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Energy & Fuels 2009, 23, 1668–1673
Pilot Study of an Aqueous Zinc-Bichromate Battery Zhang Shimin,* Chen Sulin, Zhou Debi, Qi Wei, Huang Yu, and Cheng Xiang College of Chemistry and Chemical Engineering, Central South UniVersity, Changsha, Hunan 410083, China ReceiVed October 9, 2008. ReVised Manuscript ReceiVed January 15, 2009
Active metal-zinc pieces were used as an anode, and ammonium chloride was used as an electrolyte in an anode zone, with acids and soluble oxidant-bichromate as an active cathode substance and electrolyte in a cathode zone in a zinc-bichromate battery. Carbon felt was used as an inert cathode, with a PE-01 homogeneous membrane between the anode and cathode zones as well as 50 mL of solution in both the anode and cathode zones. The discharge characteristics of the batteries at 5 Ω were investigated for various pure acids, mixed acids, various concentrations of bichromate in the cathode zone and ammonium chloride in the anode zone. The output voltages of the batteries generally exceeded 1.70 V at the beginning of discharge, and the discharge time was more than 10 h. The discharge time and output voltage of the battery increase with the augment of concentrations of hydrogen ions in the cathode zone and the decrease of solid products formed at the carbon felt or membrane. When the concentrations of sodium bichromate were smaller than 0.75 M, hardly any solid products formed at the carbon felt or membrane. The actual gravimetric energy density of the batteries with 0.75 M ammonium bichromate, 1.8 M sulfuric acid, and 4.8 M hydrochloric acid in the cathode zone and 5 M ammonium chloride in the anode zone arrived at 51.93 W h kg-1.
1. Introduction Researchers have used some metals with very negative electrode potentials, for example, manganese, aluminum, etc., as an active anode substance of batteries1-4 and some matter with very positive electrode potentials, such as potassium permanganate, hydrogen peroxide, persulfate, etc., as an active cathode substance of the batteries.5-7 However, none used chromium(VI) ions with very positive electrode potentials as the active cathode substance of the batteries. Perhaps there are various reasons for this, but the authors think that chromium(VI) ions are a sort of attractive cathode substance because they have the following strong points: (1) the standard electrode potential of Cr2O72-/ Cr3+, 1.33 V versus normal hydrogen electrode (NHE), is very high; (2) they lose or gain three electrons during oxidation and reduction reactions; (3) if bichromate [Na2Cr2O7, (NH4)2Cr2O7, etc.] is used as an active cathode substance of the batteries, 1 mol of bichromate contains 2 mol of chromium ions with a valence of +6; and (4) the solubility of bichromate is very large (the solubility of Na2Cr2O7 can arrive at 4 M at room temperature). In consideration of these excellent qualities of * To whom correspondence should be addressed. Telephone: 86-7318879616. Fax: 731-8710006. E-mail:
[email protected]. (1) Tajima, S. Aluminium and manganese as anodes for dry and reserve batteries. J. Power Sources 1984, 11 (1-2), 155–161. (2) Verma, L. K. Studies on an aluminium-carbon cell. J. Power Sources 1994, 50 (1-2), 187–192. (3) Despic, A. R. Design characteristics of an aluminium-air battery with consumable wedge anodes. J. Appl. Electrochem. 1985, 15 (2), 191– 200. (4) Licht, S.; Peramunage, D. Novel aqueous aluminium/sulfur batteries. J. Electrochem. Soc. 1993, 140 (1), 4–6. (5) Marsh, C.; Licht, S. Novel aqueous dual-channel aluminiumhydrogen peroxide battery. J. Electrochem. Soc. 1994, 141 (6), L61–L63. (6) Licht, S. A novel aqueous aluminium/permanganate fuel cell. Electrochem. Commun. 1999, 33–66. (7) Shimin, Z. Feasibility study of an aqueous zinc-persulfate battery. Energy Fuels 2007, 21 (2), 1092–1097.
Figure 1. Tafel plot for Cr2O72-/Cr3+ at a carbon-felt electrode in 1 M Na2Cr2O7 + 3.6 M H2SO4 solution. Initial E, 0 V; final E, 2 V; segment, 1; scan rate, 0.01 V s-1.
chromium(VI) ions and bichromate, we performed a pilot study for batteries using bichromate as an active cathode substance. 2. Experimental Section All chemicals, ammonium chloride, sodium bichromate, ammonium bichromate, etc., were of reagent grade. The thickness of the carbon felt and 99.99% zinc pieces were 3 and 0.15-0.25 mm, respectively. The widths of both of the carbon felt and zinc pieces were 3 cm. The anode and cathode zones of the electrolytic cell were separated by a membrane. The volume of both the anode and cathode zones were 3 cm (long) × 5 cm (wide) × 5 cm (high). The solution volume in both of the anode and cathode zones was 50 mL. The solutions were prepared using deionized water. The zinc electrode was formed by the superposition of more than one zinc piece, each of which was polished and washed using deionized
10.1021/ef800848p CCC: $40.75 2009 American Chemical Society Published on Web 02/19/2009
Aqueous Zinc-Bichromate Battery
Energy & Fuels, Vol. 23, 2009 1669 Table 3. Status of Some Solid Products Formed at the Carbon Felt or Membrane for Various Systems in Figure 5 carbon felt membrane
a
b
c
d
e
many many
few a little
largely largely
hard a little
hard a little
electrode. Two surfaces of the carbon-felt electrode were exposed to solution, and a platinum sheet with a large surface area was used as a counter electrode. Tafel and cyclic voltammetry plots for Cr2O72-/Cr3+ in a mixed solution of 3.6 M H2SO4 and 1 M Na2Cr2O7 were shown in Figures 1 and 2, respectively. From Figure 1, we obtained the electrode potential of 1.161 V versus saturated calomel electrode (SCE) for the electrode reaction Cr2O72- + 14H+ + 6e ) 2Cr3+ + 7H2O φ ° ) 1.33 V (1) The electrode potential (versus NHE) of Cr2O72-/Cr3+ is 1.161 + 0.241 ) 1.402 V, where 0.241 V is the electrode potentials (versus NHE) of the saturated calomel electrode. From Figure 2, one can see that the reduction currents in the opposite directions superposed within a wide range. This shows that the reduction of Cr2O72- can arrive at a steady state very easily. 3.2. Discharge Characteristics of the Zn-Na2Cr2O7 Batteries. 3.2.1. Case of 1 M Na2Cr2O7 and Various Acids of Different Proportions in the Cathode Zone and 4 M NH4Cl in the Anode Zone. The anode reaction of the Zn-Na2Cr2O7 batteries was
Figure 2. Cyclic voltammetry plot for Cr2O72-/Cr3+ at a carbon-felt electrode in 1 M Na2Cr2O7 + 3.6 M H2SO4 solution. Inital E, 0 V; high E, 2 V; low E, 0 V; segment, 2; scan rate, 0.1 V s-1.
(2) Zn ) Zn2+ + 2e φ ° ) -0.763 V From eqs 1 and 2, we know that the standard electromotive force of the batteries is E° ) 1.33 V - (-0.763 V) ) 2.093 V. The electromotive forces measured actually, E, for the Zn-Na2Cr2O7 batteries with 1 M Na2Cr2O7, various pure acids of different concentrations, and mixed acids of different proportions in the cathode zone and 4 M NH4Cl in the anode zone were listed in Table 1, and their discharge characteristics were shown in Figures 3 and 5. From Table 1, one can see that the electromotive forces measured of the batteries are larger than their standard electromotive forces, except that no acid was added to the batteries because eq 1 shows that, the greater the acidity of the batteries, the greater their electromotive forces. Figure 3 shows that the order of the influence of various acids on the discharge time and output voltage of the batteries is H2SO4 > HNO3 > HCl > H3PO4. The discharge time and output voltage of the batteries should be proportional to the acidity of various acids. However, this rule was broken when the increases of the acid concentrations result in the formation of some crystals or solid products at the carbon-felt and membrane. For example, when the concentrations of sulfuric acid increased from 1.8 M (curve a1) to 3.6 M (curve a2), the discharge time and output voltage of the batteries increased. However, when the concentrations of sulfuric acid arrived at
Figure 3. Discharge characteristics of the Zn-Na2Cr2O7 batteries with 1 M Na2Cr2O7 and various acids of different concentrations in the cathode zone and 4 M NH4Cl in the anode zone.
water before the experiments. The electrodes were immersed in solution to approximately 2.2 cm. Electrochemical experiments were performed with NEWARE charge/discharge equipment and a CHI potentiostat. The crystals formed in the cathode zone were analyzed by a D/MAX2500 X-ray diffraction apparatus. The batteries were discharged at 5 Ω and room temperature.
3. Results and Discussion 3.1. Tafel and Cyclic Voltammetry Plots. Tafel and cyclic voltammetry curve tests were performed at a 1 cm2 carbon felt
Table 1. Electromotive Forces (V) of the Zn-Na2Cr2O7 Batteries with 1 M Na2Cr2O7, Various Pure Acids, and Mixed Acids (M) in the Cathode Zone and 4 M NH4Cl in the Anode Zone H2SO4 HCl HNO3 H3PO4
c
E
c
E
c
E
c
1.8 2.4 2.8 5.4
2.201 2.150 2.199 2.104
3.6 3.6 3.6 10.8
2.256 2.152 2.246 2.299
5.4 4.8 5.6
2.341 2.188 2.291
0 2.4 2.8 0
E
c
2.175
1.8 2.4 0 0
E
c
2.182
3.6 2.4 0 0
E
c
2.229
3.6 0 2.4 0
E
c
2.321
0 0 0 0
E
c
E
1.927
0 0 5.6 0
1.842 (no Cr2O72-)
Table 2. Status of Some Solid Products Formed at the Carbon Felt or Membrane for Various Systems in Figure 3 carbon felt membrane
a1
a2
a3
b1
b2
b3
c1
c2
c3
c4
d1
d2
hard few
many many
largely many
hard nothing
hard nothing
hard nothing
hard nothing
hard nothing
hard nothing
nothing nothing
hard nothing
nothing nothing
1670 Energy & Fuels, Vol. 23, 2009
Shimin et al. Table 4. Status of Some Solid Products Formed at the Carbon Felt or Membrane for Various Systems in Figure 6 3.6 M 1.8 M H2SO4 + 3.6 M H2SO4 + 3.6 M H2SO4 + 4.8 M HCl 1.2 M HCl 2.4 M HCl H2SO4 carbon felt a little membrane nothing
Figure 4. X-ray powder diffraction pattern of crystals formed (the sample was dried at 60 °C).
Figure 5. Discharge characteristic of the batteries with 1 M Na2Cr2O7 and mixed acid of different proportions in the cathode zone and 4 M NH4Cl in the anode zone.
few few
more a little
a little nothing
crystals were a mixture of NaCr(SO4)2 · 12H2O, Na2S2O3, Na2S2O6, etc. (see Figure 4). NaCr(SO4)2 · 12H2O [alums, as KCr(SO4)2 · 12H2O, NaAl(SO4)2 · 12H2O, KAl(SO4)2 · 12H2O, etc.] was the major constituent, and the others were minor ones. In fact, when the concentrations of sulfuric acid arrived at 3.6 M, some crystals have already formed at the carbon felt and membrane. There were not excessive differences among 3.6 M hydrochloric acid (curve b2), 3.6 M nitric acid (curve c2), and 1.8 M sulfuric acid because the concentrations of hydrogen ions that they supplied were the same. At the beginning of the discharge, curve c2 laid on curve b2 and curve a1. This relates to the discharge of NO3- because NO3- can also discharge even without Cr2O72- as curve c4. However, curve c2 was not completely the superposition of the discharges of NO3- and Cr2O72-, owing to the form of solid products at the carbon felt or membrane. It can be seen that, the larger the concentrations of phosphoric acid, the longer the discharge time and the flatter the discharge curves of the batteries. Although 1 mol of H3PO4 contains 3 mol of H+, the output voltage of the batteries using H3PO4 was much lower than using H2SO4. This is because H3PO4 is a weak acid. Its ionization constants are very small, and it can only provide a small quantity of hydrogen ions. After a time period of several hours, curve a3 lay under curve d2 in Figure 3. The reason for this is that some crystals formed at the carbon felt and membrane for the H2SO4 system. The status of some solid products formed at the carbon felt or membrane for various systems in Figure 3 was shown in Table 2. In Table 2 and the latter tables, we use the following words to describe the status of some solid products formed at the carbon felt or membrane: nothing, no solid product formed at the carbon felt or membrane; few, hardly any solid product formed at the carbon felt or membrane; a little, a little solid products formed at the carbon felt or membrane; more, more solid products formed at the carbon felt or membrane; many, many solid products formed at the carbon felt or membrane; largely, solid products formed largely at the carbon felt or membrane; hard, carbon felt became very hard.
Figure 6. Discharge characteristic of the batteries with 0.75 M Na2Cr2O7 and mixed acid of different proportions in the cathode zone and 5 M NH4Cl in the anode zone.
5.4 M (curve a3), the discharge time and output voltage of the batteries decreased instead. The reason for this is that not all sodium bichromate has been exhausted, but the holes at the carbon felt or membrane have been blocked by the crystals formed. The X-ray powder diffraction pattern shows that these
Figure 7. Discharge characteristic of the batteries with 3.6 M H2SO4, 2.4 M HCl, and Na2Cr2O7 of different concentrations in the cathode zone and 5 M NH4Cl in the anode zone.
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Energy & Fuels, Vol. 23, 2009 1671
Table 5. Status of Some Solid Products Formed at the Carbon Felt or Membrane for Various Systems in Figures 7 and 8 Figure 7
Figure 8
c
0.50
0.75
1.00
0.25
0.50
0.75
1.00
carbon felt membrane
few few
a little nothing
largely nothing
a little nothing
more more
largely a little
largely largely
From Table 2 one can see that no solid product formed at the carbon felt or membrane for the system d2. The reasons for this were that less resultants were produced because of the lack of hydrogen ions. The discharge current can be calculated from the following formula: I (A) ) V (V)/5 (Ω) (3) where V is the ordinate in Figure 3. The amount of charge that the batteries released was Q ) 3600
3600 S (4) Vdt ) ∫ Idt ) 3600∫ RV dt ) 3600 5 ∫ 5 t
t
t
0
0
0
where S represents the area under the curves in Figure 3. When the concentrations of Na2Cr2O7 and H2SO4 were 1 and 3.6 M, respectively, the result of the numerical integral for S was 16.9. Thus, Q ) 12 168 C (Coulomb). In theory, when the concentration of Na2Cr2O7 is 1 M, the amount of electric charge that the batteries should release is 2 (mol of Cr6+) × 3 (gained electrons) × 96 485 (Faraday’s constant) × 50 (volume of the cathode zone, mL)/1000 (the volume of 1 mol of Na2Cr2O7 held, mL) ) 28 946 C. Hence, the ratio of the amount of charge that the batteries released actually and theoretically is 12 168/28 946 × 100% ) 42.04%. This shows that, when the concentrations of sulfuric acid arrived at 3.6 M, the batteries only released 42.04% amount of electric charge because some crystals formed at the carbon felt and membrane. Another reason of the low amount of electric charge was the lack of hydrogen ions. One can see from eq 1 that 1 M Na2Cr2O7 needs 14 M HCl, or 14 M HNO3, or 7 M H2SO4 (while the concentrations of the concentrated HCl, HNO3, and H2SO4 are 12, 14, and 18 M, respectively). 3.2.2. Case of 1 or 0.75 M Na2Cr2O7 and Mixed Acids of Different Proportion in the Cathode Zone and 4 or 5 M NH4Cl in the Anode Zone. The discharge characteristics of the Zn-Na2Cr2O7 batteries with 1 M Na2Cr2O7 and mixed acids of different proportion in the cathode zone and 4 M NH4Cl in the anode zone were indicated in Figure 5. From Figure 5, we can see that the discharge curve b of the batteries with 1.8 M H2SO4 + 2.4 M HCl was close to the discharge curve a of the batteries with 3.6 M H2SO4. The discharge curve c of the batteries with 3.6 M H2SO4 + 2.4 M HCl did not exhibit special characteristics, and it only became flatter than curve a. The discharge curve d of the batteries with 3.6 M H2SO4 + 2.4 M HNO3 exhibited good characteristics, and the reason for this is that HNO3 itself is a oxidant. The output voltage of the batteries with 2.4 M HCl + 2.8 M HNO3 was lower without H2SO4. The status of some solid products formed at the carbon felt or membrane for various systems in Figure 5 was shown in Table 3. One can see from Table 3 that hardly any or a little solid product formed at the carbon felt or membrane for the 1.8 M H2SO4 + 2.4 M HCl mixed acids system. The discharge characteristics of the batteries with 0.75 M Na2Cr2O7 and mixed acid of different proportions in the cathode zone and 5 M NH4Cl in the anode zone were shown in Figure 6. It can be seen that, from 3.6 M H2SO4 to 3.6 M H2SO4 + 2.4 M HCl mixed acids, the output voltage of the batteries increased slightly with the rise of the concentrations of hydrogen ions in the cathode zone. The status of some solid products formed at the carbon felt or membrane for various systems in Figure 6 was shown
in Table 4. From Tables 3 and 4, one can see that, when the concentration of Na2Cr2O7 was reduced, the solid products formed at the carbon felt or membrane decreased considerably. From Table 4, one can also see that the solid products formed at the carbon felt or membrane for 3.6 M H2SO4 and 1.2 M HCl systems were more than 3.6 M H2SO4 and 2.4 M HCl systems. This may be because more CrCl3, which is more diffluent, was produced when the concentrations of HCl increased. 3.2.3. Case of 3.6 M H2SO4, 2.4 M HCl, and Various Concentrations of Sodium Bichromate in the Cathode Zone and 5 M NH4Cl in the Anode Zone. Figure 7 was the discharge curves of the Zn-Na2Cr2O7 batteries with 3.6 M H2SO4, 2.4 M HCl, and various concentrations of Na2Cr2O7 in the cathode zone and 5 M NH4Cl in the anode zone. Figure 7 indicated that the output voltages of the batteries arrived at a maximum when the concentrations of sodium bichromate arrived at 0.75 M. The reason for this is that there was not enough active matter in the solution when the concentrations of sodium bichromate were lower and there were not enough acidity and many solid products formed at the carbon felt (see Table 5) when the concentrations of sodium bichromate were higher. 3.3. Discharge Characteristics of the Zn-(NH4)2Cr2O7 Batteries. 3.3.1. Case of 3.6 M H2SO4 and Different Concentrations of Ammonium Bichromate in the Cathode Zone and 4 M NH4Cl in the Anode Zone. The discharge characteristics of the batteries with 3.6 M H2SO4 and various concentrations of (NH4)2Cr2O7 in the cathode zone and 4 M NH4Cl in the anode zone were shown in Figure 8. It was similar to the case of Figure 7 that the output voltages of the batteries arrived at a maximum when the concentrations of ammonium bichromate arrived at 0.75 M. From Figures 7 and 8, one can see that the discharge time of the batteries with (NH4)2Cr2O7 was shorter than with Na2Cr2O7. This relates to the following fact: solid products more easily formed at the carbon felt and membrane for the ammonium bichromate batteries than the sodium bichromate batteries (see Table 5). Of course, HCl possesses a certain influence. 3.3.2. Case of 0.75 M (NH4)2Cr2O7 and Mixed Acid of Different Proportions in the Cathode Zone and 5 M NH4Cl
Figure 8. Discharge characteristic of the batteries with 3.6 M H2SO4 and various concentrations of (NH4)2Cr2O7 in the cathode zone and 4 M NH4Cl in the anode zone.
1672 Energy & Fuels, Vol. 23, 2009
Shimin et al.
Figure 9. Discharge characteristic of the batteries with 0.75 M (NH4)2Cr2O7 and mixed acid in the cathode zone and 5 M NH4Cl in the anode zone. Table 6. Status of Some Solid Products Formed at the Carbon Felt or Membrane for Various Systems in Figure 9
carbon felt membrane
1.8 M H2SO4 + 1.2 M HCl
1.8 M H2SO4 + 4.8 M HCl
3.6 M H2SO4 + 1.2 M HCl
more nothing
few few
more nothing
Figure 11. Discharge characteristics of the Zn-Na2Cr2O7 and Zn-(NH4)2Cr2O7 batteries with 0.5 M bichromate, 3.6 M H2SO4, and 2.4 M HCl in the cathode zone as well as 4 M NH4Cl in the anode zone.
Figure 12. V2 figure of Zn-(NH4)2Cr2O7 batteries with 0.75 M (NH4)2Cr2O7, 1.8 M H2SO4, and 4.8 M HCl in the cathode zone as well as 5 M ammonium chloride in the anode zone.
Figure 10. Discharge characteristics of the Zn-(NH4)2Cr2O7 batteries with 0.75 M (NH4)2Cr2O7, 1.8 M H2SO4, and 4.8 M HCl in the cathode zone and NH4Cl of different concentrations in the anode zone. Table 7. Status of Some Solid Products Formed at the Carbon Felt or Membrane for Various Systems in Figures 10 and 11 Figure 10 carbon felt membrane
Figure 11
4M
5M
(NH4)2Cr2O7
Na2Cr2O7
nothing nothing
few few
nothing nothing
alittle alittle
in the Anode Zone. The discharge characteristic of the batteries with 0.75 M (NH4)2Cr2O7 and mixed acid of different proportions in the cathode zone and 5 M NH4Cl in the anode zone were denoted in Figure 9. One can see that, for two systems of 3.6 M H2SO4 + 1.2 M HCl and 1.8 M H2SO4 + 4.8 M HCl, their concentrations of hydrogen ions in the cathode zone are the same but the discharge characteristic of the latter was better. The reason for this can be found from Table 6: hardly any solid product formed at the carbon felt and membrane for the system of 1.8 M H2SO4 + 4.8 M HCl.
3.3.3. Case of 0.75 M (NH4)2Cr2O7, 1.8 M H2SO4, and 4.8 M HCl in the Cathode Zone and NH4Cl of Different Concentrations in the Anode Zone. Figure 10 was the discharge characteristics of the Zn-(NH4)2Cr2O7 batteries with 0.75 M (NH4)2Cr2O7, 1.8 M H2SO4, and 4.8 M HCl in the cathode zone and 4 or 5 M NH4Cl in the anode zone, and the corresponding electromotive forces were 2.243 and 2.285 V, respectively. Figure 10 shows that, when the concentrations of NH4Cl increased, the output voltages of the batteries increased. This was because, when the concentrations of NH4Cl increased, the electric ability in the anode zone increased. However, 5 M has arrived at the solubility of ammonium chloride. The status of some solid products formed at the carbon felt or membrane for various systems in Figure 10 was shown in Table 7. 3.4. Comparison of Discharge Characteristics of the Zn-(NH4)2Cr2O7and Zn-Na2Cr2O7 Batteries. The discharge characteristics of the Zn-Na2Cr2O7 and Zn-(NH4)2Cr2O7 batteries with 0.5 M bichromate, 3.6 M H2SO4, and 2.4 M HCl in the cathode zone as well as 4 M NH4Cl in the anode zone were shown in Figure 11. From Figure 11, we can see that the output voltage of the Zn-(NH4)2Cr2O7 batteries was slightly higher than that of the Zn-Na2Cr2O7 batteries. This is because the electric ability of NH4+ in (NH4)2Cr2O7 is higher than that of Na+ in Na2Cr2O7. The discharge time of the Zn-Na2Cr2O7
Aqueous Zinc-Bichromate Battery
Energy & Fuels, Vol. 23, 2009 1673
and Zn-(NH4)2Cr2O7 batteries is almost the same in Figure 11. However, when the concentrations of Zn-Na2Cr2O7 and Zn-(NH4)2Cr2O7 were larger, the discharge time of the Zn-Na2Cr2O7 batteries was longer than that of the Zn(NH4)2Cr2O7 batteries, as shown in Figures 7 and 8. The reason for this was that solid products more easily formed at the carbon felt or membrane for the (NH4)2Cr2O7 system than the Na2Cr2O7 system (see Table 5). Considering these factors, using Na2Cr2O7 was a better choice. The status of some solid products formed at the carbon felt or membrane for various systems in Figure 11 was shown in Table 7. 3.5. Calculation of the Energy Density of the Zn(NH4)2Cr2O7 Batteries. Now, we calculate the energy density of the Zn-(NH4)2Cr2O7 batteries with 0.75 M (NH4)2Cr2O7, 1.8 M H2SO4, and 4.8 M HCl in the cathode zone as well as 5 M ammonium chloride in the anode zone (see Figure 10). First of all, we calculate the theoretical gravimetric energy density of the Zn-(NH4)2Cr2O7 batteries according to the following reaction: 3Zn + (NH4)2Cr2O7 + 7H2SO4 f resultant
(5)
The mass of 3 mol of Zn + 1 mol of (NH4)2Cr2O7 + 7 mol of H2SO4 is 3 × 65.38 g + 252.06 g + 7 × 98 g ) 1134.2 g ) 1.1342 kg Because E° ) 2.093 V, the theoretical gravimetric energy density of Zn-(NH4)2Cr2O7 batteries is 2.093 V × 1 × 2 × 3 × 96485 C × 1 h ) 296.75 W h kg-1 3600 s × 1.1342 kg while the theoretical gravimetric energy density of the Pb-PbO2 batteries is 170.30 W h kg-1. If above reaction is changed into 3Zn + (NH4)2Cr2O7 + 14HCl f resultant
(6)
the theoretical gravimetric energy density of Zn-(NH4)2Cr2O7 batteries is 350.888 W h kg-1. Second, we calculate the actual gravimetric energy density of Zn-(NH4)2Cr2O7 batteries with 0.75 M (NH4)2Cr2O7, 1.8 M H2SO4, and 4.8 M HCl in the cathode zone and 5 M ammonium chloride in the anode zone according to the following reaction: 3Zn + (NH4)2Cr2O7 + xH2SO4 + yHCl f resultant
(7)
Supposing that the total amount of the substance added to the batteries is n, then n ) 3 × 0.75 mol of Zn + 0.75 mol of (NH4)2Cr2O7 + 5 mol of NH4Cl + 1.8 mol of H2SO4 + 4.8 mol of HCl Thus, the total mass of the substance added to the batteries is 3 × 0.75 × 65.38 g + 0.75 × 252.06 g + 5 × 53.49 + 1.8 × 98 + 4.8 × 36.5 ) 955.204 g ) 0.9952 kg The densities of Zn, (NH4)2Cr2O7, NH4Cl, H2SO4, and HCl are 7.13, 2.155, 1.527, 1.84, and 1.18, respectively. Hence, the total volume of the substance added to the batteries is 3 × 0.75 × 65.38/7.13 + 0.75 × 252.06/2.155 + 5 × 53.49/1.527 + 5 + 20 ) 308.5 (mL) However, n is equal to the total amount of the substance added to 20 batteries because, when the concentration of (NH4)2Cr2O7 is 0.75 M, 1000 mL of solution contains 0.75 mol of (NH4)2Cr2O7. The volume of the cathode zone is 50 mL, and
the volume of 20 cathode zones is 1000 mL. Therefore, the volume of the solvent added to 20 batteries is 2000 - 308.5 ) 1691.5 (mL) Supposing that the density of solvent is 1, the mass of the solvent is 1.6915 kg. Hence, the mass of the solute and solvent added to 20 batteries is 0.9952 + 1.6915 ) 2.6867 (kg) If we ignore the mass of the electrolytic cell, the total mass of 20 batteries is 2.6867 kg. Therefore, the actual gravimetric energy density of Zn-(NH4)2Cr2O7 batteries is w)
20 2.6867
∫
16
0
20 V2 dt ) R 2.6867
∫
16
0
4 V2 dt ) 5 2.6867
∫
16
0
V2dt )
4A (8) 2.6867 where V is the output voltage of the batteries and A represents the area under the curve in Figure 12. The result of the numerical integral for A is 34.87704. Thus, w ) 51.93 W h kg-1, while the actual energy density of the Pb-PbO2 batteries is 28-40 W h kg-1. Now, we calculate the amount of electric charge that the batteries released. The result of the numerical integral for the area S under the solid curve in Figure 10 is 23.09. Substituting S into eq 4, we obtain Q ) 16 624.8 C. In theory, when the concentration of Na2Cr2O7 is 0.75 M, the amount of electric charge that the batteries should release is 2 × 0.75 × 3 × 96 485 × 50/1000 ) 21 709 C. Hence, the ratio of the amount of electric charge that the batteries released actually and theoretically is 16 624.8/21 709 × 100% ) 76.58%. The result of the numerical integral for the area S under the solid curve in Figure 11 is 16.89. Substituting S into eq 4, we obtain Q ) 12 161 C. In theory, when the concentration of Na2Cr2O7 is 0.5 M, the amount of charge that the batteries should release is 2 × 0.5 × 3 × 96 485 × 50/1000 ) 14 473 C. Thus, the ratio of the amount of charge that the batteries released actually and theoretically is 12 161/14 473 × 100% ) 84.03%. This data is twice as large as the corresponding data, 42.04%, for the curve a2 in Figure 3. 4. Conclusions (1) The standard electrode potential of Cr2O72-/Cr3+, 1.33 V (versus NHE), is very high. One chromium ion with a valence of +6 can gain three electrons during the reduction reaction. A total of 1 mol of bichromate contains 2 mol of chromium ions with a valence of +6. The solubility of bichromate is very large. These excellent characters make Cr2O72-/Cr3+ become an attractive electrode when an energy crisis is fast approaching. (2) The discharge time and output voltage of the zinc-bichromate batteries increase with the augment of concentrations of H+ in the cathode zone and the decrease of solid products formed at the carbon felt or membrane. (3) (NH4)2Cr2O7 more easily forms solid products at the carbon felt or membrane than Na2Cr2O7. The concentrations of bichromate are the main factors of the formation of solid products at the carbon felt or membrane. When the concentrations of Na2Cr2O7 are smaller than 0.75 M, hardly any solid product formed at the carbon felt or membrane. (4) The output energy of the zinc-bichromate batteries with 0.75 M bichromate, 1.8 M H2SO4, and 4.8 M HCl in the cathode zone and 5 M ammonium chloride in the anode zone is larger. The actual gravimetric energy density of the batteries arrived at 51.93 W h kg-1. The ratio of the amount of charge that the batteries released actually and theoretically is 16 624.8/21 709 × 100% ) 76.58%. EF800848P
