cis- AND ~~UZS-DICHLOROETHYLENES
Mar. 20, 1964
sumed value of 9 for minimum potential energy. Only a small and quite reasonable change in that parameter is required to bring the calculated value of VOfor SSup into the range of the more directly determined values for the disulfides. The contribution of tautomerism to the thermodynamic functions can be obtained from the partition function Q = 1 4 - exp [-AF(Dzd)/RT] -k exp [-AF(Cl)/RT] in which AF(tautomer) is the free-energy change for the reaction S g ( D 4 d ) = &(tautomer). If the energy of the DZd form and of the C1 form are taken to be equal to each other , may write and to V O one Qc i 1 A exp( - VO/RT) in which A = exp [AS(Dzd)/R] exp [AS(CJ/R], with A S (tautomer) defined as the entropy change for the reaction SS(D4d) = &(tautomer). If the valuesof AS(tautomer)aredetermined solely by differences in symmetry number and the existence of d- and I-isomers of the C1 form, then A = 2 2 ( 8 ) = 18. Differences in moments of inertia and vibrational frequencies of the tautomers will make A differ somewhat
+
+
+
[CONTRIBUTION FROM
THE
1493
from 18, but that value is a good enough estimate for purposes of the present discussion. The contributions of tautomerism to the function -( F" H : ) / T , in cal. deg.-l mole-lat 450 and 1000'K. were calculated for VOequal to 5 , 9 and 15 kcal. mole-' with the results shown below. Vo
450°K. 1000°K.
mole - 1
VO = 9 kcal. mole -1
0.14 1.80
0.002 .36
= 5 kcal.
Va
= 15 kcal
mole -1
0.000003 .02
These values are essentially upper limits of the contributions, because VOis the probable lower limit of the energy difference between the tautomers. It is seen that if VOis in the expected range of 9 to 15 kcal. mole-', the contributions of tautomerism, even a t 1000"K., are of just borderline significance. Only if VOhas an improbably low value of 5 kcal. mole-' are the contributions large a t temperatures near IOOOOK. In either case, the contributions are small a t 450°K. BARTLESVILLE, OKLAHOMA
DEPARTMENT OF CHEMISTRY AND CHEMICAL ENGINEERING, UNIVERSITY OF CALIFORNIA, BERKELEY]
cis- and trans-Dichloroethylenes.
The Infrared Spectra from 130400 Cm.-l and the Thermodynamic Properties1
BY KENNETH S. PITZER AND J. L. HOLLENBERG RECEIVED OCTOBER 16, 1953 The infrared spectrum of trans-dichloroethylene shows a strong Q branch a t 227 crn.-l and a shoulder of medium strength near 250 cm.-' which are interpreted as the heretofore unobserved A, and B, fundamentals, respectively. The spectrum of the cis isomer merely c o n h s bands known from the Raman spectrum. The force constants for out-of-plane motions are calculated. Thermodynamic functions are calculated from the completed molecular data for each isomer and are used to interpret the cis-trans equilibrium data. The cis isomer is found to be 445 f 20 cal./mole lower in energy a t O'K., and the cause of this energy difference is discussed.
I n the case of the 2-butenes the trans isomer is The samples were from the Matheson Co. The known to be the one of lower energy and this is sample of the cis isomer melted a t -80.4" which is believed to be the usual case. The dichloroethyl- within 0.1" of the accepted melting point and its enes are an exception in that the cis isomer has the infrared spectrum (3-15 p ) showed no bands of the lower energy. Thus a careful study of cis- and trans isomer or of other likely impurities. Consequently, this sample was used without further puritrans-dichloroethylenes is of considerable interest. The vibrational spectra of cis- and trans-dichloro- fication. Initially the sample of the trans isomer ethylene and the statistical thermodynamics of the showed considerable impurity of cis. This was equilibrium between them have been the subject largely removed by distillation with an efficient of an extensive series of investigations. Recent column so that, in the sample used, the infrared studies of a general nature are those of Bernstein spectrum showed only traces of the stronger bands of the cis isomer. and Ramsay2 and of Wood and S t e ~ e n s o n who ,~ give references to earlier work. In spite of extenThe spectrum of trans-dichloroethylene in the sive studies, the absence of infrared spectra for the range 130-400 cm.-l is shown in Fig. 1. The accutrans isomer below about 400 cm.-l has prevented racy of the percentage transmission becomes gradua satisfactory completion of this work. Since ally poorer with decreasing frequency. n'hile the trans molecule has a center of symmetry, the there is no doubt about the strong absorption near Kaman spectrum does not yield the frequencies of 230 cm.-l, the weak peak near 150 em.-' must be the antisymmetric modes as fundamentals and regarded as doubtful a t present. The corresponding there are two modes in the heretofore unobserved spectrum was taken for the cis isomer, but it showed range. A4ttemptshave been made to infer these no marked features beyond the expected band a t frequencies indirectly, but we shall see that these 1'73 cm.-' which was weak. Thus this spectrum have not yielded valid results. was not investigated further. Experimental.-The grating spectrometer emSpectral Interpretation.-We accept the assignployed in this investigation was described r e ~ e n t l y . ~ments of Bernstein and Ramsay2 for cis-dichloro(1) This work was assisted by the American Petroleum Institute ethylene and for all fundamentals except p,(Au) through Research ProjeQt 50. and pI2(Bu) of trans-dichloroethylene. For the (2) H. J . Bernstein a n d D. A. Ramsay, J . Chem. P h y s . , 17, 556 (1949). latter these authors suggested 192 and 263 cm. I , (3) R. E. Wood a n d D. P. Stevenson, THIS JOURNAL, 63, 1660 respectively, but i t is apparent from Fig. 1 that (1941). these are not correct. Also we must note that the (4) C. R. Bohn, N. K. Freeman, W. D. Gwinn, J. L. Hollenbergand "reststrahlen" spectrometer results presented reK. S. Pitzer, J . Chem. P h y s . , 21, 719 (1953).
KENNETH S. PITZER AND J. L. HOLLENBERG
1494 -
(re",
i
ClHC-CHCI
0
/ ' /
0 7 meter
300
320
340
360
380
400 1100
1
:
VOl. 76
overtones or combination tones is improved in almost every case where a change is made. We have substituted the Raman spectrum of Kreusch, Ziomek and Cleveland6for the older work used in previous assignments. Except for differences of a few cm.-' in some frequencies the only changes are in the polarization of the bands a t 758 and 3142 c m - l which had been assigned in violation of older polarization data. There is complete agreement now with the recent polarization values. TABLE I1
I !
I
140
I I 160
I I80
I
1
l b - + i l
200
e20
I
240
I 260
I
I 280
I 1 0
I
300
infrared spectrum of trans-dichloroethylene.
Fig. 1.-The
cently by O'Loane6 as supporting this assignment were misleading in this respect. In neither case was any error of experiment involved; rather the data allowed more than one interpretation. From Fig. 1 it is apparent that one of the frequencies must lie a t 227 cm.-'. The relatively sharp peak suggests a strong Q branch which is characteristic of a C type vibration-in this case v7 of A, symmetry. The location of the second fundamental v12 is less obvious, but the intensity of the shoulder a t about 250 cm is much greater than that of the peak a t 2.50 = 477 is 278 cm.-'. Also the sum of 227 already above the range 426450 cm.-' regarded v12 by Wood as most probable for the sum of v7 and Stevenson3 on the basis of their equilibrium data. The rather doubtful peak near 150 cm.-' is even weaker than the others and may be definitely excluded as a fundamental. There is no explanation of bands a t either 250 or 278 cm.-' as binary combination tones, but it is possible to explain the weaker band a t 278 ern.-' as the ternary difference combination 2v12 - v7 if v12 is taken a t 250 cm.-'. Thus we adopt 227 and 250 cm.-', respectively, for v7 and v12. Table I summarizes the complete assignments for both cis and trans isomers while Table I1 gives the full spectrum for the trans molecule. A comparison of our Table I1 with the corresponding table of Bernstein and Ramsay will show that the explanation of the weak bands as
+ +
TABLE I FUNDAMENTAL I;'REQUENCIES FOR Cis-
A1
1
ETHYLENE
:: u4
vg vg
u7
i
ug
Bi
vg
1
__ ( 5 ) J.
Bi
3077 1587 1179 711 173 876 406 3072 1294
PI0
848
v11
571
UIZ
697
Vapor
.. ..
227 250 278
..
(m) (w) (vw) 350 (s) pol.
541 (vvw) 614 (vvw) 763 ( m ) dp. 763 7,,}
763 (w)
823 832 ,/
817 (vs) 846 (s) pol.
898
}
llg5
1205
895 (vs) 985 (w) 1080 (w) 1166 (w) 1200 (s) 1276 (w)
""}
1663
1274 (s) pol. 1578 (s) pol. 1634 (vw) pol.
1658 (m) 1693 (w)pol.
2092
1816 (w) 2047 (w) 2082 (w) 2460 ( w )
3073 ( s ) pol. 3090
trans,
Ag
I
cm. - 1
US
3073 1578 1274 846 350 895 227 763
(
vg
3080
[
vi2
vi v? UI u4
UI
A4 us v7
Bg
K. O'Loane, 1.Chcm. Phyr., 21, 669 (1853).
250
i
+ + 2~4 + v) + + vz + Pe
Yg
= 1658 (Bu)
= 1663(Bu) 1692 ( A y ) v2 ~ 1 = 2 1828 (Bu) U, 2046 (Bu) vi1 2091 ( B u ) us u10 = 2474 ( BU) vg = 2473 (A,) vz f Y:O = 2778 ( B u ) vi (A,) l'g (Bu) 2 q = 3156 ( A R ) ~4
vi1
i
2760 ( w ) 3080 (s)
3141 ( w ) pol. AND trans-DICHLORO-
cis, cm.3 vi
SPECTRA OF ~rU?ZS-DICHLOROROETHYLENE Infrared Raman Liquid Liquid
Bending Potential Constants.-The potential function for out-of-plane bending motions of these molecules was considered by Freeman and one of us' and more recently by Bernstein and Rainsay.? We have revised the earlier calculations to take account of the present assignment of v7. We use the "atomic weight-Angstrom units" and the slightly simplified geometry used previously.' .I complete harmonic potential function was assumed with O1 and O2 the wagging angles between the planes of the CHCl groups and the C-C axis and 63 the angle of twist of the C-C double bond. The pstential constants reduce by symmetry to four in number, The principal w.ngp;fiinKconstant, (6) E. Kreusch, J. S. Ziomek a n d F. F. Clevehnrl, P h s s . Rew., 76. 334 (1949). Their band a t 711 c m . 7 prerumnbly arises f r o m a n impurity of the c i s isomer. (7) K. S. Pitzer a n d N. K. Freeman, J . Chcin. P h y s . , 1 4 , 586 (1%46),
Mar. 20, 1954
Cis- AND
h'anS-DICHLOROETHnENES
FI1(or Fzz), and the wagging interaction constant, F12,are assumed to be the same for the cis and trans isomers. The principal twisting constant, F33, and the twisting-wagging interaction constant, F13, are evaluated for each isomer separately. The signs of the constants are as defined in an earlier paper8 on the 2-butenes which also gives working equations that can readily be reduced to the case a t hand. We may remark that the sign of F12 is such as to raise the resistance to boat-like distortions and lower i t to chair-like distortions. The resulting constants are given in Table I11 together with values for the 2-butenes and for ethylene. The close similarity of the constants is striking. The near equality of F 3 3 for the cis and trans isomers of dichloroethylene indicates a corresponding equality of curvature a t the two minima in the potential curve for torsion. The constants in Table I11 may be converted to the units ergs per radian?by division by 1.698 X 10".
1495
TABLE V THERMODYNAMIC FUNCTIONS FOR trans-DICHLOROETHYLENE (UNITS,KCAL./MOLEOR CALJDEG.MOLE) ( F o - H'o) -~ Cop Ha - H'Q T SO T 200 13.07 2.003 53.52 63.53 273.16 15.22 3.038 56.80 67.92 298.16 15.93 3.427 57.79 69.29 69.39 3.457 57.86 300 15.99 5.189 400 18.58 61.38 74.35 7.155 500 20.65 64.42 78.73 600 22.28 9.304 67.14 82.64 700 23.57 11.60 69.61 86.18 800 24.62 71.89 89.40 14.01 900 25.50 16.52 74.00 92.35 1000 26.24 19.11 75.97 95.08 1100 26.87 21.76 77.82 97.61 1200 27.41 24.48 79.57 99.97 1300 27.87 27.24 81.23 102.18 30.05 82.80 104.26 1400 28.27 84.30 106.22 1500 28.62 32.89
TABLE I11 BENDINGPOTENTIALCONSTANTS FOR cis- AND trans-DIpurposes. The resulting functions are given in CHLOROETHYLESE AND RELATED MOLECULES (IN ATOMIC Tables IV and V.
WEIGHT-ANUGSTR~M UNITS) CtR2Clz cis
Constant
CnH@
trans
0.407 ,048 1.07 1.12 -0.13 -0.14
FII
FI? F33 I713
2-Butenes8 ( c i s and trans)
0.390 .056 ,915
0.41 0.04 1.08 -0.09
...
Isomerization Equilibrium.-The cis-trans isomerization equilibrium has been measured by several authors. Wood and S t e v e n ~ o n using ,~ iodine as a catalyst, obtained values a t 30' intervals from 185' to 275OC.) while Olson and MaroneylO obtained values a t 300 and 35OoC. By using the free energy function from Tables IV and V a value of AHoo for the reaction, cis = trans, can be obtained from each equilibrium measurement. These calculations are summarized in Table VI.
Thermodynamic Functions.-The functions ( F o - Hog, So and C o p were calculated for each isomer by the usual statistical methods with the vibration frequencies of Table I. The moments of inertia were given by Bernstein and Ramsay.2 Only the smallest moment of the trans isomer has been obtained spectroscopically, but the values from electron diffraction measurements of bond dis- T, O K . tances and angles are sufficiently accurate for our 458.16
- Hoo)/T, H o
488.16 TABLE IV 518.16 THERMODYNAMIC FUNCTIONS FOR cis-DICHLOROETHYLENE 548.16 OR CAL./DEG.MOLE) (UNITS,KCAL./MOLE 573.16 (F" - H'o) 623.16 -___ Ha
- HOo
-
T
Cop
200 273.16 298.16 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500
12.30 14.75 15.55 15.61 18.41 20.57 22.23 23.54 24.60 25.48 26.23 26.86
1.920 2.910 3.289 3.318 5.024 6.978 9.121 11.41 13.82 16.33 18.91 21,57
54.00 57.15 58.10 58.17 61.56 64.51 67.17 69.60 71.84 73.92 75.?7 77.71
63.60 67.80 69.13 69.23 74.12 78.47 82.37 85.90 89.11 92.06 94.79 97.32
27.40 27.87 28.27 28.61
24.28 27.04 29.85 32.70
79.44 81.09 82.65 84.14
99.68 101.89 103.97 105.93
T
SQ
(8) J. E. Kilpatrick and K. S. Pitzer, 1. Research Natl. B u r . Standurds, 38, 191 (1947).
(9) R. L. Arnett and B. L. Crawford, Jr., 1.Chcm. Phrs., 18, 118 (1950).
TABLE VI OF ISOMERIZATION ENERGY c~s-C~H~= C Itrans-CsHzCl2 ? =
trans cis
0.577 ,607 .632 .658 .645 .683
AH%, cal/mole
AFO/T - A ( - >
1.091 0.990 .910 .832 .871 * 755
-0.126 - .097 .073 - .057 - .045
-
-
.015
442 436 434 425 473 461 445 i20
If everything is correct, the values of A H 0 o in Table VI should be constant. Within the series of values from Wood and Stevenson there seems to be a slight trend downward with increasing temperature. The higher values of AH'o from the experiments of Olson and Maroney a t still higher temperatures leads us to believe this apparent trend is spurious and that these AH0o values may be accepted as constant within experimental error. We select 445 f 20 cal./mole as our final value of the heat of isomerization a t O O K . The trans isomer has the higher energy. Discussion.--While it is not practical to present any rigorous theoretical analysis of the energy of isomerization, some rough calculations seem worthwhile. The chemical bond structures which would be expected to contribute to the ground state are (IO) A. R. Olson a n d W.Maroney, THISJOURNAL, 66, 1320 (1934).
KENNETHS . PITZER AND J. L. HOLLENBERG
1496
Bi
A
c-c
f
C--C\
where there is an equivalent Bz structure in each case with the double bond to the other chlorine atom. We have used arrows to indicate the polarization of the a-bonds. Since this polarization will be substantial, we have shown the formal charges shared between pairs of atoms in the B structures. Quantitative estimates of the fraction of double bond character in mono- or dichloroethylenes have been made from the bond distance by Pauling“ and from the nuclear quadrupole interactions by Goldstein and Bragg.lz The respective values are 1s and 4YG. This leaves a wide range of plausible values to fit another observable quantity. In quantum mechanical calculations the energy depends on the exchange integrals as well as the coulomb integrals, but i t will be a reasonable approximation to consider only the coulomb terms in discussing the cis-trans energy difference. The C1-C1 distances are approximately the same in the gauche or skew form of 1,2-dichloroethane as in the cis form of 1,2-dichloroethylene, and similarly they are about the same in the trans forms of the two moleculFs. The values are approximately 3.23 and 4.27 A., r e ~ p e c t i v e l y . ~ Consequently, ~’~ i t seems reasonable to take the energy difference between the two forms of the ethane derivative as appropriate for the *A structures. This energy difference14 is about 1400 cal./mole with the trans form lower. (11) L. Pauling, “ T h e Nature of t h e Chemical Bond,” Second edition, Cornell University Press, Ithaca, N. Y., 1945, p . 216. (12) J. H. Goldstein a n d J. K . Bragg. Phrs. Rev., 75, 1463 (19491, 78, 347 (1950). (13) 0. Hassel a n d H. Viervoll, A r c h . 31alh. Natoruidenskab, B47, Xo. 13 (1944). (14) J . Powling and H. J. Bernstein, THIS J O U R N A L , 73, 1815 (1951).
1‘01. 76
We must now estimate the distribution of charge a t each end of the molecule for the B structures. A reasonable but necessarily arbitrary basis is three-fourths of a unit positive charge on the doubly bonded chlorine and one-half of a negative charge on the other chlorine. We then proceed as follows $ = (1 - 2h2)1/z$A $. X($Bi f $132) t = (I - 2XZ)AQ’*’,- t 2hzAQ(B)c- t
AE,-
+
where the delta quantities refer to cis-trans energy differences, the Q’s are coulomb terms, and X? is the fractional contribution of each B structure. The various crude approximations which are common in quantum mechanical valence theory have been made here. Then we take AQ(*)c-t to be 1-100 cal. /mole and
where e is the electronic charge and the r‘s are the C1-C1 distances in the indicated isomers. If we take our value of -445 cal.,’mole for AEc-l we may solve these equations for A?. The result is a little less than 9yofor X2 which lies well within the range -1-lSyO indicated above. Moderate changes in the assumed charge distribution in the B structures will leave the value of X2 in the range indicated. The dipole moment of the cis isomer can also be discussed in a similar manner, but still further postulates must be made concerning the charge distribution in the principal structure, A. Thus we shall merely state that reasonable agreement can be obtained with parameters such as were given above. In conclusion i t seems safe to conclude that the anomalous stability of the cis isomer of dichloroethylene is associated with the unlike charges on the chlorine atoms in the B-type mesomeric structures. ,4ssistance in the calculations by Dr. James C. M. Li and Alr. Glenn Spencer is gratefully acknowledged. BERKELEY, CALIFORNIA
