T H E HEAT CAPACITIES O F SOME METALLIC OXIDES BY GEORGE S. PARKS AND KENKETH K. KELLEY
The past fifteen years have witnessed a rather extensive study of the heat capacities of substances at low temperatures. In this connection the elements themselves and certain classes of compounds, notably the halogen salts, have been investigated to a considerable extent. On the other hand, only scanty data on metallic oxides have been published, although such information is of importance from both the theoretical and the industrial standpoint. In view of this situation, about two years ago there was initiated in this laboratory a systematic investigation of the heat capacities of oxides at low temperatures. The present paper records the results of measurements made upon the oxides of magnesium, calcium, and aluminum and upon the two iron compounds, hematite and magnetite. Experimental Part Method-The method was essentially the same as that recently employed by one of us1 in an investigation of the specific heats of aliphatic alcohols. In every case the sample of oxide studied was either in the form of a powder or of small crystals, never exceeding 3 or 4 mm. in dimensions. Such a sample was placed in a gas-tight, cylindrical copper can, 8 cm. long and 2 . 5 cm. in diameter, with a capacity of approximately 40 cc. To facilitate the attainment of thermal equilibrium the inside of this container was fitted with perforated disks, spaced 2 to 4 mm. apart along a small copper tube which ran through the center of the cylinder and served as a holder for the thermocouple used in measuring the temperatures. These disks, even though made out of extremely thin copper foil, added considerably to the weight of the calorimeter; their use, however, was justified by the fact that in this way no portion of the oxide under investigation was more than 2 mm. from a highly conducting copper surface. A 150-ohm heating coil made from B. and S. KO. 36, silkinsulated Therlo mire was wound around the outer surface of the can and baked on with electricians’ enameling fluid; it had external leads of No. 40 copper wire. To reduce heat losses through radiation thin silver foil was then wrapped tightly around the container. The bottom of the can, sealed in with soft solder and easily removable, provided a means of introducing and removing the sample of oxide. The finished calorimeter, constructed with these features, weighed about 3 5 grams. Its heat capacity in the unfilled state represented, on the average, about a quarter of the totlal heat input during a specific heat determination on the oxides and was measured in a separate series of experimental runs. The calorimeter was suspended by silk thread within a larger copper cylinder weighing about 600 gm. This sheath, fitted with a top and bottom and silvered on both its inner and outer surfaces, provided a relatively uniform temperaParks: J. Am. Chem. SOC., 47, 338 (192j).
GEORGE S. PARKS AND KENNETH K. KELLEY
48
ture environment for the heat capcity determinations. In order to control its temperat'ure it was equipped with a heating-coil and thermocouple. The cylinder and contents rested on small wooden legs in a vacuum-tight brass can, j em. in diameter and I j cm. high. A German-silver tube I em. in diameter and j o cm. long, soldered into a hole in the top of the brass can, served the three-fold purpose of connecting the system to the charcoal evacuating tube, of providing an exit path for the electrical connections and of serving as a support, the entire apparatus being suspended in a 1000 cc. Dewar jar. Details of electrical wiring, bringing out the connections, etc. were similar to those recently described by Rodebush' in his work upon cadmium and tin and will not be repeated here. A satisfactory vacuum was obtained by a preliminary evacuation with B n'elson oil-pump, followed by the use of activated charcoal immersed in liquid air. The desired temperatures were attained with the aid of various baths such a s liquid air, crystalline ethyl alcohol (melting point, 158' K.), solid carbon dioxide in alcohol, ice, and water at approximately the temperature of the room. Single-element copper-constantan thermocouples, constructed from B. and S. No. 40 silk-insulated copper and KO.30 silk-insulated constantan n'ire ' were used with a White potentiometer in measuring the temperatures of the calorimeter and copper sheath. For these thermocouples the temperatures and the rates of change of e. m. f . with change of temperature, dE/dT, were obtained by means of the two equations of Eastman and Rodebush,2 since the wire used was evidently similar to theirs. From a careful study of this Eastman-Rodebush temperature scale we have concluded that its use involves an error of less than 0.2% above zooo K. and probably not more than 0.5% in any region below this point. The actual procedure in making the measurements was as follows. The system was first evacuated and an appropriate bath was placed around the external brass can. IVhen the calorimeter and surrounding copper sheath had attained the desired temperature (a process which often required a day or more in the case of the lower temperatures), the reading of the calorimeter thermocouple was carefully recorded. Heat was then supplied to the calorimeter for a period of four to eight minutes by means of an electric current from an %volt storage battery. During this interval the energy input was measured with an accuracy of 0.1% by a calibrated stop-watch and a potentiometric evaluation of the current and voltage. In general it was such as to cause a temperature rise of about 4'. After switching off the heating current, the readings of the calorimeter thermocouple were recorded a t one minute intervals for about half an hour. As a rule a very regular cooling rate was attained within the first four to six minutes of this period, indicating that heat equilibrium had been reached, The remaining thermocouple readings sufficed for an accurate evaluation of the cooling correction during and im'Rodebush: J. Am. Chem. SOC., 45, 1413 (1923). Eastman and Rodebush: J. Am. Chem. SOC.,40, 492 (1918).
2
HEAT CAPACITIES O F S O M E METALLIC OXIDES
49
mediately following the heating period. This correction was but a small percentage of the total temperature rise. As a typical example of the way in which the results were obtained, the calculations from the data for one of the magnesium oxide runs are given in detail. Time, 3 6 I .4 seconds. Voltage a t terminals of heating coil, 7.958 volts. Current through heating coil, 0 . 0 ; ~7 0 amperes. Total heat supplied, (361.4) (7.958) (0.05270) (.2391) = 36.250 cal. Initial thermocouple reading, 5586.1 microvolts Final thermocouple reading, corrected for cooling, 5449.3 microvolts Difference 136.8 " Temperature corresponding to average thermocouple reading, 94. I O K. Corresponding dE/dT, 19.63 microvolts Heat supplied to calorimeter and contents per degree, 36.250 (19.63 + 136.8) = 5.201 cal. Heat capacity of calorimeter a t 94.1' K., 2.130 cal. Heat supplied to magnesium oxide per degree, 5.201 - 2.130 = 3.071 cal. J%'eight of magnesium oxide, 76.40 gm. C, of magnesium per gram, 3.071/76.40 = .0402 cal. C, per mean gm. atom, 0.81 cal.
Materials Magnesium Oxide.--A high-grade sample of fused magnesium oxide was employed. On examination it gave no tests for any of the common impurities, such as silica or calcium, and seemed to be 100% pure within the limits of analytical error. It had been given to Professor D. L. Webster of the Physics Department of Stanford University by the Korton Company. Calcium Oxide.-Kahlbaum's calcium oxide was used. An analysis of this material gave 98.8% CaO, 0.4% HzO and no SiOz. Aluminum Oxide.-Small, almost colorless sapphires from Ceylon were employed in the measurements. An analysis made upon them gave 99.3% A1203. Ferric Oxide.-Two samples of ferric oxide were studied, The first, consisting of large crystals of specular hematite from the Island of Elba, gave on a>nalysisg 9 , 2 F c Fe203,0.57~ HzO and 0.5% SiOz. The second sample was Kahlbaum's product, prepared from the oxalate. It gave 99.570 Fe203, the remaining 0.5% being presumably moisture. This material consisted of a fine, smooth powder and on X-ray analysis1 yielded much fainter lines than did a powered crystal of the specular hematite. A rough estimate of the relative intensities would place them, perhaps, in the For advice and assistance in making this X-ray analysis, the authors wish t o acknowledge their great indebtedness to Professor P. *4.Ross of the Physics Department of Stanford Tlniversity.
50
GEORGE S. PARKS AND K E N N E T H K. KELLEY
ratio of I to IO. Apparently, then, this Kahlbaum sample contained a large amount of amorphous substance. Magnetite.-The magnetite used was similar to that employed by Sosman and Hostetterl in an earlier investigation and was in the form of remarkably perfect, large crystals, The Sosman-Hostetter analysis gave 99.oo%Fe304 0.63% Fez03,and 0.37% impurities (chiefly quartz.) Heat Capacity Data The results of the measurements appear in Tables I-VI inclusive. In each case the first column contains the temperatures in degrees absolute; in the second column appear the corresponding heat capacities a t constant pressure per grsm of the material and in the third column are the resulting values for the mean atomic heat. These specific and atomic heats are expressed in terms of the 15' C. calorie, which is used throughout the present paper.
As to the accuracy of the results, it is very hard to state definitely. In general the measurements themselves are reproducible to 0.5% or better and probably in no region of the temperature scale involve an absolute error of more than 1.0%. On the other hand, the impurities, which in certain instances are of the order of I%, may affect the results to some extent, although the magnitude of their influence is rather problematical. For this reason no attempt to correct for the effect of impurities has been made is presenting the data. In the studies with magnetite a region of marked heat absorption was noted in the short temperature interval, I I ~ O - I I ~ O K. A rough measurement of this heat effect gave 0.69 cal. per gram or 23 cal. per mean gram atom. I n the case of no other substance was a heat absorption or transition point observed. TABLE I The Heat Capacity of Magnesium Oxide Temperature OK
Cp per gram
Cp per gram atom
94.1 97.9
0.0302
100.0
0.0442 0.0450 0.0470
0.81 0.89 0.91 0.95
151.8
0.IIO1
2.22
188.4 193.4 275.3 278.0 288.3 291 . o
0 . I452
2.93 3.03
98.5
0.1502 0.2096 0.2137 0.2170
0.2184
4.22
4.30 4.37 4.40
1 Sosman and Hostetter: J. Am. Chem. SOC., 38, 812 (1916). Dr. Sosman very kindly loaned us this material for our investigation.
HEAT CAPACITIES OF SOME METALLIC OXIDES
TABLE I1 The Heat Capacihy of Calcium Oxide Temperature OK
87.2 87.7 91. I 92.2 150.3 194.0 197.1 275.4 277.8 282. I 292 ' 7
Cp per gram 0.0535 0.0536 0.0579 0.0591 0.1158 0.1446 0 . I474 0.1762
Cp per gram atom I . 50 I , 50
0 . I794
1.62 1.66 3.25 4.06 4 . I3 4.94 4.97 5.03
0.1808
5.07
0 . I772
TABLE111 The Heat Capacity of Aluminum Oxide Temperature OK
91.1 91.7 93 ,o 95.6 150.6 193.3 197.2 200. I
275.1 276.4 288.6 291.3
Cp per gram 0.0249
0.0255 0.0260 0.0286 0.0768 0.1155 0.11go 0.1218 0,1726 0 . I743 0.1800 0.1813
Cp per gram atom
0.51 0.5 2
0.53
0.58 1.57 2.35 2.43 2.48 3.52 3.55 3.67 3.70
TABLE IV The Heat Capacity of Ferric Oxide (Specular) Temperature "K
89.8 90.3 90.5 95.5 148.4 186.9 192.8 196.3 275.9 278. I 289. I 291.9
Cp per gram 0.0404 0.0414 0.0410 0.0445 0.0827 0.1082 0.1109 0.1128 0 . I477 0.1488 0 . I534 0.1539
Cp per gram atom 1.29 I .32 1.31 1.42 2.64 3.46 3.54 3.60 4.72 4.75 4.90 4.92
52
GEORGE S. PARKS AND K E N N E T H K. KELLEY
TABLE V The Heat Capacity of Ferric Oxide (Kahlbaum's) Temperature OK
88.3 91.8 95.2 98.3 150.3 194.3 198.5 274.9 276.7 286.9 289.4
Cp per gram
0.0412 0.0442 0.0465 0.0485 0.0858 0.1141 0.1162 0. I521
0.1529 0.1551 0.1561
Cp per gram atom I .32 I .41 I .48
1.55 2.74 3.65 3.71 4.86 4.88 4.96 4.99
TABLE VI The Heat Capacity of Magnetite Temperature "I< Cp per gram Cp per gram atom 90.0 90.2 94.2 96.9 153.2 193.5 197.2 276.3 278.7 292. I 295.0
0.0488 0.0493 0.0524 0.0550 0.0968 0.1186 0.1205 0.1513 0.1525 0 . I558 0.1570
1.61 1.63 1.73 I .82 3.20 3.92 3.99 5 .oo 5.04
5.15 5.19
Discussion of Results The preceding data possess several interesting features. One of these pertains to the relatively low mean atomic heat for A1203in the sapphire form. At the temperature of liquid air this falls to 0.5 cal. per atom or 2 . 5 cal. per formula weight, a rather striking figure in view of the fact that the heat capacit y of two atoms of metallic aluminum plus that of three atoms of liquid oxygen amounts to about 24.0 cal. at goo K. Certainly this situation constitutes an excellent confirmation of the very general view that a low heat capacity is a concomitant of exceptional hardness, as corundum ranks No. g on the Mohr scale of hardness where diamond has the maximum value of IO. The two samples of ferric oxide studied are approximately of the same purity, the essential difference being in the degree of subdivision. Throughout the entire temperature range the Kahlbaum powder was found to have a higher specific heat than the specular crystals, the excess amounting t o 2 .4y0 a t 275' K. and 3.8% a t the temperature of liquid air. Now these percentage differences, while small, we believe to be greater than any that would probably
.
H E A T CAPACITIES O F SOME METALLIC OXIDES
53
result from the experimental errors in the two sets of determinations. Therefore, in our opinion these results indicate that a powder which is finely divided and somewhat amorphous possesses a higher heat capacity than large crystals of the same chemical composition. The heat absorption, found in the case of the magnetite crystals a t about I I j o K., constitutes still another noteworthy feature. This temperature would seem to be very low for a transformation in crystal structure in a metallic oxide, the melting-point of which is above 1500~K. Moreover, after the runs the large crystals of magnetite showed no signs of altemtion or disintegration, such as might conceivably be expected after a series of alternations in crystal structure. In view of these considerations we think that the observed heat effect may possibly be connected with a change in the magnetic properties of the substance, If this be the case, there might be no change in crystal structure, as Compton and Rognleyl have failed to detect such a change in a magnetite crystal upon magnetization and demagnetization. Certainly this heat absorption phenomenon should be investigated further. Entropies of the Oxides.-If we assume the validity of the third law of thermodynamics as stated by Lewis and Gibson2,all the crystalline oxides have zero entropy at oo K. The atomic heat values then provide a basis for a quantitative estimate of the entropies of the same substances a t 298' K. or 2 j oC. I n a careful study of heat capacity data Lewis and GibsonS have shown that for a number of substances the atomic heat capacities a t constant volume are expressible as functions of the absolute temperature by the equation,
Cv = f
(gy,
in which f is the same function for all substances and Ef and n are characteristic constants for each particular substance. For many substances crystallizing in the cubic system and for a number of monatomic elements, n is equal to unity (Class I). For other substances n is less than unity (Class 11). Of course in the present investigation our experimental values are for C, rather than C, but for the oxides the differences between these two quantities are relatively small a t room temperature and become entirely negligible at lower temperature^.^ 1 Compton and Rognley: Phys. Rev., 16, 464 (1920). 2Lewis and Gibson: J. Am. Chem. Xoc., 42, 1533 (1920). 3 Lewis and Gibson: J. Am. Chem. Soc., 39, 2565 (1917). I n the case of magnesium oxide there are data which permit us t o calculate these differences between Cp and Cv. Utilizing the values for the coefficients of compressibility and thermal expansion tabulated by Pease (Taylor: "Treatise on Physical Chemistry", p. 1 7 1 (1924)), we have calculated Cp-CV a t 293' K. by the thermodynamic equation used by Lewis: J. Am. Chem. Soc., 29, 1165 (1907).
Cp
- Cv
ff2VT
= .0242 -
P This difference was found to be 0.04 cal. per gram atom. The empirical rule expressed by Lindemann and Magnus (Z. Elektrochem., 16, 269 (1910)) in the equation, Cp Cv = a T 3/2 then gives 0.01 cal. for C,. - CVa t 100' K.
-
GEORGE S. PARKS AND KENNETH K. KELLEY
54
Accordingly, on plotting our results for C, we have found that the data for the oxides of magnesium and calcium, the two compounds which possess a cubic structure like that of sodium chloride, agree well with the C , curve for solids of Class I. Fig. I shows this clearly for MgO. On the other hand, the data for the remaining oxides require a slightly flatter curve at the lower temperatures, where the experimentally determined heat capacities appear to approximate the requirements for a substance of Class I1 with a value of about 0.9 for n. Whether the “ n formula’’ in these cases is more than a first approximation is, however, extremely doubtful. Its application nevertheless will involve only small absolute errors in instances, like the present, where the total entropy of each substance is small a t the temperature of liquid air. 2 Following in detail the methods of Lewis and Gibson, we have obtained the l Y results which are given in TableVII. The W a entropy value for Fez03 is that found for s the specular crystals; for the Kahlbaum powder our estimate is a t least 0.4 cal. LOG g per degree above this figure. The result FIG. I for magnetite includes the entropy Cp Values for MgO and the Lewis-Gibson change of I .4 units a t the heat-absorpCurve for Class I. tion point previously referred to.
e
TABLE VI1 Entropies of the Oxides per Formula Weight at zg8’K. Substance
log e
MgO CaO AlzO 3 Fez03 Fe304
2.28
I
2.14 2.36
I
2.21
2.15
n .oo
Entropy in cal./degree
.oo .94 .93 .90
6.6 9.6 12.8 21.5
35.1
Free Energies of the Oxides.-Lewis, Gibson and Latimerl have calculated the entropies of the various elements at 298’ K. Using their values in conjunction with our entropy results for the compounds, we have obtained the figures for AS,,s, the entropy of formation of each oxide from its elements, which appear in Table VIII, Column 2 . We are now in a position to calculate AF,,s, the free energy of formation of each oxide, by means of the fundamental thermodynamic equation, A F = AH - TAS, where AH is the increase in heat content during the process of forming the compound from its elements and is numerically equal to the negative of the 1
Lewis, Gibson and Latimer: J. Am. Chem. SOC.,44, 1008 (1922)
HEAT CAPACITIES O F SOME METALLIC OXIDES
55
heat of formation. The values selected for AH298in the case of each oxide appear in the third column of the following table. For MgO and A1203 we have employed a mean between the results of Berthelotl and those of Moose and Parr.2 The figure for CaO is that obtained by Guntz and Benoit3 in their recent investigation. For the two oxides of iron we have used the heats of formation as calculated by Tiger~chioeld~. The resulting free energies appear in the last column. In their present form they are probably accurate to 1%. I n the future, however, the accuracy of these A F values can be considerably increased by revision, as more reliable data for AH become available.
TABLE VI11 Thermal Data per Formula Weight Substance
MgO CaO A1203 Fez03 Fe30,
AS298
Entropy units
-25.7 -25.0 -72.8 -63.9 -81 . o
AH298
AF298
Cal. - 144,700 - 152,800 -378,000 - 197,500
- 137,000 - 145,300 - 356,300
Cal.
-271,000
- 246,800
- 178,400
Summary I. The heat capacities of magnesium oxide, calcium oxide, aluminum oxide, ferric oxide (two samples) and of magnetite have been measured over a wide range of temperatures. I n the case of the last compound a heat-absorption region a t I 13’-I I 7’ K. has also been observed. 2. The entropies and free energies of the several compounds have been calculated. Department of Chemistry, Stanford University, September 1 , 1026.
Landolt-Bornstein-Roth-Scheele: “Tabellen” (1923). Moose and Parr: J. Am. Chem. Soc., 46, 2660 (1924). * Guntz and Benoit: Ann. Chim., 20, 33 (1923). Tigerschioeld: Chem. Abstracts 19, 1085 (1925).
