904
HOWARD E. FLOTOW AND HAROLD R. LOHR
by equation 4, where the k’s are functions of T . With not too mpid an oscillating temperature cycle (Fig. lB), equation 4 reduces to :a
- s ) ( b - 5 ) (5)
Hon-ever, if the oscillation frequency is so high that a steady state is reached in the concentrations of A, B and C with respect to the changing temperatuw, the rate will be dxldt = K,k,(T)(n - z)(b - a) :it all times, and over the period At will be
Since in general, ( 5 ) is not equal to (6), a complex reaction would show a different rate a t oscillating temperatures than calculated from the isothermal rates at T’ and T”. Whether the difference is experimentally detectable reinailis to be seen.
Vol. 64
The method would be somewhat similar in principle to the rotating sector method for photochemical chain reactions5 in that a periodic impulse-here a thermal one-is given to the reaction. Tile use of varying temperatures also bears qome similarity to existing methods for the calculation of activation energies from non-isothermal rates6 and of integrated rates from experiments made under non-isothermal condition^.^ Acknowledgment.-I am indebted to the National Science Foundation for support of this work. (5) H. W. Xelville and G. M. Burnett, “Technique of Organic Chemistry,” (A. Weissberger, Ed.), Interscience P u b l ~ s h e r sInc., , New York, N. Y.,1953, Vol. VIII. p. 138. (6) H.J. Borchardt and F. Daniels, -1.A m . Chem. Sac., 79,41 (1957); K.S.Vorres and L. Eyring, Abstracts of Papers, 136th A.C.S. Meetiug, Atlantic City, p. 45s. (7) J. B. Malloy and H. S. Serlig, A.I.C?.E. Jour., 528 (1955): E. Baum, THISJOURYAL, 63, 1701 (19.53).
THE HEAT CAPACITY AYD THERMODYNAMIC FUNCTIONS O F URA4NIURf FROM 5 TO 350’K.l BY HOWARD E.FLOTOW .4ND HAROLD R. LOHR Contrib?itionf r o m the Chemistry Division, Argonne National Laboratory, Lemont, Illinois Received February 8, 1060
The heat capacity of uranium metal containing less than 0.01 yoimpurities v a s measured from 5 to 350°K. From these data the entropy, enthalpy and free energy function were calculated. The values of C, SO,(Ho - H n O ) and (F o - Ho0)/T a t 298.15”K. are 6.612 f 0.013 cal. deg.-l mole-’, 12.00 i 0.02 cal. deg.-’mole-’. 1521 f 3 cal. mole-‘and -6.893 zt 0.014 cal. deg. -1 mole-’, reepectively. The results are compared with previously published data.
Introduction The heat capacity of a-uranium has been previously reported by Smith and Wolcott2 in the range 1 to 20°K., bv Jones, Gordon and Long3 in the range 15 to 300°K., by Clusius and Piesbergen4 in the range 10°K. to room temperature, by Moore and Kelley5 and by Ginnings and Corruccinie in the range 298 to 935°K. Recently, uranium metal which contained substantially lesser amounts of impurities than the metal used in previous investigations became available a t this Laboratory. This paper reports a determination of the heat capacity of this high purity a-uranium from 5 to 350°K. and a calculation of the entropy, enthalpy and free energy function. Also, these results are compared with those of Smith and Wolcott and with those of Jones, Gordon and Long. Experimental Uranium Sample.-The uranium metal used for this experiment was prepared by the Metallurgical Division of (1) Based on work performed under the auspices of t h e C . S. Atomic Energy Commission. (2) P. L. Smith and N. RI. Wolcott, “Conference de Physique des Basses Temperatures,” Paris, 2-8 Sept., 1055, Annexe 1955-3, Supplement au Bulletin de 1’Institut International du Froid, pp. 283286. (3) W. hI. Jones, J. Gordon and E. A. Long, J . Chem. Phus., 20, 605 (1952). (4) K. Clusius and U. Piesbergen, Ifelu. Phya. A c t a , 31, 302 (1958). ( 5 ) G. E. Moore and K. K. Kelley, J. A m . Cham. Sac., 69, 2105 (1947). (6) 0. C. Ginninga and R. J. Corruccini, J . Research Notl. Bur. Standards, 39, 309 (1947).
this Laboratory’ by the electrolysis of UF, in a fused mixture of KCl and LiC1. The crystals obtained in this process n-ere vacuum cast into billets whirh were then swaged into rods 0 3 cni. in diameter. This uranium metal was later converted to the uranium hydride sample for which heat capacity measurements already have been published.8 Ppectroecopic analyses of the billet from which the sample was taken s h o w d the presence of the following impurities in parts per million: -41. 5 ; Cr, 2; Cu, 1; Fe, 2 ; . M q , 1; Si, 12; all other elements were below the limits of spectrosropir detwtion. Chemical analyses detected the following elements in parts per million: C, 18; N, 5; 0, 15. On the basis of the analyses it was concluded that the sample contained less than 0 01% impurities. Prior to loading the samplr into the calorimeter the uranium was annealed at 600-650° for 0 5 hour tn UUMLO and then cooled slowly to room temperature. The mass of the sample was 106 3102 8 . The cnlorimeter contained 1.20 X mo!e of helium to fwiiitnte the establishment of temperature equilibrium. Apparatus and Technique -The calorimetric measurements were made using the apparatus and adiabatic method which already have heen described in detai1.819 A capsule t o p e platinum resistance thermometer (Laboratory designation A-1) was iised to determine the tem erature of the calorimeter. The thwmometer was c a d r a t e d on the temperature wale of the Kational Bureau of Standardslo from 14 to 373°K. Below 14’K., the scale was obtained by fitting the equation R = A B T 2 f C2‘6 to the resistance at the boiling point of helium, at 14°K. and to d R / d T
+
(7) B Blumenthal and R. A. Noland, “Progress in Nurlear Energy,” Vol. I, Pergsmon Press, New Yorh, N. Y.,1456, Series V, pp. 62-80, (8) H. E. Flotow, H. R. Lohr, R. XI. Abraham and D. W. Osborne, J . A m . Cham. Soe.. 81,3529 (1359). (9) E. F. “estrum, Jr., J. B. Hatcher and D. W. Osborne, J . Chcm. Phya.. 21, 419 (1953). (10) H. J. Hogs and F. G. Brickwedde, J . Raaearch Natl. B u r Standards 22, 351 (1939).
July, 1960
)DYNAMIC FUNCTIONS OF URANIUM HEATCAPACITY AND THERM
at 14°K. A slight correction waa applied to the calibration to make the ice point equal to 273.15'K. It is estimated that the scale agrees with the thermodvnamic wale within 0 1" from 4-1pK., within 0.03" fr6m 14-90°K. and within 0.05' from 90-373°K.
905
TABLE I1 THERMODYNAMIC PROPERTIES OF URANIUM METALAT SELECTED TEMPERATURES /PS
- u.o\
Results and Discussion Heat Capacity Results.-The experimental values of the heat capacity are presented in chronological sequence in Table I. The data are expressed in terms of the defined thermochemical calorie equal to 4.1840 absolute joules. A small correction for the finite temperature interval was made by adding - (d'C,/dT2) (AT)*/24 t o the measured heat capacity. Approximate temperature increments of the individual measurements can be calculated from the differences between the successive mean temperatures within a series. The heat capacities at selected temperatures given in Table I1 were read from a large scale smooth curve through the experimental points. It is estimated that the heat capacity values giren in Tables I and I1 have a probable error of 5% at 5 " K , 1% a t 1 4 O K . ? and 0.27, above 30°K.
0.015 0.042 0.007 5 0.020 0.26 .044 ,018 10 .084 ,035 .113 1.16 15 ,308 .Oil 20 ,727 .255 3.67 25 1.312 .128 .478 8.73 ,210 .772 16.84 30 1.934 ,315 1.117 28.06 35 2.546 ,437 42.16 1.492 40 3.078 ,576 58.59 45 3.476 1.579 .726 76 70 50 3,754 2.261 1,042 116.58 60 4.212 2.986 1.370 70 4.593 3.666 160 69 1.696 80 4.899 4.299 208.18 2.019 258.44 4.891 90 5.138 2.334 5.442 310.74 100 5.315 2.639 5.955 364.61 110 5.458 2.937 419.82 6.436 120 5.583 3,223 476.21 6.887 130 5.694 TABLE I 3.500 7.313 533 63 140 5.789 IJEAT CAP4CITY O F UR.4XIVM hlETAL IN CAL. DEG.-~ 3.768 591.94 7.715 150 5.871 MOLE-1 4.026 651.01 8.096 160 5.942 1101. wt. = 238.07; 0" = 273.15"K. 4.276 710.77 8.458 170 6.009 T ,OK. CP T,OK. CP 771.15 4.518 8.803 180 6.067 Series I11 Series I 4.753 832.10 9.133 190 6.121 300.104 6 614 49.520 3.727 4.979 893.57 9.448 200 6.173 307.465 6 648 54.470 3 963 955.54 5.200 9.751 210 6,222 317.475 6 700 59 986 4.209 5,413 10.041 1018.0 220 6.270 327.514 6 745 66 134 4.463 5.620 10.321 1080.9 230 6.316 337 489 6 790 73 049 4.691 5,822 10.591 1144.3 240 6.360 347.540 6 827 80 640 4.916 6,017 10,851 1208.1 250 6.404 88.873 5.118 6.208 11.103 1272.4 260 6.445 Series I1 98.141 5.281 6.394 11.347 1337.0 270 6.486 108,041 5 . 703 0.027 5.428 6.575 1402.1 11.584 280 6.530 118.131 7 204 ,038 5.561 6.752 11.814 1467.6 290 6 574 128.225 8 906 ,060 5.675 6.924 1533.6 12.037 300 6.619 138.123 ,105 5.772 10.784 7.093 12.247 1600.0 310 6.664 147.980 12 644 .I76 5.856 12.459 7.257 320 6.709 1666.9 157.765 .287 14.648 5.925 7.418 1734.2 12.666 330 6.7h4 16 653 167.755 ,426 5.994 12.860 1801 . 9 7.576 340 6.799 177.804 ,597 18 645 6.056 7.730 1870.2 13,066 350 6.842 ,799 20.662 186.311 6.101 6.452 1338 11.42 273.15 6.499 196.331 1.029 22 682 6.155 1521 6.893 298.15 6.612 12.00 24,927 206.324 6.202 1,304 k0.014 f 0 . 02 = t O ,013 k3 216.322 27.490 6.250 1.624 226.307 30.297 1.972 6.309 average 0.032 cal. deg.-l mole-' higher than those 236.222 33 432 6.342 2 360 of the present investigation. Since the uranium 246.154 36.911 2 762 6.389 specimen used by Jones, Gordon and Long3 was 256.120 40.852 3 154 6.429 reported to be only 99.7% uranium, it is likely that 4.7.148 266.096 6.467 3 486 a significant fraction of this disparity is due to 278.483 6.529 3 744 49 711 chemical and physical differences in the samples. 285.104 6.556 Clusius and Piesbergen report in a brief paper4 294.998 6.611 that they have measured the heat capacity of ura304.950 6.639 nium between 10°K. and room temperature. A 314,904 6.678 comparison with their results cannot be made until
A comparison of these heat capacities with those previously reported by Jones, Gordon and Long3 show that between 15 and 50°K. the heat capacity values of the two investigations agree within h0.13 cal. deg.-' mole-' and that between 50 and 300°K. the values of Jones, Gordon and Long are on the
a more detailed publication of their data is available. In the region 5 to 20°K. a comparison can be made with the data of Smith and Wolcott.2s11 From a smooth curve drawn through one of their (11 ) W. hf. Wolcott, private communication.
D. W.SCOTT,W.T. BERGAND J . P. ~ I C C U L L O U G H
906
T-01, 64
most reliable runs the values of the heat capacities thalpy from 0 to 5°K. The value of the entropy at a t 5, 10, 15 and 20°K. were found to be 0.020, 0.100, 298.15"K. reported in Table 11, 12.00 f 0.02 cal. 0.328 and 0.760 cal. deg.-l mole-l, respectively. deg. mole-l, agrees within experimental error d comparison of these values with those in Table I1 with the value published by Jones, Gordon and shows that the values of the heat capacities are LongJ3 12.03 f 0.03 cal. deg.-I mole-'. Jones, identical a t 5°K. but that the values diverge a t Gordon and Long did not report a value of the higher temperatures, the results of Smith and Wol- enthalpy of uranium a t 298.15"K. However, cott' being substantially higher than those of this using their heat capacity data we calculate that investigation. The reason for the disagreement is H2s8.15 - Hoois 1526 =k 3 cal. mole-I which agrees not known. Thermodynamic Functions.-The thermody- well with the value 1521 i. 3 cnl. mole-1 given namic functions derived from the heat capacity are in Table 11. Acknowledgments.-We thank Dr. D. W. Osshown in Table I1 at selected temperatures. The heat capacity values reported by Smith and Wol- borne and Dr. B. M.Abraham for their guidance cott2 were used to evaluate the entropy and en- and helpful discussions.
CHEIJIICAL THERMODYi?;AJIIC PROPERTIES OF XETHYLCTCLOPESTASE AKD 1-cis-3-DIMETHYLCYCLOPESTASE RY D. W, SCOTT, W. T. BERGAND J. P. MCCCLLOUGH Contr thution
S o . 86
from the Thermodynamics Laboratory, Bartlesdle Petroleum Research Center, Burrnu 05 Mines, U . 8. Department of the Interaor, Bartlesville, Okla. Receaued February 8 , 1960
Thermodynamic functions were calculated for methylcyclopentane by methods of statistical mechanics and for l-cis-3dimethylcyclopentane by a refined method of increments. Values of the heat, free energy and equilibrium constant of formation also were calculated for both substances.
Thermodynamic functions of methylcyclopentane and the isomeric dimethylcyclopentanes were calculated previously by approximate incrementa1 methods by staff members of American Petroleum Institute Research Project 4 4 . l ~ ~More recently the vapor capacities of methylcyclopentane and 1czs-3-dimethylcy~lopentane~ were determined in this Laboratory. The experimental values of vapor heat capacity, in addition to the experimental values of entropy (ref. 4) that were available to the earlier workers, made possible more accurate calculations of the thermodynamic functions of Inethylcycloprntaiie by methods of statistical mevhanics and of 1-czs-3-dimethylcyclopentane by n refined method of increments. These calculation5 are described herein. Thermodynamic Functions of Methylcyclopentane.6-The 54 degrees of freedom of the methylcyclopentane molecule may be classified as 3 translations, 3 OT er-all rotations, 46 vibrations, one 111ternal rotation of the methyl group, and one pseudo-rotation of the 5-membered ring. The contributions of translation and over-all rotation to the thermodynamic functions were calculated 11y standard formulas. In the simplified model (1) J.
E Kilpatrirh IS G Werner C. RT Beckett, K S Pitier and
F 11 Rossini J Reseoich Vatl B u r Standarda 39, 523 (1947) (2) l f B. Cpstein C: \ I Barrow, I< S Pitier and F D Rossini, ? b i d , 43, 245 (19491 (3) l-c~-3-Dimethvlcyclopentane IS the lower boiling (90 77") iaomer of 1 3-dimrthylcy~lopentane. This isomer was incorrectlv labeled I-lran,-3-dirrietti3 lcyclopentane in literatuie before 1956 See F D Rossini ani1 Iiun Li, Scrence, 122, 513 (1955) (4) J. P McCullough, R E Pennington, J C Smith. I lopp and G u y Waddington, J Am. Chem Soc , 81, 5SSO (1959). ( 5 ) The gas constant IS taken t o be 1.98719 ea1 deg - 1 mole-' and the atomto weights of carbon and hydrogen are taken t o be 12 010 and 1.0080.
used for calculating moments of inertia, the ring was planar, and the bond dist.ances and angles were: C-C, 1.54 A.; C-H, 1.09 8.;C-C-C(ring), 108"; H-C-H(methylene), H-C(ring)-C(methy1) and all methyl group angles, 109" 28'. For this model, the product of principal moments of inertia is 1.438 X 10-113 g.3 cm.6, and the reduced moment of inertia for internal rotation of the methyl group is 5.155 X Corresponding values for the actual 10-40 g. molecule with a slightly puckered ring cannot differ much from the foregoing values. The set of fundamental vibrationa,l frequencies listed in Table I was selected aft'er consideration of all available Raman and infrared spectral datma6 and comparison wit,h t,he frequencies of cyclopent,ane, other monosubst'ituted cyclopentanes and related heterocyclic compounds. The descriptive names for the modes of vibrat>iori are somewhat schematic and are intended merely to show that the expected number of frequencies are assigned in t'he several regions of the spectrum. The two lowest, frequencies, for ring puckering and a CH3-C-C bending mode, are assigned t o the doublet 307-320 cm.-' reported in the Raman spectrum by Bazhu(6) Raman: R. W. F. Kohlrausch, A. W. Reitz and W. Stockmair, %. phusik. Chem., B32, 229 ( 1 9 3 6 ) ; E. J. Rosenbaum and H. F. Jacobson, J . A m . Chem. Soc., 63,2841 (19411: P. A. Bazhulin, Kh. E. Sterin,
T. F. Bulanova, 0. P. Solovava, AI. B. Turova-Pollak and B. A. Kazanskii, Izuest. A k a d . S a u k S. S . S . E . Otdel. R h i m . i y a u k , 7 (1946); A P I R P 44 at the Carnegie Inst. of Tech.. Catalog of Raman Spectral Data, Serial S o . 139. Infrared: P. 1m:ibert and J. Leconite, .4nn. phus., 10, 503 (19381; D. BbrcS-GSlZteanu, Buli. soc. roumaine phys., 38, 109 (1938); E. K. Plyler, J . Optzcal Soc. Am., 3'7,746 (1947); E. K. Plyler, R. Stair and C. J . Humphreys, .I. Reseawl, A'atl. BUT.Standards. 38, 211 (1947); A P I R P 44 a t the Carnegie Inst. of Tech., Catalog of Infrared Spectral Data, Serial Nos. 14, 15, 255, R-L4, 510, 511, 597, 616. and 1556; F. F. Bentley and E. F. Wolforth, WADC T R 58-198, May 1958; A. Cornu, BuZE. soc. chim. France, 721 (19%).
