu 2 + + e− → Cu +, E 0 = +0.155 V © 2017 American Chemical Society
Although Cu(I) is not stable in aqueous solution, Cu+ ions still exist in the equilibrium concentration. It is enough for the operation of the cell. With the connection to the electrical load occurs a shift of equilibrium to the left that is oxidation of the reduced form of the metal on the surface of copper electrode, at the same time on a platinum electrode is restored the reduced form. Due to diffusion, supported by external heat, there is the movement of ions Cu+ to the copper electrode, where the whole cycle is repeated again. On the surface of platinum electrode, traces of copper and in the solution (metallic copper precipitate) visually are not detected. Concentration of Cu+ is less than 10−4 mol/L, which makes it difficult to do quantitative analysis, as there is less sensitivity of the photometer. Therefore, Cu+ ions are not reduced on a platinum electrode to the metal, thus creating the conditions for cyclic processes in the system. Connecting to the external circuit created gradient Cu+ concentrations, which are then maintained by the absorption of external heat produced by thermostat. At 1 cm3 of the electrolyte with equilibrium constant (Kc) in the range 10−4−10−2 and higher, charge of the oxidized form ion can produce voltage in the range of 10−100 mV and also the amperage in the range of 0.1−1 mA. Such systems can exist among complex compounds, for example, AuBr3 and AuBr solution in concentrated hydrobromic acid: Received: December 7, 2016 Revised: January 27, 2017 Published: January 30, 2017
(1) 3234
DOI: 10.1021/acs.jpcc.6b12317 J. Phys. Chem. C 2017, 121, 3234−3240
Article
The Journal of Physical Chemistry C
The values of the dissociation constant (Kdiss) of CuSO4 for each value of temperature are calculated according to the van’t Hoff equation:
[AuBr4]− + 2Au + 2Br − ↔ 3[AuBr2]− , 0 ΔG298 = 8.6 kJ/mol, Kc = 3.1 × 10−2
(3)
Theoretically, it can be useful to create commercial batteries that generate electricity by absorbing the low-potential external heat.
ln
μ = 0.5∑ Cizi 2
and Cu
CCu2+ =
(5)
CCuSO4Kdiss
2+
(7)
activity factor,
lgfi = −0.5zi 2
μ 1+
Then activity of Cu
2+
μ
(8)
is calculated using the formula
aCu2+ = fi CCu2+
(9)
In the case of contact the copper electrode with an electrolyte Cu2+ is reduced to Cu+: 0 Cu 0 + Cu 2 + ↔ 2Cu+, ΔG298 = 35.8 kJ/mol, 0 ΔH298 = 77.0 kJ/mol
(10)
ΔG0298
As we can see in eq 10 the reaction has > 0. It is limited thermodynamically; in solution it will significantly predominate parent ion Cu 2+ . Moreover the Cu 2 SO 4 compound does not exist in solution, and therefore all formed copper(I) which can exist in the equilibrium concentration will be in the form of Cu+. Knowing the value of ΔG0298, we are counting the value of the equilibrium constant: ⎡ ΔG 0 ⎤ 298 ⎥ Kc = exp⎢ − ⎣ RT ⎦
(11)
According to eq 6, we calculated the equilibrium constant value for each temperature value. We can see that the dissociation constant decreases with increasing temperature, and equilibrium constant increases opposite. Thus, with increasing temperature, Cu2+ concentration will reduced, thereby linearly increasing the potential of cells (Table 1). The system is derived from thermodynamic equilibrium when connecting an external circuit and trying to get back to equilibrium by absorbing external heat. By connecting the external circuit, on the surface of the copper electrode Cu+ is oxidized to Cu2+, and at the same time on a platinum electrode, Cu2+ is reduced to Cu+:
3. RESULTS AND DISCUSSION 3.1. EMF Measuring Results. Copper sulfate is a weak electrolyte with dissociation constant (Kdiss) of 5 × 10−3 and pH = 4.1. Therefore, it is necessary to calculate the concentration of Cu2+ ions in the resulting solution. (4)
(6)
where T0 = 298 K and Kc0 is the equilibrium constant at T0. Then activity of Cu2+ was calculated at each temperature value. To do this, first we calculated the ionic strength,
2. EXPERIMENTAL SECTION Chemicals. Copper(II) sulfate pentahydrate (>99,0%, Sigma-Aldrich, 2015) and chemically demineralized water were used to prepare the electrolyte. EMF measurements were performed on a precision multimeter Keithley 2110. The external temperature was controlled in a laboratory thermostat with cooling LAUDA Alpha RA 8. Electrolyte No. 1. In a 100 mL flask were added 5.0 g of copper(II) sulfate pentahydrate and freshly boiled chemically demineralised water to 100 mL. Electrolyte No. 2. In a 100 mL flask were added 4.125 g of copper(II) sulfate pentahydrate and freshly boiled chemically demineralized water to 100 mL. The solutions were stirred on a magnetic stirrer until the salt is completely dissolved. The concentration was chosen arbitrarily, but then it was possible to calculate precisely the activity of the ions through ionic strength of solutions. Sulfate was selected because all Cu(I) in solution can exist only in the ionic form. This will allow accurate assessment of its contribution to the generation of EMF. Construction of a Galvanic Cell. In cylindrical glass cuvette 5 cm in height and 2 cm in diameter, 15 cm3 aliquot of prepared electrolyte was placed. It was closed with a rubber plug with two electrodes: platinum and copper. The electrodes are rectangular metal plates with square of 1 cm2. The distance between the electrodes is 0.5 cm. The plug is further sealed with epoxy to prevent penetration of oxygen into the cell. After assembly of the cell its potential was about 100 mV. Potential decreases with time. It is caused by dissolved air that is present in the electrolyte (i.e., copper−air battery is formed). Gradually whole oxygen from dissolved air reacts with metallic copper (from the electrode) and the potential becomes constant and starts to show temperature dependence. To accelerate the removal of traces of oxygen in the electrolyte, the electrodes are short-circuited with a platinum wire and thus left for 5 days at 30 °C. After removal of traces of oxygen from the electrolyte, the electrodes were connected to a load resistor of 10 kΩ. The resistor is used as the electrical load. It is necessary to measure the internal impedance of the cell and its dependence on temperature. The cells were placed in a working thermostat chamber and held there at a predetermined temperature for 1 h. After that, the measurements of voltage and EMF were made.
CuSO4 ↔ Cu 2 + + SO4 2 − , Kdiss = 5 × 10−3
0 ⎛ ΔH298 Kc 1 1⎞ = ⎜ − ⎟ K c0 R ⎝ T0 T⎠
cathode (Pt): Cu 2 + + e− → Cu+
(12)
anode (Cu): 3Cu+ − e− → Cu 0 + 2Cu 2 +
(13)
total: 2Cu+ → Cu 0 + Cu 2 +
(14)
Knowing the equilibrium constant, dissociation constant, and the initial concentration of Cu2+ ions, we calculated equilibrium composition of the electrolyte at each temperature value. The calculated data were compared with the results of measurement of EMF and voltage of the cell with electrolyte no. 1 and the cell with electrolyte no. 2. With increasing temperature the concentration of Cu2+ decreases and Cu+ conversely increases, which provides EMF of cell no. 1, and cell no. 2 is directly 3235
DOI: 10.1021/acs.jpcc.6b12317 J. Phys. Chem. C 2017, 121, 3234−3240
Article
The Journal of Physical Chemistry C
As we see in eq 15, the potential depends on the ion concentration. Copper sulfate is a weak electrolyte, and as all the weak electrolytes, it is partially hydrolyzed. But its hydrolysis constant is 2.9 × 10−8. With this value of hydrolysis constant, influence of hydrolysis on the ionic strength of the solution will be negligible and can be ignored. However, eq 15 does not allow satisfactory calculation of the potential of the system at a temperature that is different from 298 K. To accurately calculate the potential of cells in the eq 15, one must enter the correction factors A and B for each cell:
Table 1. Values of the Dissociation Constant (Kdiss) and Equilibrium Constant (Kc) at Different Temperatures T, K 274
291
292
1.02 × 10−2 9.21 × 10−3 −7 2.48 × 10 2.76 × 10−7 T, K
293
Kdiss Kc
6.754 × 10−2 3.433 × 10−8
8.3 × 10−3 3.08 × 10−7
294
295
296
297
Kdiss Kc
7.49 × 10−3 3.43 × 10−7
6.76 × 10−3 3.81 × 10−7
6.11 × 10−3 4.24 × 10−7
5.53 × 10−3 4.71 × 10−7
298
299
300
301
5.0 × 10−3 5.23 × 10−7
4.53 × 10−3 5.8 × 10−7
T, K Kdiss Kc
Kdiss Kc
4.1 × 10−3 6.43 × 10−7 T, K
3.72 × 10−3 7.13 × 10−7
302
303
307
3.37 × 10−3 7.9 × 10−7
3.06 × 10−3 8.74 × 10−7
2.09 × 10−3 1.35 × 10−6
(16)
cell no. 2: E = B +
RT [Cu 2 +]2 ln nF [Cu+]
(17)
A = NA
K T ln c T0 K c0
(18)
B = NB
K T ln c T0 K c0
(19)
where NA and NB are some empirical coefficients that are constant over the wide temperature range. Further calculations show that NA and NB are the initial concentration of Cu2+ in the prepared electrolyte calculated at 298 K: 298 A = B = CCu 2+
K T ln c T0 K c0
(20)
Therefore, the final form of the Nernst equation to calculate the EMF for the reaction
2+ 2
RT [Cu ] ln nF [Cu+]
RT [Cu 2 +]2 ln nF [Cu+]
Correction factors as well as the potentials of the cells have a linear dependence on temperature. Moreover, the higher is the concentration, the more intense is the dependence. The correction factors A and B show the following dependence (Figure 4):
proportional to the linear temperature dependence (Table 2 and Table 3). The greater is the concentration of the electrolyte, the more intense is the rising of EMF (Figure 1 and Figure 2). At 18 °C (291 K) in both cells change polarity of the electrodes occurs. Copper electrode becomes the cathode, and a platinum electrode becomes an anode (Figure 3). Calculation of heat in the cell and out is difficult because of its very low value (less than 0.05 J). This value is below the sensitivity of the calorimeter. The intense heat the cell is when measurements are not possible because of loss of tightness of the cell. However, the thermodynamic efficiency can be calculated; it is 45.5%. According to these data, we can derive the form of the Nernst equation to calculate potential of the system at 298 K: E=
cell no. 1: E = A +
Cu 0 + Cu 2 + → 2Cu+, Kc = 5.23 × 10−7
(15)
Table 2. Dependence of Cell Voltage and Electromotive force of 0.2 M CuSO4 from Equilibrium Concentration of Cu2+ and Cu+ T, K 274
291
292
293
294
Cu2+, mol/L Cu+, mol/L E, mV U, mV
1.794 × 10−2 2.482 × 10−5 −18.675 −12.46
1.139 × 10−2 5.32 × 10−5 −0.678 −0.453
1.107 × 10−2 5.536 × 10−5 0.188 0.125 T, K
1.076 × 10−2 5.766 × 10−5 1.150 0.768
1.048 × 10−2 6.004 × 10−5 2.138 1.429
295
296
297
298
299
Cu2+, mol/L Cu+, mol/L E, mV U, mV
1.021 × 10−2 6.246 × 10−5 3.110 2.110
9.929 × 10−3 6.499 × 10−5 4.038 2.690
9.746 × 10−3 6.788 × 10−5 5.285 3.529 T, K
9.37 × 10−3 7.014 × 10−5 5.761 3.843
9.118 × 10−3 7.286 × 10−5 6.672 1.438
300
301
302
303
307
2+
Cu , mol/L Cu+, mol/L E, mV U, mV
−3
8.85 × 10 7.56 × 10−5 7.378 4.918
−3
−3
8.622 × 10 7.858 × 10−5 8.406 5.599
8.381 × 10 8.155 × 10−5 9.296 6.201 3236
−3
8.123 × 10 8.119 × 10−5 11.081 7.394
7.227 × 10−3 9.912 × 10−5 13.732 9.160 DOI: 10.1021/acs.jpcc.6b12317 J. Phys. Chem. C 2017, 121, 3234−3240
Article
The Journal of Physical Chemistry C
Table 3. Dependence of Cell Voltage and Electromotive Force of 0.165 M CuSO4 from Equilibrium Concentration of Cu2+ and Cu+ T, K 274
291
292
293
294
Cu2+, mol/L Cu+, mol/L E, mV U, mV
1.719 × 10−2 2.43 × 10−5 −12.875 −7.806
1.084 × 10−2 5.18 × 10−5 −0.378 −0.230
1.056 × 10−2 5.41 × 10−5 0.249 0.150 T, K
1.026 × 10−2 5.62 × 10−5 0.854 0.515
9.94 × 10−3 5.84 × 10−5 1.348 0,821
295
296
297
298
299
Cu2+, mol/L Cu+, mol/L E, mV U, mV
9.71 × 10−3 6.08 × 10−5 2.130 1.29
9.45 × 10−3 6.32 × 10−5 2.838 1.71
9.14 × 10−3 6.57 × 10−5 3.141 1.902 T, K
8.911 × 10−3 6.82 × 10−5 3.880 2.350
8.66 × 10−3 7.081 × 10−5 4.452 2.703
300
301
302
303
307
2+
Cu , mol/L Cu+, mol/L E, mV U, mV
−3
−3
8.42 × 10 7.36 × 10−5 4.998 3.015
−3
8.19 × 10 7.64 × 10−5 5.590 3.399
7.919 × 10 7.92 × 10−5 5.896 3.571
−3
7.737 × 10 8.22 × 10−5 6.691 4.055
6.840 × 10−3 9.646 × 10−5 8.820 5.350
Figure 1. Dependence of cell electromotive force of 0.2 M CuSO4 on temperature.
is
r= 2+ 2
298 E = CCu 2+
K T RT [Cu ] ln c + ln T0 K c0 nF [Cu+]
(23)
The cell is operated as a generator, absorbing low-potential external heat continuously and converting it directly into electricity. The internal resistance is r ≈ 5000 Ω for cell no. 1 and r ≈ 6500 Ω for cell no. 2. With the change in a temperature the internal resistance of the cells does not change significantly. After finishing a series of experiments measuring the EMF, both cells retain continuous operation with resistor (R = 10 000 Ω) for the past 3 months. The cells were in laminar box at a temperature of 19−21 °C. Voltage was varied during operation in accordance with the change of temperature: 0.2−1.5 mV for 0.2 M CuSO4 and 0.15−0.81 mV for 0.165 M CuSO4. Current (in short circuit) also changed: 0.04−0.61 μA and 0.023−0.092 μA, respectively. Average output power was 5.5 × 10−11 W × s and 2.4 × 10−11 W × s, respectively. The thermodynamic
(21)
or for the reaction 2Cu+ → Cu 0 + Cu 2 +, K −c = 1.91 × 106
is ⎡ K −c ⎤ RT [Cu 2 +]2 298 T ln ⎥+ E = −⎢CCu ln 2+ [Cu+] T0 K−c0 ⎥⎦ nF ⎢⎣
R (E − U ) U
(22)
3.2. Working with the Electrical Load. While working with the load, the cell provides a voltage reduction in accordance with Ohm’s law and is stable all the time: 3237
DOI: 10.1021/acs.jpcc.6b12317 J. Phys. Chem. C 2017, 121, 3234−3240
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Figure 2. Dependence of cell electromotive force of 0.165 M CuSO4 on temperature.
Figure 3. Ratio of dependencies of EMF on temperature of two cells.
4. CONCLUSIONS We investigated the electrochemical cell consisting of an inert electrode and the active metal electrode immersed in a solution of its oxy-form salt. This cell produces electricity by reversible reactions at the electrodes. The operation of the cell is supported by absorption of external heat. The internal resistance of the cells varies slightly across the temperature range. At a temperature of 18 °C (291 K) in cells, change of polarity of the electrodes occurs. Cells produced the amount of electricity in 5−10 times exceeding that which can be obtained from the equilibrium concentration of Cu+. This indicates the presence of primary energy source which is external heat. The disadvantages of the cells are high internal resistance value and low value of electromotive force, which is caused by low values
efficiency is 45.5%. Visually, the chemical changes were not found in cells. More sensitive methods are difficult only for technical reasons (too low concentration of Cu+). During the 100 days the cells have produced an average of 4.75 × 10−4 and 2.07 × 10−4 W of electricity, respectively. It is at 10 and 5 times, respectively, exceeding the amount of electricity that can be produced by oxidation of whole Cu+ which is present in equilibrium concentration at that temperature. This indicates the presence of the outer (primary) power source for the functioning of the cells, which is the external heat. This demonstration model shows the possibility of using low-potential external heat to generate electricity. 3238
DOI: 10.1021/acs.jpcc.6b12317 J. Phys. Chem. C 2017, 121, 3234−3240
Article
The Journal of Physical Chemistry C
Figure 4. Temperature dependence of the correction factors. (5) Leung, P. K.; Ponce-de-Leon, C.; Walsh, F. C. The influence of operational parameters on the performance of an undivided zinccerium flow battery. Electrochim. Acta 2012, 80, 7−14. (6) Gonzalez-García, J.; Bonete, P.; Exposito, E.; Montiel, V.; Aldaz, A.; Torregrosa-Macia, R. Characterization of a carbon felt electrode: structural and physical properties. J. Mater. Chem. 1999, 9, 419−426. (7) Friedrich, J. M.; Ponce-de-Leon, C.; Reade, G. W.; Walsh, F. C. Reticulated vitreous carbon as an electrode material. J. Electroanal. Chem. 2004, 561, 203−217. (8) Zheng, Q.; Xing, F.; Li, X.; Liu, T.; Lai, Q.; Ning, G.; Zhang, H. Investigation on the performance evaluation method of flow batteries. J. Power Sources 2014, 266, 145−149. (9) Xi, X.; Li, X.; Wang, C.; Lai, Q.; Cheng, Y.; Zhou, W.; Ding, C.; Zhang, H. Impact of proton concentration on equilibrium potential and polarization of vanadium flow batteries. ChemPlusChem 2015, 80, 382−389. (10) Kazacos, M.; Skyllas-Kazacos, M. Performance characteristics of carbon plastic electrodes in the all-vanadium redox cell. J. Electrochem. Soc. 1989, 136, 2759−2760. (11) Leung, P. K.; Mohamed, M. R.; Shah, A. A.; Xu, Q.; CondeDuran, M. B. A mixed acid based vanadium-cerium redox flow battery with a zero-gap serpentine architecture. J. Power Sources 2015, 274, 651−658. (12) Hoffmann, P. Tomorrow’s Energy: Hydrogen, Fuel Cells, and the Prospects for a Cleaner Planet; MIT Press, Cambridge, MA, 2002. (13) Ferrigno, R., Strook, A. D., Clark, T. D., Mayer, M., Whitesides, G. M. Presented at the 53rd Annual Meeting of the International Society of Electrochemistry; Düsseldorf, Germany, 2002. (14) Girault, H. H., Ed. Electrochimie Physique et Analytique, 1st ed.; Presses Polytechnique et Universitaires Romandes: Lausanne, Switzerland, 2001. (15) Yang, Z.; Zhang, J.; Kintner-Meyer, M. C. W.; Lu, X.; Choi, P.; Lemmon, J. P.; Liu, J. Electrochemical energy storage for green grid. Chem. Rev. 2011, 111, 3577−3613. (16) Leung, P.; Heck, S. C.; Amietszajew, T.; Mohamed, M. R.; Conde, M. B.; Dashwood, R. J.; Bhagat, R. Performance and polarization studies of the magnesium-antimony liquid metal battery with the in-situ reference electrode. RSC Adv. 2015, 5, 83096−83105. (17) Leung, P. K.; Xu, Q.; Zhao, T. S. High-potential zinc-lead dioxide rechargeablecells. Electrochim. Acta 2012, 79, 117−125.
of equilibrium constant and the degree of dissociation of CuSO4 (α ≈ 15%). The cells demonstrate the possibility of constructing cells for the use of external heat as the primary energy source for electricity production.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b12317. Highlights of the dependencies of the electromotive force of two cells on temperature (PDF)
■
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Sergey S. Lemishko: 0000-0001-5554-5663 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors acknowledge the technical support from Ivan Nikolayevich Grigoriev, chemical engineer of Novovoronezh Nuclear Power Plant.
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REFERENCES
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DOI: 10.1021/acs.jpcc.6b12317 J. Phys. Chem. C 2017, 121, 3234−3240
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