562
J. A. DUIBMAN AND W. F. GIAUQUE
Thermodynamics of the Lead Storage Cell. The Heat Capacity and Entropy of Lead Dioxide from 15 to 318'K1 by J. A. Duisman and W. F. Giauque Low Temperature Laboratory, Departments of Chemistry and Chemical Engineering, University of California, Berkeley, California 94730 (Received July 17,1967)
The heat capacity of an electrolytic sample of lead dioxide has been measured from 15 to 318°K. The composition was PbO2.1.519 X 10-2Pb0.2.558 X 104H20. After correction, the entropy of PbOz was found to be 17.16 gibbs/mol at 298.15'K. The entropy change in the cell reaction, H2 PbO2 H2S04 (z M ) = PbSO4 2H20 (in x M H2S04), calculated from the third law of thermodynamics, is in excellent agreement with dE/dT, as determined by Beck, Singh, and Wynne-Jones. This agreement supports the use of third-law data on PbO2, Pb, PbS04, and H2S04 (z M ) to calculate the temperature coefficient of the lead storage cell. The table of Giauque, Hornung, Kunzler, and Rubin, on the thermodynamic properties of aqueous sulfuric acid, has been extended from 1 to 0.1 M . A table giving the change of voltage of the lead storage cell over the range 060" and from 0.1 to 14 M H2S04 has been based on the third law of thermodynamics. For the reaction P b PbO2 2HzS04 (pure) = 2PbS04 2H20 (pure), AF" = -120,200 cal/mol and AH" = -121,160 cal/mol at 298.15"K. Numerous unsuccessful attempts to prepare stoichiometric PbO2 are described.
+
+
+
For some time, one of the projects of this laboratory has been directed toward the accumulation of third-law entropy values on the reactants and products of the lead storage cell. The present work on lead dioxide completes the necessary data. Previous researches are on lead12aqueous sulfuric acidJ3and lead sulfates4 The possibility that any of these substances might have "frozen in" entropy due to remnent disorder at limiting low temperatures has always been considered as negligible, with the exception of aqueous sulfuric acid, where hydrogen bonds at least gave rise to suspicion. However, this possibility was thoroughly eliminated by highly accurate third-law agreementa among the phases HzS04, H2S04.H201 H2804' 2H20, HzS04.3H20, HzS04.4H20, and H2S04.6.5HzO. A very significant third-law comparison is available by means of the cell reaction H2
+ PbOz + HzS04 (Z M ) PbS04 + 2Hz0 (in z M H2S04) =:
(1) in which the PbOz, H2S04(aq),and PbS04 are largely subject to the same conditions as those existing in the lead storage cell. The principal investigations on cell 1, which cover the range up to about 7 M H2S04,are those of Hamer16 and Beck, Singh, and Wynne-JoneslBwho review previous work. There is a t least a reasonable expectation that the variable sulfuric acid concentration does not alter the thermodynamic properties of the solid phases in this cell. Thus, since the thermodynamic properties of aqueous sulfuric acid are accurately The J O U Tof~Phyaical Chemistry
+
+
+
known, one of the tests of the above cell is to investigate the effect of H2S04concentration on the cell potential, and we are particularly interested in its effect on the temperature coefficient. Beck, Singh, and WynneJones* apply this test to their data by means of the Gibbs-Helmholz equation. They also calculate the results of Hamer,5 who presents his temperature coefficient data only as smoothed equations. Hamer's results show a total spread in the calculated heat of reaction of the order of 400 cal/mol. Their own data agree quite accurately with the known properties of aqueous sulfuric acid. We have now found that the temperature coefficients of the cell potential measured by Beck, Singh, and Wynne-Jones,6 agree with those derived from low-temperature heat capacity measurements and the third law of thermodynamics, thus providing a very substantial basis for the use of the third law in evaluating the temperature coefficient of the lead storage cell. For this cell the generally accepted reaction is (1) This work was supported in part by National Science Foundation Grant GP-6782. (2) P.F. Meads, W. R. Forsythe, and W. F. Giauque, J. Am. Chem. SOC.,63, 1902 (1941). (3) W.F. Giauque, E. W. Hornung, J. E. Kunzler, and T. R. Rubin, ibid., 82, 62 (1960). (4)K. Gallagher, G. E. Brodale, and T. E. Hopkins, J . Phys. Chem., 64, 687 (1960). (6)W.J. Hamer, J . Am. Chem. Soc., 57, 9 (1936). (6) W. H. Beck, K. P. Sin& and W. F. K. Wynne-Jones, Tram. Faraday Soc., 55, 331 (1969).
THERMODYNAMICS O F THE
Pb
563
LEADSTORAGE CELL
+ PbO2 + l2HzSO4 (5 M HzS04) = 2PbS04 + 2Hz0 (in 2 M H2S04)
(2)
Preparation and Analysis of PbOz Samples. This research was started with the hope that some way could be found to prepare a sample, close in composition to stoichiometric I'bOz. We did not succeed. In every case there was a deficiency of active oxygen. It was also found that small amounts of water could not be removed by drying in air, oxygen, or under vacuum without serious loss of oxygen. This gave rise to the suspicion that water molecules may occupy some positions to the exclusion of the second oxygen atom as an alternative or additional explanation to simple oxygen vacancies. Meyers' has also commented on his inability to dry Pb02. An additional problem was that many preparations were not crystalline in the macroscopic sense. Experimenters, preparing PbOz for use in cells, typically digest it with hot aqueous sulfuric acid with the expectation that any PbO present would be converted to PbS04. Since PbS04 is a product of the lead cell, its presence is also typically ignored, which seems reasonable. However, the typical ignoring of the analysis of Pb02 samples for oxygen content by experimenters seems much less reasonable. For analysis, samples were reduced by means of a known excess of primary standard grade AszOa in 2 m hydrochloric acid: method A, the excess As203 was titrated with standardized potassium permanganate solution from a weight buret; the color of the KMn04 served as the indicator; method B, the acid solution was neutralized with sodium bicarbonate, and the lead ions were complexed by the addition of ethylenediaminetetraacetic acid (EI4TA)s immediately before titration with a standardized iodine solution to a starch end point. The present attempts to obtain stoichiometric PbOz may be divided into five categories: 1, chemical preparations ; 2, elevated temperatures and high oxygen pressures; 3, attempts at slow crystal growth in liquids at 1 atm; 4, PbO2 mineral; and 5 , electrolytic preparations. Chemical Preparations. Most of these experiments involved the oxidation of sodium plumbite in sodium hydroxide solu.tion with chlorine, bromine, hydrogen peroxide, and 37 M nitric acid. Also attempted was the hydrolysis of a saturated solution of lead tetraacetate in glacial acetic acid. Three agents were used: (1) water, (2) acetic acid containing 10 vol % water, and (3) absolute ethanol. One short experiment involved the hydrolysis of lead tetrachloride with precooled water in hydrochloric acid solution a t 0". The product was identical in appearance with the starting material (magnification = SOX). No andysis was attempted. None of these preparations produced a crystalline product. Experiments at Elevated Temperatures and High
Oxygen Pressures. These experiments were performed in a steel bomb. In order to protect the bomb from corrosion, a nickel reaction vessel was made with a Teflon check valve built into its top. The function of this valve was to allow oxygen to enter the reaction vessel when the bomb was pressurized but to prevent sodium hydroxide solution from leaking out. In order to release the pressure inside the reaction vessel when the bomb was vented, a disk-type safety valve was also built into the top of the reaction vessel. The usual load for this apparatus was a slurry of chemically prepared lead dioxide in 5 m sodium hydroxide. The bomb was pressurized with oxygen gas to 2200 psig. Pressures as high as 8000 psig were obtained a t the highest temperatures. Experiments were made from 240 to 320" a t 20" intervals for periods ranging from 5 days to 2 weeks. At the higher temperatures, small crystals were indeed formed, but analysis by method B disclosed the active oxygen content to be only 97-98% of the theoretical amount for PbOz. Also attempted was the formation of crystalline lead dioxide from powdered PbOz in a melt of 23.07% LiN03, 53.85y0 KN03, and 23.07?70 NaNOs, by weight. The melting point of this mixture was 145 f 5". The experiment was performed a t an oxygen pressure of 4000 psig and a temperature of 214 rJ, 5". Microscopic examination (60X) of the lead dioxide indicated no increase in particle size, and analysis by method B showed no significant increase in active oxygen content, which was typically 98.5% of the theoretical for PbOz, after the mixture was held a t these conditions for 7 days. This experiment was repeated with 2% added Na202. The mixture was allowed to stand for 10 days a t 225 & 5" under a total pressure of 4000 psig. Again no crystalline product was obtained. Finally a mixture of 200 g each of PbO, KN03, and KCIOz was placed in the nickel container and heated to a temperature of 260" under 2000 psig of oxygen in the bomb. A brown powder was formed which was identical in appearance with ordinary chemically prepared PbOz. Its analysis gave an active oxygen content of 98y0 of the theoretical for PbOz. Solubility Experiments Performed under a Pressure of 1 Atm. The idea behind these experiments was that if a liquid could be found in which lead dioxide had a reasonable solubility (say, mol/l.), this liquid phase would provide a mechanism for the Pb02 in the powdered form to convert itself to a macroscopic crystalline form. The starting material in all of these experiments was commercially available lead peroxide, a brown powder. The most thoroughly investigated solvent was concentrated nitric acid, and 1: 2, 1: 1, and 2: 1 dilu(7) R. G . Meyers, Anal. Chem., 20, 654 (1948). (8) R. Pribil and J. Cihalik, Collect. Czech. Chem. Commun., 20, 562 (1955).
Volume 72, Number R
February 1968
564 tions with water. A Pyrex flask containing nitric acid mixed with the PbOz powder was placed in a thermostat at 35" and mechanically agitated for periods up to 6 months. The PbO2 was inspected under a microscope before and after this treatment. No evidence of any increase in particle size was observed. Analysis by method B showed that the active oxygen content of the material had actually decreased. Other experiments a t 100" for shorter periods of time showed similar results: before, 98.5-98.7y0; and after, 98.0-98.4% of the theoretical active oxygen. Other solvents were tested by the simple expedient of placing them in a suitable container with some PbO2 powder and stirring them with a Teflon-clad magnet a t ambient temperature for several weeks. niIicroscopic examination indicated all these attempts to be failures. Among the solvents tested in this manner were: perchloric acid (HC104~2H20),hydrofluoric acid (48%), sodium hydroxide (various concentrations), formic acid, acetic acid (various concentrations), and acetic acid with 10% acetic anhydride. Since lead dioxide has properties in common with metals, liquid ammonia was also tested as a solvent, merely by placing some powdered PbO2 in a dewar full of solid ammonia, allowing the ammonia to melt, and then slowly evaporating over a period of about 16 hr. This experiment was performed in an explosion-proof cubicle to minimize the danger of an explosion. None occurred. Microscopic examination showed that the lead dioxide did not benefit from this treatment. In each case the mixture of Pb02plus test solvent was poured onto a medium-porosity glass frit and washed with water, 1 : l nitric acid (-18 N), and then more water. It was then dried in air a t 150" for 2-4 hr. Mineral Pb02. A sample of naturally occurring lead dioxide (Plattnerite) was obtained through the courtesy of Professor A. Pabst for this investigation. Its source was a mine in Mullan, Idaho. Analysis of this black crystalline material by method A showed it to contain -92% of the theoretical amount of active oxygen for PbO2. Electrolytic Experiments. Various materials were tested for use as anodes. Among them were graphite, Hastelloy C (Union Carbide Stellite Co., Kokomo, Ind.), nickel, stainless steel, and platinum. Platinum was found to be the most suitable, and most of the experiments utilized a rotating cylinder 6 cm in diameter and 9 cm tall, made of 0.013 in. thick platinum sheet. Various electrolytes were tested, the most notable of which was a nearly saturated solution of lead perchlorate in perchloric acid-water eutectic.9 The electrolysis was perforped a t anode current densities of 1 and 2 mA/cm2, using a platinum anode and a graphite cathode a t temperatures near -50". Analysis of the product by method A gave 96.4% of the theoretical active oxygen for PbO2, with no significant difference The Journal of Physical Chemistry
J. A. DUISMAN AND W. F.GIAUQUE between the materials prepared at the different current densities. Also electrolyzed were solutions of lead perchlorate in water, lead acetate in water and in glacial acetic acid, lead nitrate in water with various nitric acid concentrations, and solutions of sodium plumbite a t various concentrations of plumbite and sodium hydroxide. A lead cylinder served as a cathode in these experiments. The effect of acid concentration was investigated using lead nitrate-nitric acid solutions in water by adding neutral lead nitrate solution to the electrolysis solution at such a rate to maintain the concentration of nitric acid at a fixed value. Experiments covered the range from nearly neutral solutions to a hydrogen ion concentration of 2 M. At the highest acidities, the active oxygen content of the product declined, but there was no clear evidence that a solution of 0.1 M "03 was superior to one with 1.0 M "03. It was suspected that NO2- ions, formed at the cathode by reduction of Nos- ions, might be having an adverse effect on the oxygen content of the sample. This possibility was investigated and eliminated through the use of a solution of lead nitrate and copper nitrate as electrolyte, since Collat and Linganel" have shown that electrolytic reduction of nitrate ions proceeds all the way to NH4+in the presence of Cu2+. No significant change in the active oxygen content of the samples produced was observed. In the case of the lead nitrate solutions, the effect of rotating the anode a t different speeds was also investigated. It was observed that a t high speeds the porosity of the sample decreased slightly. The products, prepared at speeds higher than 100 rpm, all had essentially the same active oxygen content. The effect of current density was also investigated. Using 1 m lead nitrate solution as the electrolyte, several current densities ranging from 1.2 to 46.3 d/ cm2 were tested. Again, no significant effect on the active oxygen content was observed. However, the samples prepared a t low current densities had a more crystalline appearance. All of the samples contained about 98.5% of the theoretical active oxygen for PbO2. Since the search for a method of preparing stoichiometric Pb02 had produced nothing better, it was decided that the heat capacity of the electrolytic material would be measured and corrections applied to the experimental heat capacity for the effect of the impurities. Preparation of the Calorimetric Sample. The calorimetric sample was prepared by electrolysis of 1 M aqueous lead nitrate. The rotating cylindrical platinum anode was 6 cm in 0.d. and 9 cm long. It was concentric with a cylindrical lead cathode. The electrodes (9) A. Seidell and W. F. Linke, "Solubilities of Inorganio Compounds," 4th ed, John Wiley and Sons, Inc., New York, N. Y., 1968. (10) J. W. Collat and J, J, Lingane, J . Am. Chem. Soc., 7 6 , 4214 (1964).
565
THERMODYNAMICS OF THE LEADSTORAGE CELL were separated by a vessel of sintered aluminum oxide, which was friction-fitted internally with four radial stationary Teflon paddles to facilitate stirring within the anode chamber. The base of the platinum cylinder was fitted with a Teflon plug, so that only the outer surface served as an anode. As recommended by Palmaer,ll the platinum cylinder was rotated a t 450 f 20 rpm. The lead nitrate solution was prepared from Baker Analyzed Pb(NO&. The anode current density was A/cm2. This current stabilized a t about 2.3 X density was chosen because, according to Singh'sla experience, onky p-PbOz (tetragonal) was formed by electrolysis of neutral solutions of lead nitrate with a current density of 1-2 mA/cm2. During the electrolysis, new solution was added to the anode chamber to maintain a steady flow rate of 1 cmS/ min through the porous aluminum oxide diaphragm. This was done to prevent a decrease in lead ion concentration and to keep the hydrogen ion concentration from rising. The product was a dense gray layer with a definite metallic luster. The conglomerate was broken with a mortar and pestle to pass a 10 mesh/in. screen, placed in a beaker with 2 1. of distilled water, and stirred vigorously with a motor-driven stirrer for 12 hr. This washing procedure was repeated five times. The sample was then treated with 2 1. of ~ 2 M4"OS for 3.5 hr in an attempt to dissolve any oxide lower than PbOz. The water-washing procedure was then repeated four times. It was dried in air a t 125" for 2 hr. Two batches were prepared in this manner. Analysis of the Sample. The two batches were analyzed separately for active oxygen by treating samples of approximately 2 g with an excess of an accurately known weight of primary standard grade arsenious oxide, in the presence of hydrochloric acid, under 1 atm of nitrogen. The reaction flask was fitted with a reflux condenser to prevent evaporation of arsenic trichloride. The solution was then neutralized with sodium bicarbonate and the lead ions complexed with EDTA.* The excess arsenite was titrated from a weight buret to a starch end point with standard iodine solution. In each case, a measured correction was applied for the effect of the starch and EDTA on the end point. The results were as follows: batch I (weight per cent of active 0),6.5880; 6.5826; 6.586070; and 6.5855 f 0.0023, av wt yo; and batch I1 (weight per cent of active 0), 6.5753; 6.5867; 6.5746%; and 6.5789 0.0052, av w t %. A 306.74-g sample of batch I was then thoroughly mixed with 185.92 g of batch 11, giving a weighted average of 6.5830 f 0.0034% for the active oxygen content. The combined sample wm then analyzed for lead by converting approximately 2-g samples to lead sulfate. The results are given in Table I. A test was made for nitrate in the original sample,
Table I : Lead -Content of Combined Sample % Pb
% PbO
86.537 86.547 86.316" 86.550 AV 86.545 k 0.008% a
93.219 93.230 92.981" 93.233 93.227 k 0.009%
The third test was given no weight in computing the average.
using diphenylamine and concentrated sulfuric acid under the conditions suggested by Treadwell and Hall13 after dissolving it with acetic acid and hydrogen peroxide. The nitrate content of the sample was less than 0.005%, which was the limit of detection. The sample was analyzed for water by heating 55-g portions in a stainless steel tube with a diameter of about 2 cm; the water was swept through the tube into a weighed trap containing phosphorous pentoxide by a stream of dry nitrogen gas. A blank run was performed immediately before each determination, while the stainless steel tube was heated to a dull red heat by means of a gas-air torch. No water was evolved. Nitrogen gas was passed over the sample a t a rate of 3 l./min. As %I check, the experiment was repeated on the residue left in the stainless steel tube; no further water was evolved. Three samples were analyzed in this manner. The results for the water content of the combined sample are 0.1902, 0.1893, and 0.1894%. The average water content is 0.1896 f 0.0004%. As a check, one can add: Pb as PbO, 93.227 f: 0.009; 0, 6.583 f 0.0034; and HzO, 0.190 f 0.0004'%. The sum of these is 100.000 f 0.013%. All atomic weights used are based on the carbon-12 s~a1e.I~ Although we had enough confidence in Singh's'2 experience to complete heat capacity experiments on the above sample, we decided that an X-ray examination should be made to complete the record. This was done through the courtesy of Professor D. H. Templeton with the disagreeable result that the sample was found to contain some of the orthorhombic form (a-PbOz) discovered by Zoslavskii, Kondrashov, and Tolkachev.lS On the basis of rough intensity measurements, the investigated material may be estimated to have contained about 25% a-PbOz. In this situation, it was decided to prepare a new sample with a repetition of the heat capacity measurements. This sample was made in the manner used for (11) W.Palmaer, Medd. Nohelinst., 5 , 1 (1919). (12) K. P. Singh, personal communication. (13) F. P. Treadwell and W. T. Hall, "Analytical Chemistry," John Wiley and Sons, Inc., New York, N. Y., 1937,p 418. (14) A. E. Cameron and E. Wichers, J. Am. Chem. SOC.,84, 4175 (1962). (16) A. I. Zoslavskii, Y. D. Kondrashov, and S. S. Tolkachev, Dokl. Akad. Nauk SSSR, 7 5 , 559 (1950). Volume 78, Number W FehruaTy 1968
566 making the calorimetric sample with the following exceptions: (1) the current density used was 1.07 X loF3A cm-2 and (2) to maintain the lead and hydrogen ion concentrations, lead carbonate was added to the bath instead of the previously used flow system. Unfortunately the new sample contained about the same fraction of a-PbO2 (orthorhombic) as the previous one. Several additional samples were then prepared: I, electrolysis of 1 M Pb(NOa)z with H + maintained a t 0.5 M ; the current density was held a t 6 mA/cm2; and X-ray examination showed about the same fraction of a-PbOz as before; 11, the same procedure as method I was used, except that the bath was maintained at 60" during electrolysis; the a-Pb02 impurity persisted in about the same percentage; 111, aqueous 0.6 M PbAcz was electrolyzed, with a current density of about 2 mA/ cm2; X-ray examination showed an unacceptable, nearly amorphous substance in which about 1% of crystalline a-Pb02 was present; and IV, a commercial sample (method of preparation unknown, but presumably chemical) was washed with -18 M " 0 3 followed by distilled water; after drying in an oven a t 125", X-ray analysis showed a crystalline product with about 5% of the orthorhombic form. There was no reason to believe that any of the above materials would be appreciably superior to that already measured. Unfortunately we were unaware of the work of White, Dachille, and RoyJL6 which showed that a-PbO2 slowly converts to P-Pb02 at 100". Singh12has estimated that a-PbOz gives a potential 10 mV higher than P-Pb02 in reaction 1. There is probably little difference in their heat capacities. However, it is difficult to see how definitive answers can be obtained until stoichiometrically pure, macroscopically crystalline samples become available for each of these crystalline forms, in the considerable amounts needed for accurate calorimetry. Another difficult problem is concerned with the discovery of Clark, Schieltz, and Quirke," that PbsOs also has essentially the same tetragonal lattice as PbOz. The presence of this material, which is essentially oxygen deficient PbOz, could explain the difficulty in attaining 100% active oxygen in our numerous preparations and the difficulty in removing the PbO by treatment with acid. Davidson18 also carried out an X-ray analysis of Pb508 and showed an excellent photograph of crystals of this material prepared for his investigation. In the case of the sample prepared for our calorimetric measurements, we have simply assumed that the deficiency of active oxygen corresponds to a PbO content, and since the fractional amount is small, there is unlikely to be appreciable error due to a heat capacity correction based on the assumption of simple additivity. Heat Capacity Measurements. The low-temperature heat-capacity apparatus was similar to one described by The Journal of Physical Chemistry
J. A. DUISMANAND W. F. GIAUQUE Giauque and Egan,l8 and the particular copper calorimeter has been described by Kemp and Giauque.20 The more recent record of the calorimeter has been summarized by Bartky and Giauque.21 The original He thermometer temperature scale was corrected to 0" = 273.15"K. Laboratory standard copper-constantan thermocouple no. 105 was used as a temperature reference before and after every heat input. High-precision thermometry utilized a gold resistance thermometer heater wound on the exterior surface. The standard thermocouple was checked against the triple (13.95"K) and boiling (20.39"K) points of normal hydrogen, and the triple (63.14"K) and boiling (77.32"K) points of nitrogen. It was 0.09" low a t 13.95"K, 0.07" low at 20.37"K, and 0.01" low at both the triple and boiling points of nitrogen. Appropriate corrections were made. The heat capacity of 1 mol of sample is given in Table 11. The mole was defined as 1 mol of PbO2 0.01519 mol of PbO 0.02558 mol of H20,with a molecular weight of 243.040. The temperature rise of the individual runs is not given; however, the runs were continuous and the AT'S may be inferred approximately from the separations of their average temperatures. Corrections for the amount of PbO and H 2 0 present were made from the data of King22for red lead monoxide and the data of Giauque and Stout2afor ice, with an extrapolation above 0", since, as expected, the heat capacity measurements indicated that fusion of the entrapped H2O did not occur. The corrected values are given in Table I1 as the molal heat capacity of PbOz. The smoothed thermodynamic properties of PbO2 are given in Table 111. Although the measurements terminated near 308"K, they have been extrapolated to 330"K, since cell data involving PbO2 extend through this range. The extrapolation below 15°K was made by plotting CJT2 us. T , which leads to the result
+
+
CP(O-15"K)
=
7.0 X 10-5T3 gibbs/mol
S(O-15°K) = 7.0 X 10-5Ta/3 gibbs/mol S(15"K) = 0.079 gibbs/mol The heat capacity data of Millar24 on PbO2 average about 7% higher than the present results. As will be (16) W. B.White, F. Dachille, and R. Roy, J . Am. Ceram. Soc., 44, 170 (1961). (17) G. L.Clark, N. C. Schieltz, and T. T. Quirke, J. Am. Chem. Soc., 59, 2305 (1937). (18) H.R. Davidson, Am. Mineralogist, 26, 18 (1941). (19)W. F. Giauque and C. J . Egan, J. Chem. Phys., 5, 45 (1937). (20) J. D. Kemp and W. F. Giauque, J. Am. Chem. SOC., 59, 79 (1937). (21) I. R.Bartky and W. F . Giauque, {bid., 81, 4169 (1959). (22) E.G. King, ibid., 80, 2400 (1958). (23) W. F. Giauque and J. W. Stout, ibid., 58, 1144 (1936). (24) R. W. Millar, (bid., 51, 207 (1929).
567
THERMODYNAMICS OF THE LEADSTORAGE CELL Table 11: Heat Capacity of Lead Dioxide Samplea~b~o T,
CP
QK
Sample
13.87 15.56 17.65 19.44 21.48 23 -49 25.33 27.45 30.23 33.63 37.47 41.64 45.73 50.31 55.30 60.29 65.90 72.03 78.43 84.96 91.52 98.41
Series 2 0.168d 0.276 0.397 0.524 0.696 0.878 0.987d 1.231 1.478 1.799 2.137 2.590 3.001 3.410 4.061d 4.378 4.879 5.375 5.864 6.330 6.783 7 229
71.42 78.38 85.54 91.65 98.05 104.53 111.21 117.37 126.05 133.06 140.13 147.27 154.33 161.14 168.03 179.42 186.39 193.56 200.65 207.14 214.44 221.92 229.63 237.09 244.42 251.58 258.61 265.76 272.61 279.12 286.67 295.65 304.34
Series 1 5.311 5.904 6.363 6.793 7.208 7.573 8.029 8.403 8.897 9.269 9.641 10.040 10.358 10.683 11.000 11.448 11.755 11.999 12.222 12.546 12.764 13.043 13.394 13.495 13.697 13.884 14.096 14.351 14.405 14.572 14.805 14.918 15.227
I
Table I11 : Thermodynamic Properties of Lead Dioxide5gb
CP
T, "K
PbOv
0.157d 0.262 0.377 0.500 0.666 0.842 0. 945d 1.182 1.421 1.732 2.059 2.501 2.903 3.302 3.943d 4.251 4.741 5.226 5.704 6.159 6.602 7.037 5.172 5.744 6.191 6.611 7.016 7.371 7.818 8.183 8.665 9.028 9.392 9.782 10.092 10.408 10.718 11,153 11.452 11.688 11.903 12.220 12.430 12.701 13.044 13.137 13.332 13.517 13.716 13.964 14.012 14,173 14.398 14.502 14.803
5 Sample: Pb0~~0.01519Pb0.0.02558H20;molecular weight 243.040; and C, is in gibbs per mole. b482.087-g sample in the calorimeter. 1 defined cal = 4.1840 abs J; 1 gibbs = 1 defined cal/defi.ned OK. d These measurements were given no weight when the smooth curve was drawn.
15 20 25 30 35 40 45 50 55 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 273.15 280 290 298.15 300 310 320 330 (I
(HO
CPO
0.238 0.539 0.982 1.407 1.848 2 339 2.827 3.284 3.765 4.231 5.067 5.812 6.488 7.141 7.762 8.334 8.869 9.416 9.908 10.35 10.79 11.19 11.58 11.94 12.27 12.63 12.93 13.21 13.47 13.74 14.01 14.08 14.23 14.45 14.58 14.60 14.73 (14.85) (14.97) I
SO
0.079 0.184 0.351 0.567 0.817 1.095 1.364 1.685 2.021 2 369 3.085 3.812 4.536 5.254 5.964 6.664 7.352 8.029 8.696 9.350 9,991 10.619 11.234 11.838 12.428 13.008 13.577 14.135 14.679 15,213 15.736 15.899 16.250 16.753 17.156 17.246 17.727 (18.196) (18.655)
All units are gibbs per mole. = 1 defined cal/defined
J; 1 gibbs
-
-(PO
-
HOe)/T
H0d/T
0.059 0.136 0.260 0.414 0.588 0.775 0.949 1.160 1.375 1.603 2.039 2.466 2.875 3.270 3.650 4.017 4.370 4.710 5.041 5.359 5.666 5.962 6.247 6.523 6.789 7.047 7.297 7 * 539 7.771 7.996 8.213 8.280 8.424 8.628 8.790 8325 9.014 (9.194) (9.367)
0.020 0.048 0.091 0.153 0.229 0.320 0.415 0.525 0.646 0.766 1.046 1.346 1.661 1.984 2.314 2.647 2.982 3.319 3.655 3.991 4.325 4.657 4.987 5.315 5.639 5.961 6.280 6.596 6.908 7.217 7.523 7.619 7.826 8.125 8.366 8.421 8.713 (9,002) (9.288)
1 defined cal = 4.1840 abs OK.
evident from the third-law comparison to be given below, his entropy value of 18.27 gibbs/mol a t 25", in comparison with the present result of 17.16 gibbs/moI, would lead to a discrepancy of about 1 gibbs/mol. The Reaction of Hydrogen, Aqueous Sulfuric Acid, and Lead Dioxide. Beck, Singh, and Wynne-Joness measured the emf of the cell for the reaction
H2
+ PbO2 + HzS04 (ZM ) = PbSO4 + 2H20 (in z M HzS04)
a t 5, 10, 20, 25, 35, 45, and 55", with ten sulfuric acid concentrations which ranged from 0.1000 to 7.199 M . Their measurements were made with great care and showed excellent reproducibility. They have calculated the temperature coefficient of the emf a t 25" Volume 72, Number 2
Felrruary 1968
J. A. DUISMAN AND W. F. GIAQUUE
568 Table IV : Entropy Change from the Third Law and from the Temperature Coefficient of Cell Reaction I%*
--dE Heso4
0.1000 0.1996 0.2917 0.4717 1.129 2.217 3.900 4.973 6.095 7.199
Discrepanoy cell 3rd law
-A#,
dT
-AS,
10'
0011
third law
19.93 18.30 17.16 15.18 11.85 9.79 9.70 10.67 11.15 11.59
20.00 18.21 16.82 15.15 11.93 9.65 9.46 10.29 11.16 11.81
0.4320 0.3967 0.3721 0.3290 0.2570 0.2122 0.2104 0.2314 0.2417 0.2512
-0.07 f0.09
f0.34 f0.03 -0.08 +0.14 $0.24
+0.38 -0.01 -0.22
a Cell data of Beck, Singh, and Wynne-Jones.' The H & % concentration is given in molar units; dE/dT is given in absolute volts per degree; AS is given in gibbs per mole of PbOz (1 gibbs = 1 defined cal/defined deg).
for the various concentrations, and we have reproduced the values given in their Table 3 in our Table IV, which also gives the entropy change from the relation AS = nF(dE/dT), where n F = 2 X 23062.4 = 46125 cal/ abs V equiv. The entropy change for reaction 1 is given by
AS
= So(PbS04) #'El
Their results have been multiplied by the factor 1.00111 to convert them to gibbs/mol (Le,, defined cal/deg mol). The extension of the tablea of the partial molal properties of aqueous sulfuric acid is given as Table V. The values for 1 M are taken from ref 3. The entropy change, based on the third law of thermodynamics, for reaction 1, is given at even values of concentration in Table VI and is shown as the curve in Figure 1, along with the experimental points of Beck, Singh, and Wynne-Jones." The agreement is qcellent and gives strong support to the use of closely related third-law data in deriving the temperature coefficient of the lead storage cell. The entropy change, as calculated from the temperature coefficients given by Hamer,6 is also included in Figure 1. It is evident that there is a serious error. The results of Hamer6 have received owing to the fact that the variations with sulfuric acid concentration are similar to those found in the cell for Hz
+ 2Hg
(4)
by Harned and HamerS80 However, Brackett, Hornung, and Hopkinssl have shown that the results of H z t PbO2rHZSO4(iMI* PbSO*+ ZHeO (in aMtizS041
+ 2.%(H20in x M HzS04) -
- S'(Pb0z) - sz(HzS04 in x M
+ HgzSOc
Curve based on third l o w x Beck, Singh, and Wynne-Jones
19
(dUdT call-1959)
HzS04) (3)
I§''(P~SO~)~ = 35.509 gibbs/mol at 298.15'K S(PbO2) = 17.156 gibbs/mol a t 298.15'K and S(Hz)26= 31.211 gibbs/mol
at 298.15' K. Sl(HzO in x M HzS04)and Sz(HzS04 in x M HzS04) are given, a t 298.15'K, for concentrations above 1 M in Table I of ref 3. In order to cover the range of the experimental data for reaction 1, we have extended Table I of Giauque, Hornung, Kunzler, and Rubina on the thermodynamic properties of aqueous sulfuric acid to 0.1 M . This has been done by utilizing the activity and osmotic coefficients of Stokesz6to give the free energy change. Since the reference states for the above table3 are pure %?So4and HzO, we are concerned only with the relative rather than the absolute values of the activity coefficients of Stokes, because they appear only as ratios in extending the table. The relative partial molal enthalpies of sulfuric acid and water, needed to give their partial molal entropies, are taken from the work of Young, Groenier, and WU.~' The partial molal heat capacities of HzS04 and HzO in their solutions have been given by Randall and Taylor.28 The Journal of Physical Chemistry
8.01 0
I
1
1
2
I
3
I
4
I
5
I
6
1
7
I
I 8
1 9
M HZSO4
Figure 1. Entropy change during reduction of PbOa by HZin z M HzSO4. (25) "JANAF Thermochemical Tables," Thermal Research Labore tory, Dow Chemical Co., Midland, Mich., March 1961. (26) R. H. Stokes, Trans. Faraday Soc., 44, 295 (1948). (27) T. F. Young, private communication; W. L. Groenier, Thesis, University of Chicago, Chicago, Ill., 1936; Y. C. Wu, Thesis, University of Chicago, Chicago, Ill., 1957. (28) M. Randall and M. D. Taylor, J . Phys. Chem., 45, 959 (1941). (29)H. S. Harned and B. B. Owen, "The Physical Chemistry of Electrolytic Solutions," Reinhold Publishing Corp., New York, N. Y., 1968,p 577. (30) H. 9. Harned and W. J. Hamer, J . Am. Chem. Soc., 57, 27 (1935).
THERMODYNAMICS OF THE LEAD STORAGE CELL ~~~~
569
~
Table V : Relative Partial Molal Free Energies, Enthalpies, Entropies, and Heat Capacities for Aqueous Sulfuric Acid from 0.1 to 1 M at 298.15"K4
555.06 227.53 185.02 138.77 111.01 92.51 79.29 69.38 61.67 55.506
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 (l.O)b
2.15 4.23 6.35 8.50 10.71 12.96 15.28 17.71 20.24 (22.84)
18 656 17 850 17 369 17 020 16 744 16 514 16 314 16 131 15 903 (15 811)
1.08 1.13 2.04 2.42 2.80 3.19 3.62 4.09 4.63 (5.29)
17 742 17 525 17 428 17 369 17 322 17 282 17 245 17 210 17 174 (17 138)
16.714 16.720 16.724 16.730 16.737 16.743 16.749 16.756 16.762 (16.769)
40.567 38.591 37 303 36.330 35.562 34.925 34.378 33.882 33.439 (33.050) I
17.994 17.989 17.984 17.976 17.966 17.955 17.942 17.928 17.913 (17.896)
10.15 11.87 13.10 13.86 15.49 16.64 17.84 18.96 19.86 (21.03j
0 A = moles of H20per mole of HzS04; M = moles of HzSOaper 1000 g of HzO; 1, H20; 2, HzS04; F and L are in defined calories per mole; S and C', are in gibbs per mole (1 gibbs = 1 defined cal/defined deg). Values for 1M are taken from ref 3.
Table VI: The Entropy Changes a t 298.15"K, from the Third Law of Thermodynamics, and the Change in Heat Capacity, for Reactions 1 and Zntb
-
A
M
AB(l), 298.15'K
Acp(1)
As(2), 298.15OK
Acp(2)
E(2)So 298.15"K
555.06 277.53 185.02 132.77 111.01 92.51 79.29 69.38 61.67 55.506 50.0 40.0 30.0 25.0 20.0 17.5 15.0 12.0 10.0 9.0 8.0 7.0 6.5 6.0 5.5 5.0 4.5 4.0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.110 1.388 1.850 2.220 2.775 3.172 3.700 4.626 5 551 6.167 6.938 7.929 8.539 9.291 10.092 11.101 12.335 13.877
20.00 18.01 16.71 15.73 14.95 14.30 13.74 13.23 12.77 12.37 12.00 11.17 10.13 9.65 9.30 9.22 9.35 10.01 10.74 11* 19 11.67 12.12 12.29 12.43 12.52 12.57 12.60 12.64
29.03 27.30 26.06 25.29 23.64 22.47 21.24 20.09 19.16 17.96 16.94 15.30 13.82 13.31 13.02 12.96 13.63 15.73 24.53 25.38 25.60 24.96 23.87 21.57 18.44 15.32 12.88 10.79
-9.36 -5.39 -2.81 -0.85 +0.70 1.98 3.09 4.10 4.99 5.79 6.52 8.14 10.15 11.08 11.76 11.91 11.66 10.43 9.09 8.26 7.40 6.59 6.29 6.04 5.89 5.80 5.75 5.69
44.03 40.57 38.10 36.58 33.30 30.97 28.55 26.27 24.44 22.07 20.07 16.86 13.98 13.01 12.44 12.34 13.59 26.18 33.87 35.42 35.82 34.68 32.76 28.71 23.26 17.88 13.73 10.21
1.7971 1.8322 1.8531 1,8683 1.8804 1.8905 1.8993 1.9073 1.9147 1.9213 1.9283 1.9441 1.9669 1.9833 2.0065 2.0223 2.0425 2.0760 2.1076 2.1278 2.1559 2.1812 2.1981 2.2169 2.2382 2.2633 2.2897 2.3210
I
A = moles of HzO per mole of HzSO4; M = moles of HzSO~per 1000 g of HzO; A S and AC, are in gibbs per mole (1 gibbs = 1 defined cal/defined deg); E is in absolute volts. Data for computing A S and AC, are taken from ref 2, 3, 4, and 25 and Tables I1 6nd 111. (1) HZ PbOz HzS04 (in HzS04.AHzO) = PbSO4 2Hz0 (in HzSO4.AHzO); (2) Pb PbOz 2H~S04(in HzS04. 0 HBOd.AHz0). 0 Calculated from AF"tss.1~= 120,200 cal/mol. (See eq 10.) AHzO) = 2PbSO4 2 H ~ (in
+
+
+
Harned and Hamer on this cell also show third-law deviations which are comparable in magnitude to the discrepancies shown in Figure 1. The actual observations of Harned and Hamer30 and of Hamers have never been published, so it is particularly to attempt to trace the source of the discrepancy; how-
+
-
+
+
ever, we believe that their equations should be given no weight with respect to the variation of the properties of aqueous sulfuric acid with concentration or temperature. (31) T. E. Bracket$, E. W. Hornung, and T. E. Hopkins, J . Am. Chem. sot., 82,4155 (ieso).
Volume 78, Number 8 February 1968
J. A. DUISMAN AND W. F. GIAUQUE
570 IS
Table VI also includes values of AC, for reaction 1. With the assistance of A8298.15 from the third law and the measured ACp, we may write
AFT
- AF298.15
AFT - AF298.16 = (ACp
=
- ~ F ( E T- E298.16)
10
(5)
- ASz98,lj)(T - 298.15) AC,T In (T/298.15) (6)
It should be noted that the effect of AC, nearly cancels in the two terms on the right side of eq 6 for moderate values of ( T - 298.15). Thus variation of AC, with temperature should have little effect over the range of existing experimental data. It is due to this fact that Beck, Singh, and Wynne-Jones were able to derive accurate values of ASZgs.ljby considering derivatives over a total range of some 50". Equation 6, with values of AS and AC, from Table VI, should accurately represent the change of emf with temperature for reaction 1, over all concentrations of aqueous HzS04, excepting those limiting situations where the solubility of PbS04 could interfere with the properties of the solution. The Thermodynamic Properties of the Fundamental Reaction in the Lead Storage Cell. I n Table VI, we have also included values of AS2g8.1j and AC,, over a range of concentration, for the reaction Pb
+ PbOz + 2HzS04 (Z M ) = 2PbS04 + 2H20 (in z M H2S0J
which has been generally accepted as applicable to the lead storage cell. I n Figure 2, we have shown the third-law value of ASze8.150Ii: for reaction 2 as a curve. The experimental values of Vosburgh and Craigla2the 1933 values of Vinal and Craig,33and those of Hamerj6 all of which are taken from the dE/dT summary of Craig and are shown as points. The temperature coefficient values of Vosburgh and Craig are in good agreement with the third law of thermodynamics. They were given only to 0.01 mV/ deg or about 0.5 gibbs/mol. Vosburgh and Craig studied reaction 2 by indirect means which separated the two most troublesome substances, namely, the PbO2 and Pb, in contact with sulfuric acid. The cell reactions were Pb(two-phase amalgam)
+
+ 2Hg
(7)
+ PbOz + 2HZS04 M ) = PbSOl + Hg2S04 + 2Hz0 (in z M HzS04)
(8)
Hg2S04 = PbSOd 2Hg
(Z
Pb
=
Pb(two-phase amalgam)
(9)
Reaction 9 and its temperature coefficient had been investigated by Gerke.35 The emf of reaction 7 was found to be E298.16 = The Journal of Physical Chmistry
-
