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. C h e m 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, %. p h u s i k . C h e m . , B32, 229 ( 1 9 3 6 ) ; E. J. Rosenbaum and H. F. Jacobson, J . A m . C h e m . 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. r o u m a i n e phys., 38, 109 (1938); E. K. Plyler, J . Optzcal S o c . Am., 3'7,746 (1947); E. K. Plyler, R. Stair and C. J . Humphreys, .I. R e s e a w l , A'atl. BUT.S t a n d a r d s . 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%).
CHEMICAL THERMODYSAMIC PROPERTIES OF METHYLCYCLOPENTANE 907
July, 1960
lin, et al. However, other Raman investigations, as well as the infrared spectrum, indicate only a single frequency in that range. If there is only a single frequency a t about 315 cm.-', another frequency, unobserved in the Raman spectrum, could occur in the range below 285 cm.-', where tJhe infrared spectrum has not been observed. FCJhl)4ME\ 141,
TABLE I FREQUE~CILS 01' ~ ~ K T I i Y 1 , -
VIRR4TIONAL
CYCT.OPENTANE, CM.-In
Skeletal bending C-C stretching CH, rocking CH2 wagging CH2 twisting CH wagging CH2 rocking C " 3 and CH2 bending C-H stretching a Parentheses indicate used a second time.
307, 320, 429, 534, 593 891, 901, 979(2), 1000, 1134 730, 845, 1012, 1195 1024(2), 1225, 1305 1087, 1140, 1276, 1317 1294, 1352 (891), (1087) 1380, 1436(2), 14.53(2), 1477(2) 2030( 12) multiple weights or frequencies
methyl rotation is somewhat smaller than expected from the value in the related molecule 2-methylprodifferences in molecular pane (3600 cal. geometry may account for this difference, if real. The calculated values of the thermodynamic functions of methylcyclopentane are listed in columns 2-6 of Table II.9 Comparison with expwimental results is shown in Table IT. Thermodynamic Functions of 1-cis-3-Dimethylcyc1opentane.-Thermodynamic functions of 1cis-3-dimethylcycloperitane were calculated by :I refined method of increments. l o The formulas used were
+ +
c,"
+
C," = (methylcyclopentane) C,"(CH,) 0.81 So = S"(methy1cyclopentane) S"(CH,) 0.81 In T 7.60 ( H " - H o a )= ( H " - Hoo)(methylcyclopentane) ( H " HDo)(CH?) 0.81T
+
+
+
In these formulas, Cpo(CH2),So(CH2)and ( B o Ho,)/(CH2) are the methylene increments of Person and Pimentel" for the indicated functions. These
TABLE I1 T,
( P o - H"o)/T, OK.
cal. deg.?
THEM O L A L
THEHXODYNAMIC PROPERTIES O F ~fETHYI,CYCLOPENT.4XEa
(H' - H o o ) / T , cal. deg.-1
H" -
HOD,
kcal.
CP",
SO,
cal. des.-'
cal. deg.-1
4Hf",b kcal.
AFf",b kcal.
log Kfb
0 0 0 0 0 0 -16.52 Infinite -16.52 273.15 -64.23 14.80 4.044 79.03 23.87 -24.81 $5.73 - 4.59 298 1.5 - 65.58 15.66 4.670 81.22 26.24 -25.50 - 6 27 8.55 300 -65.65 15 .7:3 4,719 81.38 26.42 -25.55 8.76 - 6.38 -70.70 19.62 7.850 400 90.32 36.16 20.59 -11.25 -28.07 -75.53 23.83 500 11.92 99.36 44.96 33.01 -14.43 -30.10 -80.24 27.99 600 16.80 108.23 52.36 -31.69 45.78 -16.68 -84.85 31.93 22.35 700 116.78 58.56 -32.89 -18.36 58. 80 -89.36 35,59 28 48 124.95 63.80 -33.76 800 -19.66 71.95 - 0 3 75 38.98 900 35.08 132.73 68.27 -34.34 -20.69 85.21 -98.02 42.11 1000 $2.11 140.13 72.10 -34.66 -21.53 98,5l -102.18 44.98 1100 49.48 147.16 75.39 -34.76 -22 22 111.82 - 106.21 47.64 1200 57.17 153.85 78.23 -34.70 -22.79 125.13 -110.12 50.09 1300 65.12 160.21 80.67 -23.27 -34.52 1%.44 -113.91 52.35 1400 73.29 166.26 82.79 151.74 -34.25 -23.69 1500 -117.60 54.44 81.66 172.04 84.63 -33.90 -24.04 165.02 To retain internal consistency, some values are given to one more decimal place than is justified by the absolute accuracy For the reaction 6C(c, graphite) 6Hz(g) = CcH1?(g). ,
+
Values of three molecular-structure parameters were selected to fit the experimental calorimetric data: the height of the potential barrier restricting internal rotation of the methyl group, 3000 cal. mole-'; the height of the potential barrier restricting pseudo-rotation of the 5-membered ring, 750 pal. mole-'; and the effective moment of inertia for pseudo-rotation, 18.0 X g. cm.2. Effects of vibrational anharnionicity were neglected. The values given for the three molecular-structure parameters are Foniewhat uncertain because of neglect of anharmonicity as well as uncertainties in the moments of inertia and vibrational frequencies. Nevertheless, these values are reasonable in terms of present knowledge of the structure of related molecules. In particular, the height of the potential barrier to pseudo-rotation agrees well with the value, 900 cal. mole-', calculated by Pitzer and Donath7 from conderations of differences in torsional strain energy. The barrier height for the (7) K. S. Pitaer and IT. E. Donath, J. Am. Chsm. Soc., 81, 3213 (1959).
increments are strictly for normal paraffins above n-heptane; their use in the foregoing formulas is justified only by the good empirical fit t,o the experimental calorimetric data over a wide range of temperatures. [No advantage could be gained by use of less empirical but more complicat,ed formulas like C,"
2C,"(methylcyclopentane) - C,"(cyclopentane) [corn. for restricted pseudorotation! [constant]
=
+
+
where the term "correct8ionfor restricted pseudorotation" is necessary bemuse pseudorot,atioii is restrict>edin thc substituted compounds but not in cyE. Kitpatrick, Chem. Reus., 39, 435 (1946). (9) T h e vibrational contributions were computed a t the Bureau of 18) K. S. Pitzer and J.
Mines Computation Laboratory. Pittsburgh, Pa.: the contributions of internal rotation and restricted pseudo-rotation were compuwd a t Southwestern Computing Service, Denver, Colo., by two-way curvilinear interpolation in the tables of I
