Dec., 1948
THERMODYNAMICS AND STRUCTURE OF CYCLOPENTENE AND CYCLOHEXENE
4227
[CONTRIBUTION FROM TEE DEPARTMENT OF CHEMISTRY, UNIVERSITY OF CALIFORNIA]
The Thermodynamic Properties and Moleculai. Structure of Cyclopentene and Cyclohexene'
c. w. BECKETT,~N. K. FREEMAN3 AND KENNETHs. PITZER* 109.5)'] + 1.95[1 38121 f 2.8[1 The molecules cyclopentene and cyclohexene 3(9ls - 60)] have been studied by methods which followed natBY
COS
COS
(1)
urally from earlier work on cyclopentane5 and cy- where a1 is the skeletal bond angle at carbon 1, clohexane.6 The potential energy relationships for etc., and (012 and (p16 are the twist angles about bond bending and twisting (internal rotation) were bonds 1-2 and 1-5. The latter are measured with transferred from the most analogous molecules respect to deviation from the planar configuration. where they are known and are used to deduce It should be observed that in the planar structure the equilibrium configurations of these slightly the hydrogens about bond 1-2 are staggered, givstrained' ring molecules. With the aid of these ing a potential minimum for torsion, whereas the results and the vibrational spectra the thermody- hydrogens about bond 1-5 are opposed, giving a namic properties are correlated and extended by maximum. The difference in form of the terms in calculation to other functions and temperatures. the potential function for these bonds is a conseCyclopentene. Structure.-The torsional quence of this fact. forces about a double bond are so much larger The symmetry of atoms 1 and 4 and of 2 and 3 than those about single bonds as to justify the is considered in the formula. The bond distances assumption of planarity for four of the five C-C, 1.54 A. and C=C, 1.35 A. were assumed. carbon atoms of cyclopentene. These are atoms 1 Figure 1 shows the resulting potential energy as to 4 in the diagram. However, if atom 5 is also a function of Z. The various CY'Sand (p's were adjusted, so far as the geometry allows, to mini2 3 mize the energy for each Z value. Since there is I=\ some uncertainty as to the correctness of the 6 potential constants, one should not regard the slight potential drop from Z = 0 to Z = 0.22 A. in this plane, bonds 1-5 and 4-5 are at the maxi- as significant. However, one can conclude that, mum torsional energy since the methylene hydro- within the magnitude of thermal energy a t room gens are in opposed configuration. Therefore, we temperature, the potential energy of cyclopencalculated the total potential or strain energy of tene is unchanged by puckering atom 5 out of the cyclopentene as a function of the distance, Z, of plane by any amount up to about 0.3 A. For the carbon atom 5 from the plane of the other four. purpose of statistical mechanical calculation this The C-C-C angles were adjusted to optimum val- potential function was expressed as ues for each assumed value of 2. The various potential constants employed are as follows: C-C-C and C 4 - C angle bending, This function is shown dotted in Fig. 1 with a = K = 1.0 x ergs/radian2 (a rounded average 0.277 A. and b = 17.25 kcal./mol At., and is seen of values from various molecules); twist of 1-5 to approximate the solid curve rather well. and 4-5 bonds, Vo = 2800 cal./mole from ethane Cyclopentene. Vibration Spectrum.-The (and used for cyclopentane) ; twist of 1-2 and 3-4 Raman spectrum of cyclopentene was taken from bonds, Vo= 1950 cal./mole from propylene.* the work of re it^,^ which is in good agreement The final formula is, then, in kcal./mole with earlier studies. The infrared spectrum has been observed by V = 0.022[2(a1 - 109.5)' 4- 2(a2 - 120)' (a, several laboratories in the 3 to 15 micron rangei0 (1) This research was supported by the American Petroleum Inand by the Shell Development Company from 15 stitute under Research Project 44 at the National Bureau of Standto 24 microns." ards and the University of California. (2) Research Associate, Project 44 of the American Petroleum The various bands were assigned on the asInstitute. sumption of an average symmetry of CzVand with (3) Research Assistant, Project 44 of the American Petroleum full consideration of the corresponding frequencies Institute. in related molecules. The result is given in Table (4) Associate Director of Project 44 of the American Petroleum Institute and Professor of Chemistry, University of California. I. While this assignment is far from certain in ( 5 ) J. E. Kilpatrick, K. S. Pitzer and R . Spitzer, THIS JOURNAL, every detail, it seems probably correct for the 9, 2483 (1947).
'V
+
(6) C. W. Beckett, K. S. Pitzer and R . Spitzer, i b i d . , 69, 2488 (1947). (7) R. S. Pitzer, Science, 101, 672 (1945). (8) Note that the cis-2-butene potential barrier value is not appropriate because hydrogen atoms on the two methyl groups interfere. In cyclopentene these hydrogens are absent and the bonds go instead to the third methylene group.
(9) A. W.Reitz, 2. p h y s i k . Chem., BSS, 179 (1936). (10) Catalog of Infra-red Spectrograms issued by the American Petroleum Institute Research Project 44 at the National Bureau of Standards, Serial Nos. 200 and 456 from the Shell Development Company and 362 from the Socony-Vacuum Oil Company. (11) Private communication from the Spectroscopic Department of the Shell Development Company.
C. W. BECKETT] N. K. FREEMAN AND KENNETH S. PITZER
4228
VOl. 70
TABLE I VIBRATIONAL SPECTRUMOF CYCLOPENTENB CW symmetry assumed Where values are given in parentheses, these are average observed or merely expected values. The second parenthesis gives the number of modes assumed to have this frequency. Ai
At
Selection rules Ring bending C-H rockinj: CH2 rocking
Ra., I. R. 607 Ra, I R
Ra.386 Ra1020 Ra935 Ra-
C-C stretching
900 Ra. IR 1104 Ra 1287 Ra, IR 1208 ?, I R
Sym. class
......... .........
C-H wagging CH1 wagging
(I
........
.......
9.6 __L_1
0.1
0.2
2,A.
0.3
0.4
0.5
Fig. l.-Total strain energy as a function of the out of plane distance of apical carbon atom. Solid line is calculated curve; dotted line, approximation employed for thermodynamic calculations.
Cyclopentene. Thermodynamics.-The entropy of cyclo entene, liquid, is 48.10 cal./deg. mole a t 298.16 K. from the experiments of Huffman and collaborators,12 while the entropy of vaporization1ato the ideal gas a t that temperature is 21.13 cal./deg. mole. This gives an experimental value for the ideal gas entropy of 69.23 cal./deg. mole a t 298.16'K. The moments of inertia of cyclopentene, with
E
(12) H. M. Huffmen, private eommunicaton.
(18) F. D. R o d n i , private communication.
975-Ra, IR 1129-IR 1352-IK 1201R ? 1300 ? IR
........
....... .......
thermodynamically important low frequencies and statistically correct for the higher frequencies.
............ ............
........
......
.........
Ra, IR 717-IR
696-IR 1046-IR 1143-IR
(1330) (2) 1437 Ra ? 1462 Ra, I R C=C! stretching 1623 Ra, I R ....... ....... C-H str. (olefinic) 3060 Ra, I R C-H str. (CHI) (2950) (2) (2950) This is the ring puckering motion whose potential is shown in Fig. 1.
CH? twisting CH8 bending
B*
Bi
Ra, IR
............
(1330) (1)
........
1445 ?, IR
............
........
........
3060 Ra, I R (2950)
(29.30) (2)
the dimensions given above, are 11.53, 11.87 and 21.80, all X g. cm.*. Using these values, and the vibrational assignment given above, one calculates 65.13 cal./deg. mole for the entropy, excepting the peculiar ring puckering motion. This leaves 4.10 cal./deg. mole for that motion. Thermodynamic functions are readily calculated (see Appendix I) for the potential energy of eqn. 2 on the classical mechanical basis. For heavy particles and a low effective frequency the quantum mechanical effects will be negligible. However, to make the entropy calculations entirely theoretical an effective reduced mass of the ring puckering motion is needed. Since the calculation of this mass would be quite laborious and would contribute relatively little in view of other approximations already made, we merely solved TABLE I1 CYCLOPENTENE, THERMODYNAMIC FUNCTIONS (Units: cal. per degree mole)
- (P - H:)
U P - H:)
T,O K . 200 298.16 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500
T
0
T
so
9.97 11.61 11.65 14.12 16.98 19.90 22.71 25.36 27.82 30.09 32.19 34.13 35.92 37.57 39.10
12.33 17.95 18.08 25.08 31.62 37.19 41.86 45.78 49.11 51.94 54.37 56.45 58.24 59.79 01.13
53.37 57.62 57.69 61.37 64.82 68.18 71.46 74.67 77.80 80.85 83.81 86.70 89.50 92.23 94.87
63.34 69.23 69.34 75.49 81.80 88.08
94 17 100.03 105.62 110.94 116.00 120.83 125 42 129.80 133.97
Dec. 1948
THERMODYNAMICS AND STRUCTURE OF CYCLOPENTENE AND CYCLOHEXENE
for the effective mass that gives agreement with the above entropy contribution. This gives 20.6 in atomic weight units which is not unreasonable for a methylene group type of motion. Using all of the above data, the thermodynamic properties of cyclopentene in the ideal gas state were computed by the usual statistical mechanical formulas and are given in Table 11. Although the second decimal place is given, the uncertainty is several tenths of a unit in these results. Cyclohexene. Structure.-Cyclohexene, like cyclohexane,6probably has one predominant configuration and various higher energy forms which may affect thermal properties. The most stable form, as suggested earlier by Lister,I4 appears to be a configuration having Cz symmetry and to be slightly strained.' Using bond distances, force constants, etc., described above for cyclopentene this strain energy was found to be about 1.6 kcal./ mole; whereas the energy of another form, which resembles the cyclohexane boat, was calculated as 3.8 kcal./mole. Since these calculations are subject to considerable error we shall evaluate the exact potential energy difference, A V , between the tautomers from the thermal data. Taking into account both symmetry numbers and also d,l forms, one obtains the equation @(taut) = 1
+ exp. ( -
AV/RT)
for the tautomerism factor in the partition function. This is analogous to the chair-boat tautomerism of cyclohexane. Cyclohexene. Vibration Spectrum.-By comparing the observed Raman and infrared spectra'j of cyclohexene with the spectra of cyclohexanefiand of various olefins16a rough correspondence between the frequencies of these related compounds was observed. A tentative list of frequencies is given in Table I11 which is suitable for the estimation of thermal properties. The distribution of frequencies is approximately right. The list, however, has only a rather dubious plausibility as a detailed assignment. Cyclohexene. Thermodynamics.-The entropy of cyclohexene in the liquid state has been measured by Huf€mauand co-workers12to be 51.67 cal./deg. mole a t 298.16"K. while the entropy of vaporization to the ideal gas is given by Rossinila as 22.53 cal./deg. mole a t 298.16'K. This yields the total, 74.20 cal./deg. mole, as the entropy of cyclohexene ideal gas a t 298.16'K. In addition, the heat capacity of gaseous cyclohexene has been measured by Montgomery and (14) M. W. Lister, TEISJOURNAL, 63, 143 (1941). (15) K . W. F. Kohlrausch and R. Seka, Bcv., 69, 729 (1936); F. F. Cleveland, J . Chem. Physics, 11, 301 (1943); Catalog of Infrared Spectrograms issued by the American Petroleum Institute Research Project 44 at the National Bureau of Standards, Serial No. 201 from the Shell Development Company and No. 697 from the National Bureau of Standards, Radiometry Section. Also private communication from the Spectroscopic Department of the Shell Development Company. (16) J. E. Elpatrick and K S. Pitzer. J . Rescurch Nail. Bur. Standards. 37, 363 (19461
4229
DeVries" in the range near 400'K. The interpolated value from their data for 400'K. is 34.65 cal./deg. mole. Both of these quantities were calculated statistically for the low energy tautomer alone, using the value 11,260 X lo-"' g.3cm.Bfor the product of the principal moments of inertia. The resulting entropy value, 74.16 cal./deg. mole, agrees well with experiment, but the heat capacity is at variance by 0.73 cal./deg. mole. When the tautomerism is introduced, it is found that a potential energy difference between the tautomers of 2700 cal./mole accounts for the discrepancy in the heat capacity without seriously TABLE I11
CYCLOHEXENE VIBRATION FREQUENCY ASSIGNMEKT Raman
190 281 394 451 492 642 715 823 875 904 966
1047 1066 1138 1219 1246 1267
1350 1431 1454 1.651
Cyclohexene Infrared Assigned
456 645 670 719 810 876 904 917 966 1008 1037 1062 1138 1220 1241 1266 1307 1323 1340 1351 1437 1649
190 281 394 456 492 642 670 715 810 823 875 904 917 966 1008 1035 1047 1066 1138 1219 1241 1246 1267 1307 1323 1340 1351 1435 (2) 1454 (2) 1648 2950 (10)
Cyclohexane
cis-2-
Butene
231 (2) 382 426 (2) 522 673 802 (3) 864 (2) 903 1030 (5)
1050 1155 1176 1185 1261 (2) 1266 (2) 1308 1346 (2) 1348 (2) 1375 1443 (3) 1456 (3)
1267
1390 1672
disturbing the entropy agreement. Including tautomerkm, with AV = 2700 cal./mole, the calculated entropy becomes 74.27 cal./deg. mole, and the heat capacity, 34.64 cal./deg. mole. While this A V is slightly higher than the estimate from strain considerations, it must be granted that the latter is only a rough approximation, and the difference is therefore of no importance. In Table IV are given the calculated values of various thermodynamic properties of cyclohexene in the ideal gas state and at various temperatures. (17) J. B. Montgomery and T. DeVries, THIS JOURNAL, 64, 2375 (1942).
H. R.
4230
SNYDER AND JAMES
As in Table I 1 the uncertainty in these values is several tenths of a unit.
H. BREWSTER
Vol. 70
Let us define y = 2 a ( b / ~ k T ) ' /in~ terms , of which the thermodynamic functions may be written as
TABLE IV CYCLOHEXENE, THERMODYNAMIC FUNCTIONS (Units: cal./degree mole)
-- - rf3
T, OK.
200 298.16 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500
- ( p - H$
T
09
10.75 13.98 14.05 18.04 22.20 26.20 29.93 33.35 36.47 39.33 41.94 44.34 46.53 48.55 50.42
16.32 25.10 25.28 34.64 42.78 49.45 54.92 59.49 63.34 66.62 69.43 71.85 73.92 75.72 77.27
T
9
T
55.43 60.29 60.38 64.96 69.43 73.84 78.16 82.38 86.49 90.48 94.36 98.12 101.75 105.27 108.68
66.18 74.27 74.43 53.00 91.63 100.04 108.09 115.73 122.96 129.81 136.30 142.46 148.28 153.82 159.10
Appendix I In order tcr calculate thermodynamic functions for the mode of osdllation with potential energy given by equation ( 2 ) above, the partition function is needed
On integration the result is Q =
(2?rmkT)'/z h [%a f (?rkT/b)'/Z)
[CONTRIBUTION FROM
THE
(4)
Summary
By the use of bond bending and bond twisting (internal rotation) potential constants from related molecules the potential or strain energy of cyclopentene and cyclohexene was calculated for various configurations. It was found that cyclopentene can pucker by moving the carbon opposite to the double bond out of the plane of the other four carbon atoms by about 0.3 A. without significant change in energy from the planar configuration. Cyclohexene, by contrast, shows two tautomeric forms related to chair and boat cyclohexane which differ by about 2.7 kcal ./mole. The available Raman and infrared spectroscopic data are interpreted for cyclopentene and cyclohexene. With reasonable adjustments of otherwise somewhat uncertain parameters, agreement is obtained with the thermodynamic data for the two substances. The thermodynamic functions (- (Fo - H:)/T, (Ho - H,)/T, So and Ci) are then calculated for the ideal gas state from 200 to 1500OK. BERKELEY, CALIFORNIA
RECEIVED AUGUST7, 1948
NOYESCHEMICAL LABORATORY, UNIVERSITYOF ILLINOIS]
Amine Exchange Reactions of Mannich Bases BY H. R. SNYDER AND Amine exchange reactions occur when quaternary ammonium salts are heated with ammonia or primary or secondary amines2 (eqn. Al). Similar reactions have been observed with Mannich bases of nitromethane3 and of indole* (eqn. B l ) ; the phenylhydrazones of ketonic Mannich bases form pyrazolines by internal amine exchange5 (eqn. C). (1) Present address: Department of Chemistry, University of Chicago, Chicago, Illinois. (2) Scholtz., Btr., 94, 2402 (1891); 31, 414, 1700 (1898); von Braun and Zohel, Ann., 445, 247 (1925); Ber., 59, 1786 (1926); von Braun, Kuhn and Goll, ibid., 59, 2330 (1926); Hultquist, cf a!., THISJOURNAL, 70, 23 (1948). (3) Duden, Bock and Reid, Bcr., 38, 2036 (1905). (4) Howe, Zambito, Snyder and Tishler, THISJOURNAL, 67, 38 (1945). (5) Mannich and Bauroth, Bcr., 67, 1108 (1924); Xisbet and Gray, J . Chcm. Soc., 839 (1933); Levvy and Nisbet, ibid., 1053,1572 (1938); Nisbet, ibid., 1237, 1568 (1938); 126 (1945); Harradence and Lions, J . Proc. Roy. SOC.N. S, Wales, 73, 14 (1939) [C.A . , 33, 8196 (1939)l.
JAMES
H. BREWSTER~
Since these reactions appear to be similar in their mechanisms to the corresponding amine replacement reactions which occur in alkylations with quaternary salts of benzylamine6*'J' (eqn. A2), and with Mannich (eqn. B2) and their quaternary saltss*10(eqn. A2), it seemed desirable to determine whether amine exchange reactions occur readily with ketonic and phenolic Mannich bases. A.
+
1 R'-NRs
+ : B +R'B+ + : NRs
R' = ~ - c H ? - - , CH~-, etc.; B = H N R ~ " (6) von hleyer, Abhandl. math.-$hys. Klasse szchs. Akad. Wiss.. 31, 179 (1908) [Chem. Zsntr., 80, 11, 1800 (1909)l. (7) Snyder and Speck, THISJOURNAL, 61, 668,2895 (1939). (8) Snyder, Smith and Stewart, ibid., 66, 200 (1944). (9) Mannich, Koch and Borkowsky, Bcr., 70, 355 (1937); Reichert and Posemann, Arch. Phavm., 976, 67 (1937). (10) duFeu, McQuillin and Robinson, J . Chcm. SOC..53 (1937).
