1303
THERMODYNAMICS OF GLOBULAR MOLECULES
Thermodynamics of Globular Molecules.
XVII.
Heat Capacities and
Transition Behavior of Bicycle[2.2.Z]octane and Bicyclo[2.2.2]octene1
by Wen-Kuei Wong2 and Edgar F. Westrum, Jr.S Department of Chemistry, University of M i c h i g a n , Ann Arbor, M i c h i g a n
48104
(Received November 8,1060)
The thermal properties of two globular molecules, bicyclo [2.2.2]octane and bicyclo [2.2.2]oct-2-ene, have been determined from 5°K into their liquid ranges (465°K and 411°K, respectively). The former undergoes a solid-solid phase transition at 164.25"K and melts at 447.48"K. The associated entropy increments, ASt = 6.66 cal/mol OK and AS, = 4.48 cal/mol OK, are positive evidence that the material is a plastic (or embefic) crystal. The octene undergoes solid-solid phase transitions at 110.50"K and at 176.47'K and melts at 389.75OK. The sum of the entropies of transition, 8.44 cal/mol "K, and the low entropy of fusion, 2.43 cal/ mol OK, are evidence that this material is also an embefic crystal. Mechanistic considerations, consistent with the molecular geometries, that accord with the observed transitional entropies are presented. The standard molal value of heat capacities, entropies, and Gibbs energy functions for the crystalline octane and octene are 37.69, 37.46; 50.18, 50.30; and -25.68, -24.63 cal/mol "K, respectively, at 298.15"K. The standard Gibbs energies of formation are 18.21 kcal/mol of bicyclooctane and 38.48 kcal/mol of bicyclooctene, also at 298.15'K.
Introduction Several of the previous papers in this series4 have reported the results of thermal studies on globular molecules whose geometry is related to that of bicyclo[2.2.2]octane. This family of open, cagelike structures is of particular interest because the thermodynamics describing the transition and fusion phenomena can be linked to subtle variations in the symmetry of the cage. The entropy values for transition and fusion of several of these compounds have been included in a recent review.6 This paper presents the results for the octane, bicyclo [2.2.2]octane, and the octene, bicyclo[2.2.2]oct-2-ene, and related substances and will cover the experimental data on which the review article was based and will discuss further mechanistic interpretations of the transitional entropy increments. Of the several compounds in this family the octane can, with some logic, be considered the prototype and has been reported to possess either DBh or CDsymmetry.6 The latter formulation would provide a mechanism for strain relief. It has the most symmetrical cage structure and exhibits all the properties normally associated with embefic crystals.' I n the closely related octene, the threefold axis passing through the bridgehead carbons is lacking so that it is only an "almost" symmetrical-top type of molecule. The nature of the transitions in these materials has drawn the attention of several groups and three interpretations have been made.8-10 Experimental Section A crude sample of the octane was obtained from the Hi Laboratory, Inc., and was subjected to multiple fractional sublimation followed by 20 passes of zonemelting refining. The elemental analysis results were 87.07'% C and 12.75% H and are in satisfactory accord
with theoretical values of 87.19% and 12.81%. A sample (52,5856 g vacuum mass) of this material was sublimed into calorimeter W-42 for the cryogenic thermal measurements; and a sample (53.1178 g vacuum mass) into calorimeter W-22 for the intermediate temperature-range measurements covering the fusion region. The octene was also obtained from the Hi Laboratory, Inc., and was treated in a similar manner. No impurities were detected by vapor-phase chromatography and the elemental analyses, 88.69% C and 11.05% H, accord well with the theoretical values, 88.82% and 11.18%. The cryogenic thermal measurements were conducted on a sample (22.5552 g vacuum mass) that had been sublimed into calorimeter W-37. A sample (36.2478 g vacuum mass) contained in calorimeter W-
(1) This work was supported in part by the Division of Research, United States Atomic Energy Commission. (2) Abstracted in part from a dissertation submitted in partial fulfillment of the requirements for the Ph.D. degree from the Horace H. Rackham School of Graduate Studies at the University of Michigan. (3) To whom correspondence concerning this paper should be addressed. (4) 9. S. Chang and E. F. Westrum, Jr., J. P h y s . Chem., 64, 1551 (1960); C. M.Barber and E. F. Westrum, Jr., ibid.,67, 2373 (1963); J. C. Trowbridge and E. F.Westrum, Jr., ibid.,67,2381 (1963); C. A. Wulff and E. F. Westrum, Jr., ibid.,68, 430 (1964). (5) E. F. Westrum, Jr., "Thermochemistry and Thermodynamics'' in "Annual Review of Physical Chemistry," Vol. 18, H. Eyring, Ed., Annual Reviews, Inc., Palo Alto, Calif., 1967, p 135. (6) 0. Ermer and J. D. Dunitz, Chem. C o m m u n . , 10, 567 (1968); A. F. Cameron, G. Ferguson, and D. G. Morris, ibid., 6, 316 (1968). (7) C. A. Wulff, cited in ref 5 (p 137). (8) I. Darmon and C. Brot, Mol. Cryst., 2,301 (1967). (9) L. M. Amzel and L. N. Becka, J. P h y s . C h e m . Solids, 30, 521 (1969). (10) J. A. Pople and F. E. Karasz, ibid., 18,28 (1961).
V o l u m e 74, N u m b e r 6
M a r c h 19, 1070
1304
WEN-KUEIW o ~ AND a EDGAR F. WESTRUM,JR.
Table I : Experimental Heat Capacity Determinations on Bicyclo[2.2.2]octane and Bicycl0[2.2.2]octene-2~ T
-
T
T C, Bicyclo[2.2.2]octane
Ce
Data Taken. in Mark I1 Calorimetric Cryostat Series I Series I1 11.06 0.5577
12.22 0.7561 16.46 139.37 1.038 17.20 AHt Run A 20*04 13.48 14.82 1.376 18.06 16.25 1.769 18.99 Series I11 17.88 2.262 20.07 2.908 21.67 ' 141 05 20.30 19.90 3.639 27.96 145.88 21 -04 22.12 4.412 62-40 150.52 22.38 24.46 27.22 5.301 227.5 154.81 25 80 6.275 291.3 158-45 34.65 30.45 34.09 7.298 145.9 161.39 55.52 38.06 8.284 56.67 163.34 129.2 42.28 9.196 29.32 164.16 423 46.65 10.04 25.90 164.56 413 51.52 10.87 26 35 165.08 255 56.78 11.64 27.10 165.80 204 62.28 12.40 27.90 167.05 93.0 68.32 13.12 28 84 169.45 45.2 29.78 172.89 30.46 75.27 13.85 30.87 176.85 26.01 83.50 14.71 31.88 181,04 25,81 92.63 15.57 16.38 32.96 185.23 25.83 102 25 AH Run 34.00 138.35 19.96 35.18 Series IV 36.41 Series V 37.57 5.24 0.0371 38.71 6.25 0.0636 A H t R u n B 40.00 7.07 0.1022 Series VI 41.25 7.96 0.1685 42.25 8.95 0.2707 140.30 20.22 43.51 9.99 0.4111 AHtRun C Data Taken in Mark I V Calorimetric Thermostat Series VI1 446.82 1940 456 22 63.29 446.95 461.56 63.73 2080 309.31 39.13 466.72 63 99 319.73 40.58 447.05 3200 471.87 64.73 330.00 42.00 447.12 3700 477.00 65.64 188 340.14 43.30 448.64 482.14 66.14 350.04 44.71 Series IX 359* 79 45.96 Series XI1 369.36 47.27 AH Run 1 AH Run 2 AH Run 3 378.94 48.53 426.95 55.18 413.20 53.28 Series VI11 AHf Run A 423.11 54.54 55 * 59 428.86 AH Run 1 Series X 56.40 433.96 382.36 49,03 53.89 438.45 56.97 392.03 50.25 418.57 55.40 442.80 61.30 401.64 51.62 427.85 AHf Run D 411.20 52.94 AHf Run B 62.47 450.65 420.65 54.25 Series X I 454.89 62.84 429.91 55.67 55.83 459.12 63.54 438.97 57.21 430.93 463.33 63.86 445.00 200.0 a H r Run C 446.65 1210 103.55 111.87 120,67 129.99 139.37 148.32 156.47 162,16 164.60 165.50 166.71 169.56 175.17 183.15 192.17 201.57 211.20 220,79 230.61 240.62 250.32 259.83 269.12 278.46 287 72 296.88 306 21 315.60 324.73 333.66 342.38
I
I
I
I
I
I
I
Bicyclo[2.2.2]octene Data Taken in Mark I11 Calorimetric Cryostat 273.76 34.87 36.64 Series I
19.98 283.37
136.41
Units: cal, mol, OK.
The Journal
CS
140.97 147.49 155.12 164.34 172.36 175.87 176.41 177.04 180.29
20.53 21.34 22.44 24.54 44.54 464.9 793.4 393.4 50.48
I
I
a
T
CS
of
Physical Chemistry
35.83
41.40
CS
292.77 302.10 311.48 320.80 330.06 339.27
36.93 37.99 39.12 40.21 41.31 42.45
Series V
151.76 161.45
21.95 23.59
AzHt Run A
Series I1
184.44 28.70 20.13 194.37 28.12 18.90 204.23 28.70 19.24 20.04 Series VI 21.02 154.35 22.35 162.73 24.09 Series I11 AzHt Run B 28.74 103.65 19 20 184.03 111.68 21.55 Series VI1 120 66 19.04 5.96 0.0533 130 07 19.35 6.75 0.0835 139.28 20.34 7.72 0.1416 148.34 21.51 8.68 0.2240 157.46 22.89 9.64 0.3214 166.38 25.58 0.4389 173.06 58.68 10.64 11.69 0.5799 175.73 496.6 13.00 0.7977 176.28 644.2 14.45 1.084 177.18 278.0 1.405 181.74 34.79 15.90 1.791 190.87 27.99 17.50 2.200 201 * 12 28.55 19.09 20.61 2.603 22.29 3.057 Series IV 24.22 3.591 231.49 30.83 26.68 4.249 243-41 31.82 29.62 5.006 254.01 32 83 32.86 5.804 264.06 33.83 115.43 121.52 128.82 136.56 144.69
I
I
I
I
-T
C.
46.40 51.16 56.41 62.14 68.21 75.12 83.17 91.91
8 438 9.173 9.889 10.62 11.29 12.02 12.97 14.45 e
Series VI11 AH Run (I)
86.52 13.43 92.96 14.68 97.46 16.49 102.04 18.30 106.85 20.64 111.46 21.98 116.04 20.13 120.78 18.90 125.55 18.97 130.23 19.37 145.67 21.17 155.42 22.55 AzHt Run C 183.18 32.03 193.99 28.13 204.31 28.71 213.64 29.33 222.77 30.08 230.60 30.61 Series I X
110.00 110.99 111.97
22.01 22.21 22.06 Al.%HtRunD Series X
81.27 88.46
12.74 13.79
AIHt Run A Data Taken in Mark IV Calorimetr -ic Thermostat Series X I 389.20 1001 AH,,, Run A
294.59 302.49 311.37 320.34 329.41 338.30 347.01 365.47 363.66 371.71 379.60 385.35 387.85 388.81
36.50 37.60 38.69 361.72 40.86 41.98 43.18 44.23 45.41 46.50 48.13
78.95 255.6 621.8
Series XI1
378.00 382 45 385.97 387.93 388.79 I
6.642 7.577
-T
47.86 53.20 92.46 252.4 531.0
389.81 392.47 396.76 402 69 I
309.4 Series XV 53.17 53,61 362.53 45.25 54.49 371.09 46.53
Series XI11
299.39 307.94
AH, Run
37.15 Series 38.40 380.89 AH Run (I) 384.29 370.70 46.52 386.60 379.70 50.63 387.87 385.52 81.67 388.57 387.33 177.7 388.97 388.21 334.0 389.21 388.72 586.1 389.41 389.03 935.3 391.04 389.20 1911 394.68 389.38 9Gl7.1 399.11 403.72 Series XIV 368.88 46.22 408.29
B XVI
49 * 37 63.56 125.1 249.8
471.8 799.1 1273 1185 55.52 53.52 53 70 54.77 55 17 I
I
THERMODYNAMICS OF GLOBULAR MOLECULES
1305
Table 11: Thermodynamic Properties of Bicyclo[2.2.2]octane and Bicyclo[2.2.2]0ctene-2~ T
8"
CS
Ha
- Hoo
-(a0
-
H0o)/T
Bicyclo [2.2.2]octane Crystal I1 Phase 5 0,032 10 0.400 15 1.420 20 2.940 25 4.590 30 6,147 35 7.530 40 8.722 45 9.740 50 10.62 60 12.08 70 13.31 80 14.37 15.31 90 100 16.18 110 17.05 120 17.98 130 18 * 99 Transition Region 140 20,15 150 22.06 160 42.20 164.25 540 170 41.40 180 25.82 Crystal I Phase 190 26.18 200 26.97 210 27.82 220 28.74 230 29.73 30.78 260 250 31 -77 260 32.99 270 34.15 273.15 34.53 280 35.36 290 36.63 298.15 37.69 300 37.93 310 39.26 320 40.60 330 41.93 340 43.26 350 44.59 360 45.95 370 47.33 380 48.71 390 50.07 400 51 -40 410 52.72 420 54.15 430 55.72 440 (57.35) 447 * 12 (58.38) Liquid Phase 447.12 (61.93) 450 62.29
0,010 0.108 0.442 1.050 1.884 2.861 3.915 5,000 6,088 7.160 9.230 11.19 13.04 14.78 16.44 18.02 19.55 21.03
0,039 0.847 5.125 15.888 34.728 61.626 95 898 136.61 182 82 233.77 347.53 474.65 613.18 761.69 919.15 1085.2 1260.3 1445.1
22.47 23.92 25.70 28.22 33.14 34.82
1641 1850 2130 2540 3350 3650
10.76 11.59 12.41 12.78 13.42 14.56
36.22 37.58 38.91 40.22 41.52 42.81 44 09 45.36 46.63 47.02 47.89 49.16 50.18 50.42 51.68 52.95 54.22 55.49 56.76 58.04 59.32 60.60 61.88 63.17 64.45 65.74 67.03 68.32 69.25
3905 4171 4445 4728 5020 5322 5636 5960 6296 6404 6643 7003 7306 7376 7762 8161 8574 8999 9439 9891 10358 10838 11332 11839 12360 12894 13443 14008 14419
16.66 16.72 17.74 18.73 19.70 20 -64 21.55 22.44 23 31 23.58 24.17 25.01 25.68 25.83 26.65 27.45 28.24 29.02 29.79 30.56 31.32 32.08 32.83 33.57 34.31 35.04 35.76 36.49 37 .oo
73.73 74.12
16415 16593
37 .OO 37.24
I
#
I
0.003 0.024 0.100 0.256 0.495 0.807 1,175 1.585 2.025 2,485 3.438 4.407 5.371 6.321 7.251 8.159 9.045 9.910
I
-T
CB
460 470
63.49 64.69
SO
I
- H'o
75.50 17222 76 88 17863 Bicyclo [2.2.2]octene-2
Crystal I1 5 0,026 10 0.355 15 1.203 20 2.438 25 3.799 30 5.106 35 6.282 40 7.311 45 8.209 50 9.000 60 10.355 70 11.484 80 12,567 Lower Transition Region 90 14,022 100 17.120 110 22.170 110.50 22,450 120 19.042 130 19.347 140 20.433 150 21.709 160 23,445 Crystal I 170 31 -65 176.47 (807) 180 59.20 Higher Transition Region 190 27 958 28.445 200 210 29.106 220 29.841 230 30.635 31.497 240 250 32.429 260 33.420 270 34.452 273.15 34.783 280 35.507 290 36.576 298.15 37.457 300 37.659 310 38.767 320 39.911 330 41.096 340 42.318 350 43.568 360 44 871 370 46,344 380 48.67 389.75 (48.97) Liquid 389.75 (52.75) 395 53.50 400 53.70 405 54.32 500 56.05 I
Ha
I
0 009 0 * 101 0 388 0.897 1.587 2.397 3.274 4.182 5.096 6.003 7.767 9.451 11.053 I
I
0.034 0.785 4.471 13.47 29.058 51.363 79,893 113.94 152.79 195.85 292.84 402.20 522.30
-(GO
-
Hoo)/F
38.06 38.87
0,002 0,022 0.090 0.224 0 425 0.685 0,992 1.333 1.701 2.086 2.887 3.705 4.524
12.607 14.230 16.094 16.196 17.888 19.415 20.887 22.340 23.791
654.41 808.71 1005 1016 1211 1401 1599 1810 2035
5.336 6.143 6.961 7.002 7.800 8.640 9.462 10 273 11.072
25.343 27.798 29.791
2292 2721 3075
11.864 12.378 12.710
35.980 37.425 38.829 40 200 41.544 42.865 44.169 45 460 46.74 47.143 48.013 49.278 50.304 50.536 51.789 53.037 54.283 55 528 56.773 58.018 59.268 60.527 61.680
4178 4460 4748 5043 5345 5656 5975 6304 6643 6753 6993 7354 7656 7725 8107 8500 8905 9322 9752 10194 10650 11120 11565
13 988 15.124 16,220 17.279 18,305 19.300 20.269 21.213 22.135 22.421 23.037 23,920 24 627 24.786 25.637 26.473 27 ,297 28 109 28.910 29.702 30.484 31.258 32.016
65.123 65.77 66.45 67.12 67.80
12851 13159 13428 13698 13974
32.150 32.46 32.88 33.30 33.71
I
I
I
I
I
I
I
'Units: cal, mol, "K. Volume 74, Number 6 March 10, 1970
WEN-KUEIWONGAND EDGAR F. WESTRUM,JR.
1306
Table I11 : Enthalpy Increments of Transition and Melting for Bicyclo[2.2.2]octane and Bicyclo [2.2.2]octene-2" Source of data
Number of runs
Ti
Tz
H T ~ H T ~ HIQO- His5
Bicyclo [2.2.2]octane Transition Series I Series I1 Series I11 Series V Series VI
Source of data
10 2 17 2 2
134.80 187.55 2300 2362 134.62 188.67 2338 2365 138.61 187.33 2225 2366 133.69 189.19 2368 2364 135.70 189.39 2333 2363 Average value H19a - HI85 = 2364 i 1 Graphical integration H ~ Q-O HI35 = 2364 Lattice contribution HI50 - Hla5 = 1268 AH$= 1096 ASt = 6.66 Tt = 164.25
Number of run8
Ti
Tz
H T ~- H T ~ Haec
8 1
375.68 394.63 2216 2276b 373.13 391.79 2192 2276 1 375.33 393.55 2183 2276 Average value HS86= 2276 i 0 Graphical integration H 3 9 ~ = 2276 Lattice contribution Ha56 - Ha75 = 990 AH, = 1286 i 0 AS, = 2 . 4 3 T, = 389.75 Average value H126 - H80 = 783 i= 1 Graphical integration H126 - HaO= 783 Lattice contribution Hlz5- Hsa = 738 AIHt = 45 f 1 A186 = 0 . 7 8 IT^ = 110.50
Units: ca1, mol, OK.
Series I Series I11 Series V Series VI Series VI11
Number of runs
Source
Number of runs
Series VI11 Series I X
H T ~- H T ~ Him
- Hlao
Ti
TS
H T ~- H T ~ Hiso - His6
Bicyclo [2.2.2]octane Pill elting 8 434.47 450.13 2929 2872b 1 430.19 449.59 3116 2871 1 432.44 461.94 3136 2870 1 433.75 450.46 2867 2868 4 436.22 452.77 2975 2870 2870 i 1 Average value H ~ S O H435 Graphical integration H450 - Ha5 = 2870 Lattice contribution H4b0 - Ha36 = 875 AH, = 1995 f 1 A&, = 4 . 4 8 T, = 447.48
Series VI11 Series I X Series X Series X I Series XI1
Source data
Tz
2199 2199b 2200 2198 2200 2199 f 1 2200 849 1350 i 1 A I I S ~= 7 . 6 6 IITt = 176.47
of data
of
Ti
Bicyclo [2.2.2]octene-2 Transition I1 6 159.55 177.38 1957 185.69 2247 7 162.10 189.39 2202 3 156.74 188.68 2135 3 158.66 3 160.18 199.61 2409 Average value Hlst - H M O= Graphical integration H192 - H160 = Lattice contribution H I ~ Z Hi60 = A I I H ~=
- Hsia
Bicyclo [2.2.2]octene-2 Melting Series XI1 Series XIV Series XV
Source data
of
Number of runs
Ti
Tz
H T ~- H r l Hinc - Hsa
Bicyclo [2.2.2]octene-2 Transition I 809 9 82.46 127.92 3 76.64 123.99 806
784 783
A correction has been made for quasi-adiabatic conditions.
22 was utilized for the intermediate range thermal measurements extending through the fusion region. The cryostats" (Mark I1 for the octane and Mark I11 for the octene) and the intermediate range thermostatI2 (Rlark IV) have been described previously. The circuitry used to maintain adiabaticity as well as the calculational procedures have also been reported. l 1
Results The measured heat capacities are presented in Table
I a t the mean temperatures of each determination. The data are stated in terms of the defined thermochemical calorie equal to 4.1840 abs. J and an ice point of 273.15"K, and are presented in chronological sequence to facilitate estimation of temperature increments for measurements within a given series. Except in regions containing heat capacity anomalies, these have been corrected for curvature. Probable errors decrease from 5% a t the lowest temperatures to 1% at 10°K and to O.l%, or less, above 25OK. The data are depicted in Figures 1and 2 . T h e Journal of Physical Chemistrg
The molal values of the thermodynamic functions are presented in Table 11. These were obtained from suitable integrations of computer-fitted polynomials through the data points with extrapolations below 5°K obtained from the Debye limiting T3 relation. Increments through transition and fusion regions were integrated from large scale plots of the data. The probable errors in the derived functions are comparable to those in the heat capacities themselves. The octane undergoes a solid-solid phase transition at 164.2S"K. The process is apparently first order with heat capacities as high as 540 cal/mol "K and with characteristically slow thermal equilibration. (11) E. F. Westrum, Jr., G. T. Furukawa, and J . P. McCullough, "Adiabatic Low-Temperature Calorimetry" in "Experimental Thermodynamics" J. P. McCullough and D. W. Scott, Ed., Butterworth and Co., Ltd., London, 1968. (12) E. D. West and E. F. Westrum, Jr., "Adiabatic Calorimetry from 300 t o 800OK" in "Experimental Thermodynamics," J. I?. MoCullough and D. W. Scott, Ed., Butterworth and Co., Ltd., London, 1968.
1307
THERMODYNAMICS OF GLOBULAR MOLECULES Temperature, *K.
300
0
Table IV : Fractional Melting Data for Bicyclo[2.2.2]octane
400
and Bicyclo[2.2.2] octene-2'
I
T
-
CB
60 -
F
446.65 446.82 446.95 447.05 447.12
-
D 0
2E 4 0 -
1210 1940 2080 3200 3660
AT
2AH
1/F
Tfinal
Bi cy clo [2.2.21 o ct m e b 0.210 693 446.70 0.132 948 446.89 0.122 1203 447.01 0.080 1459 447.09 0.070 1715 447.16
2 879 2.104 1.658 1.368 1 163 I
I
0.
J
-
Triple point of sample 447 190 Triple point of pure compound 447.476 Mole fraction impurity 0.0014 I
20 -
10 20 Tamperalure , O K .
0
388.21 388.72 389.03 389.20
30
Figure 1. The heat capacity of bicyclo[2.2.2]octane.
Crystal
I
1 4
E
'Units: cal, mol, OK. * Data from melting runs series VIII. Data from melting runs series XII.
Liquld
-..L-
0
10
20
30
Temperature , O K .
Figure 2.
2.683 1.840 1,384 1.113
6
60
0
Bicyclo [2.2.2]octene-20 388.53 0.638 479 388.91 699 0.375 389.15 0.238 929 389.26 0.118 1155
Triple point of sample 389.32 Triple point of pure compound 389.75 Mole fraction impurity 0.0018
Temperature , O K .
Crystal II
334 586 935 1911
The heat capacity of bicyclo[2.2.2]octene.
Drifts extending from 10 to 14 hr were required for equilibrium. Six series of measurements through the transition region are listed in Table 111. The crystal I phase melted at 447.48"K with ASl,, equal to 4.48 cal/ mol OK. Bartlett and Woods1a have reported 169170°C as the melting temperatures. The AHm value is based on five series of determinations also listed in Table 111, while the melting temperature is derived from a fractional melting analysis presented in Table IV. Implicit in that analysis is the absence of solidsolution formation between octane and its 0.0014 mole fraction of total impurity. The course of the solid-state heat capacities of the octene is marked by two thermal anomalies with apparent maxima at 110.50"K and 176.47"K. That the former is a higher than first-order transition is evidenced by the rapid attainment of equilibrium and hump-like shape. The rate of attainment of thermal
equilibrium between 85 and 120°K is the same as in the adjacent regions. The transition at 176.47"K is apparently first order with a sharp onset, slow equilibrium, and heat capacities in excess of 800 cal/mol O K . The results of several series of measurements through these transition regions and through fusion may also be found in Table 111. Crystal I melts at 389.75"K with AS, equal t o 2.43 cal/mol OK. Table IV, which contains the fractional-fusion analysis, indicates a 99.82% purity on the assumption that the impurity is liquid-soluble, solid-insoluble. Recent unpublished enthalpy of combustion datal4 together with tabular values for the entropies of the elements16 can be combined with the third-law entropies of this study to provide standard enthalpies and Gibbs energies of formation. The results are AHf" = -35.15 -I: 0.10 lical/mol and AGf" = 18.21 f 0.11 kcal/mol of octane and AHf" = -5.60 0.08 kcal/ mol and AGf" = 38.48 f 0.09 kcal/mol of octene at 298.15 OK.
*
Discussion The low values of the entropies of fusion and the existence of highly energetic solid-solid transitions are clear evidence that both compounds fall into the embe(13) P. D.Bartlett and G. E'. Woods, J . Amer. Chem. Soc., 62, 2933 (1940). (14) S.-w. Wong and E. F. Westrum, Jr., unpublished data. (15) D. D. Wagman, W. H. Evans, I. Halow, V. B. Parker, 5. M. Bailey, and R. H. Schumm, U. S. National Bureau of Standards Technical Note 270-1,"Selected Values of Chemical Thermodynamic Properties," U. S. Government Printing Office, Washington, D. C. 20402,1965.
Volume 74, Number 6 March 19, 1970
1308 fic crystal series. It is believed that the crystal I phases of such materials permit a considerable degree of orientational disorder for each molecule and that the low entropies of fusion reflect only the disappearance of long-range structure-the short range order having been dissipated a t the solid-solid transition. If one assumes Dah symmetry for the octane, a mechanistic model of the solid-solid transition can be developed along the lines proposed by Guthrie and McCullough.lB The requirements of such a model are that the effec'tive point symmetry of the molecule must be a subpoint group of the symmetry of the lattice site. The threefold molecular axis can be aligned with any of the four threefold axes of the cubic ( O h ) lattice in two different ways that differ by a 60" rotation. The eight configurations arising in this manner can be augmented by twelve more arising from alignment of the molecular and lattice twofold axes and of the molecular mirror planes with the horizontal and diagonal mirror planes of the lattice. The twenty orientations considered possible correspond to a transitional entropy increment of ASt = R In 20 = 5.95 cal/mol OK. (The implicit assumption that the crystal I1 phase is ordered is considered a t greater length e1se~here.l~)The difference between the observed A S t and R In 20 or 0.7 cal/mol OK may well be due to increases in overall vibration of the molecules above the transition temperature. The principal difference between the octene and the octane is the additional threefold asymmetry in the former caused by the double bond. While the crystal
The Journal of Physical Chemistry
WEN-KUEIWONGAND EDGAR F. WESTRUM, JR. structure of this material has not been determined, it is reasonable to assume that the molecules occupy Oh sites similar to those of the octane. If this is true, and the disordering process is mechanistically similar, one could expect 3 X 20 isoenergetic configurations for the molecules in the crystal I phase of the octene. The predicted entropy increment, ASt = R In 60 = 8.14 cal/ mol OK, is in fair accord with the sum of the two ob7.66 = 8.44 cal/mol OK. served increments, 0.78 The magnitude of the difference is again that which might be expected for increases in overall vibration. It is interesting to note that the threefold "rotational" asymmetry in the octene may also be reflected in the entropies of fusion. The difference in these quantities 4.48 (octane) - 2.43 (octene) = 2.05 cal/mol OK is tantalizingly close to R In 3. Amzel and BeckaQhave shown that these mechanisms are consistent with their extension of the melting theory of Pople and Karasz."J They have included observations concerning the nmr interpretations of Darmon and Brat.*
+
Acknowledgment. The authors appreciate the support of the U. s. Atomic Energy Commission and the assistance of William G. Lyon in the experimental measuremen ts. (16) G . B . Guthrie and J. P. McCullough, J. Phys. Chem. Solids, 18,
53 (1961).
(17) C. A. Wulff and E. F. Westrum, Jr., submitted to J. Chem. Therm.
