2938 The most pronounced difference between the studies on the acids and on the thioacids lies in the temperature range. The present experiments were performed with HBS2(s) mostly at temperatures below loo", where the principal species are (HBS2)3(g) and H2S(g), but the experiments on the oxygen acids employed the reaction between water and boric oxide above 800°, where the principal species is HB02(g). The great difference in the volatilities of the acids and thioacids arises presumably because of hydrogen bonding in the former. The second difference is that the species found mass spectrometrically in the sulfur system are more numer-
ous and more complicated than in the oxygen ~ y s t e m . ~ The third difference is that metastable decompositions have not been reported for the oxygen acids. Finally, the extensive studies on the spectra and thermodynamic properties of oxygen specie^^-^ have not yet been accomplished for the sulfur analogs. Acknowledgments. The authors are pleased to acknowledge the support of this research by the United States Atomic Energy Commission under Contract AT(l1-1)-1140. They also wish to acknowledge the help of the University of Kansas Computation Center for the calculation of the relative intensities and the metastable masses.
Bond Energies and the Interactions between Next-Nearest Neighbors. 111. Gaseous and Liquid Alkanes, Cyclohexane, Alkylcyclohexanes, and Decalins' A. Joseph Kalb,2 Alice L. H. Chung, and Thomas L. Allen
Contribution f r o m the Department of Chemistry, University of California, Davis, California 9.5616. Received January 20, 1966 Abstract: The heats of formation of alkanes, cyclohexane, alkylcyclohexanes,and decalins are expressed as a linear function of seven structural parameters for both the gaseous and liquid states. Root-mean-square differences between calculated and experimental values are *0.0185 kcal mole-' bond-1 for 56 gases and 10.0214 kcal mole-' bond-' for 63 liquids. In branched hydrocarbons the energy contributions by gauche-n-butane and gauche-gauche prime n-pentane structures are similar to those in the rotational isomers of normal paraffins. In some molecules the effect of a gauche-n-butanestructure is accentuated by locking, where the H . H distance cannot be increased by internal rotation about any carbon-carbon bond without simultaneously decreasing the H . . .H distance in another interaction. The energetic effects of H . H interactions in ordinary and locked gauche-n-butane have been calculated independently by energy minimization.
-
-
a
I
n the first paper3 of this series it was shown that inclusion of a single parameter, the next-nearestneighbor interaction energy, removed practically all of the deviation from constancy in bond-energy calculations. Two other parameters, a trigonal interaction and a steric interaction between fifth-neighbor hydrogen atoms of the gauche-n-butane type, gave additional small but significant improvements. Molecules which were treated included the CI through C, alkanes, some cyclanes, diamond, the sulfanes, Ss, and some alkyl mercaptans, sulfides, and disulfides. This approach has been applied to many other molecules by McCullough and Good,4 and by Skinner and co-workers,"'O and the theoretical basis of the method has been explored. 11s12 (1) Abstracted in part from the Ph.D. dissertation of A. J. Kalb, University of California, Davis, Calif., 1963. (2) Public Health Service Predoctoral Fellow, 1962-1963. (3) T. L. Allen, J . Chem. Phys., 31, 1039 (1959). (4) J. P. McCullough and W. D. Good, J . Phys. Chem., 65, 1430 (1961). ( 5 ) H. A. Skinner, Anales Real Soc. Espan. Fis. Quim. (Madrid), B56, 931 (1960). (6) H. A. Skinner, J . Chem. Soc., 4396 (1962). (7) H. A. Skinner and G. Pilcher, Quart. Reu. (London), 17, 264 (1963). (8) G . Pilcher, H. A. Skinner, A. S. Pell, and A. E. Pope, Trans. Faraday SOC.,59, 316 (1963). (9) G. Pilcher, A. S. Pell, and D. J. Coleman, ibid., 60, 499 (1964). (lo) A. S. Pell and G . Pilcher, ibid., 6:, 71 (1965).
Journal of the American Chemical Society
1 88:13
July 5, 1966
The present study was undertaken to obtain more accurate equations for the heats of formation of saturated hydrocarbons and to obtain further information about steric interactions in these molecules. We were also interested in applying the method to liquids as well as gases. Treatment of Data Our general approach was to adjust the coefficients in linear equations for heats of formation (similar to eq 33 and 35 of ref 3) so as to give optimum correlation with the experimental data. The equations were of the form
-AHfo = AKK
+ Ann + A x X + A T T + A S S + A z Z f A L L (1)
The A's are the coefficients to be determined, and K,n, etc., are the structural parameters. K reflects differences between the numbers of C-H and C-C bonds; it is 1 for acyclic, 0 for unicyclic, and - 1 for bicyclic compounds. n is the number of carbon atoms; X is the number of pairs of next-nearest-neighbor carbon atoms. For the alkanes beyond methane it is conveniently calculated by eq 8 of ref 3. T i s the number of trigonal (11) T. L. Allen and H. Shull, J . Chem. Phys., 35, 1644 (1961). (12) M. Cignitti and T. L. Allen, ibid., 43, 4472 (1965).
2939 Table I. Comparison of Calculated and Experimental Heats of Formation
Molecule" -1 -2 -3 -4 2m3 -5
2m4 22m3 -6 2m5 3m5 22m4 23m4 -7 2m6 3m6 3e5 22m5 23m5 24m5 33m5 223m4 -8 2m7 3m7 4m7 3e6 22m6 23m6 24m6 25m6 33m6 34m6
S
2
L
0 0 0 0 0 0 1 0 0 1 2 2 2 0 1 2 38 2 3 2 4 4 0 1 2 2 3 2 3 3 2 4 4
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 0 1 2
- AHf"(exptl, 25 o ) b Gas Liquid
17.889 20.236 24.820 30.15 32.15 35.00 36.92 39.67 39.96 41.66 41.02 44.35 42.49 44.89 46.60d 45.96d 45.34 49.29 47.62 48.30 48.17 48.96 49.82 51.50 50.82 50.69 50.40 53.71 51.13 52.44 53.21 52.61 50.91
... 22.500' 28.789' 35.34' 36.9Y 41.40' 42.9Y 45.02' 47.52 48.82 48.28 51.00 49.48 53.63 54.93 54.35 53.77 57.05 55.81 56.17 56.07 56.63 59.74 60.98 60.34 60.17 59.88 62.63 60.40 61.47 62.26 61.58 60.23
AHf"(calcd) AHr '(exptl) Gas Liquid -0.01 0.10 -0.30 0.05 0.12 -0.08 0.45 -0.40 -0.10 0.21 0.11 0.39 -0.35 -0.16 0.17 0.07 0.00 0.35 0.34 0.48 0.71 -0.04 -0.21 0.08 -0.05 -0.18 0.07 -0.22 -1.13 0.18 0.41 0.17 -0.02
-0.17 -0.10 0.23 0.26 0.08 0.60 -0.29 -0.02 0.25 0.27 0.59 -0.11 -0.13 0.15 0.12 0.10 0.42 0.56 0.36 0.79 0.01 -0.23 -0.02 -0.10 -0.27 -0.01 -0.22 -1.07 0.00 0.23 0.08 -0.21
Molecule"
S
Z
L
2m3e5 223m5 224m5 233m5 234m5 3m3e5 2233m4 -9 33e5 2233m5 2234m5 2244m5 23341-115 - 10 -11 - 12 - 16 c6 mc6 ec6 1lmc6 cis12mc6 rrunsl2mc6 cis13mc6 trunsl3mc6 cis14mc6 trunsl4mc6 PC6 bc6 dc6 rrans-Decalin cis-Decalin Av difference
5 5
0 0 1 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 2 0 2 2 4 6 0 8 8 2 0 8 0 0 0 0 0 0 0 2 2 0 0 2 2 0 0 0 0 0 3
1 6 5 6 6 0 8 8 4 0 8 0 0 0 0 0 0 1 2 3 1 0 2 2 0 1 1 1 0 3
-
-AHf'(exptl, 25 Gas Liquid 50.48 52.61 53.57 51.73 51.97 51.38 53.99 54.74
AHrO(ca1cd) AH{ '(exptl) Gas Liquid
59.69 61.44 61.97 60.63 60.98 60.46 . . .8
65.84* ... 65.85' ... 66.54i , ., 66.40i .., 66.956 ... 66.46i 59.67 71.99 . .. 78.06h ... 84.16h ... 108.61h 29.43 37.34 36.99 45.45 41.05 50.72 43.26d 52.31 41.15 50.64 43.02 52.19 44.16 53.30 42.20 51.57 42.22 51.55 44.12 53.18 46.20 56.98 50.95 62.91 . . . 100.04i 43.57k 55. 14k 40.38k 52.45k
0 . 1 0 -0.19 -0.83 -0.84 (0.OO)f 0.57 -1.17 -1.10 -0.35 -0.48 1.20 0.80 -0.39 ... - 0 . 2 7 -0.35 ... 2.04 -1.26 ... -0.65 ... -0.04 ... -0.52 -0'.32 -0.46 ... -0.57 ... -0.68 ... -1.10 -0.46 0.04 0.18 0.35 -0.20 -0.04 0.29 0.18 -0.15 -0.11 -0.16 -0.16 0.44 0.40 0.35 0.26 0.37 0.24 0.40 0.28 -0.03 0.00 -0.26 -0.29 . .. -0.46 0.05 0.04 --0.33 _ _ _-0.26 10.29 h0.36
The last digit is the longest carbon chain, m is 0 The symbolic nomenclature is adapted from J. R. Platt, J. P h y s . Chem., 56, 328 (1952). methyl, e is ethyl, p is n-propyl, b is n-butyl, d is n-decyl, and c6 is cyclohexane. For example, 2231114 is 2,2,3-trimethylbutane, 2m3e5 is 2methyl-3-ethylpentane, and 1lmc6 is 1,l-dimethylcyclohexane. b All values in kcal mole-'. Except as noted, experimental data are from F. D . Rossini, K. S. Pitzer, R . L. Arnett, R . M. Braun, and G. C. Pimentel, "Selected Values of Physical and Thermodynamic Properties "Selected Values of Properties of Hydroof Hydrocarbons and Related Compounds," Carnegie Press, Pittsburgh, Pa., 1953, p tables. carbons and Related Compounds," American Petroleum Institute Research Project 44, Chemical Thermodynamic Properties Center, Texas A and M University, College Station, Texas, April 30, 1955, Table l p . d The heats of vaporization of these substances are based on the experimental vapor pressure data of A. F. Forziati, W. R. Norris, and F. D. Rossini, J. Res. Nutl. Bur. Srd., 43, 555 (1949), together with the required auxiliary values for the compressibility factor and change in heat content with pressure for the gas and the molal volume of the As this liquid evaluated from data for analogous substances (F. D. Rossini, private communication). e Erroneously listed as 4 in ref 3. is the only gaseous substance with 2 # 0 in this study, the difference vanishes automatically. 0 The heat of formation listed in ref b should refer to the solid. Reference c, October 31, 1954, Table 20p (part 1). 4 A. Labbauf, J. B. Greenshields, and F. D. Rossini, J. Chem. Eng. Data, 6,261 (1961). 2 Based on the heat of combustion determined by M. C. Loeffler and F. D. Rossini, J. P h y s . Chem., 64,1530 (1960). T. Miyazawa and K. S . Pitzer, J. A m . Chem. SOC.,80, 60 (1958).
interactions (sets of three carbon atoms bonded to a fourth carbon). If C3 and C4 are the numbers of tertiary and quaternary carbon atoms, respectively, then
T
+ 4C4
(2) S is the minimum number of fifth-neighbor H . . H interactions of the gauche-n-butane type. The last two parameters, 2 and L, were not considered in part I. It has been known for some time that certain alkanes (starting with 2,2,4-trimethylpentane) exhibit severe crowding and high steric strain e n e r g i e ~ .13~ , ~l7, Molecular models with a staggered configuration about each C-C bond show steric inter= C3
(13) K.s. Pitzer, Chem. Reu., 27, 39 (1940). (14) W.J. Taylor, J. M. Pignocco, and F. D. Rossini, J . Res. Nutl. Bur. Std., 34, 413 (1945). (15) H.C. Brown, G . K. Barbaras, H. L. Berneis, W. H. Bonner, R. B. Johannesen, M. Grayson, and I
