Research: Science & Education
The Heats of Combustion of Gaseous Cyclotetradecane and trans-Stilbene—A Tale of Long-Standing Confusion Ernest L. Eliel W. R. Kenan Jr. Laboratories, University of North Carolina, Chapel Hill, NC 27599-3290 Jan J. Engelsman Department of Chemistry, Vrije Universiteit, Amsterdam, The Netherlands1 It is not often that one publishes a doctoral dissertation (1) nearly 40 years after it first appeared. We take this unusual step for two reasons. First, that the results obtained in 1955 were never disclosed in a scientific journal 2 led to a long-lasting confusion in the literature, which, in one case (cyclotetradecane) has been dispelled only very recently (2) and in another (trans-stilbene) still persists, as will be discussed in the sequel. Second, we think that the story to follow is historically interesting and that it contains a few universal messages. One of these, frequently mentioned to his colleagues by the late thermochemist F. D. Rossini (personal communication to E. L. Eliel), is that a piece of research is never complete until it has been published in the open literature. Cyclotetradecane The heat of combustion of solid cyclotetradecane was determined by H. van Kamp in 1957 (3) as –46,449 ± 3 J g{1, which may be converted (MW of C14H28 is 196.372) to –9,121.3 ± 0.6 kJ mol {1 or –2,180.0 ± 0.2 kcal mol{1 (1 kcal = 4.184 kJ). After making the volume correction (4) this yields an enthalpy of combustion of –9,135.7 ± 1.3 kJ mol{1 or –2,183.5 ± 0.3 kcal mol{1 (5), in good agreement with a later determination (6) of –2,184.2 ± 0.9 kcal mol{1. However, to compare the enthalpy of combustion with that of other cyclanes—as is necessary to assess strain (7)—one must obtain data in the vapor phase. In the case of (solid) cyclotetradecane, this requires adding to the algebraic value of the enthalpy of combustion that of the enthalpy of sublimation. Accurate determination of the latter is thus crucial. It was the objective of the dissertation of one of us (1) to determine the heats of sublimation of, among other compounds, cyclotetradecane by measuring saturation vapor pressure as a function of temperature. The result for C 14H 28 was ∆H subl = 1 Present address: Liviuslaan 11, 5624 JD Eindhoven, The Netherlands. 2 In the Netherlands (and some other European countries) it is required that doctoral dissertations be printed in editions of several hundred copies, which are then distributed to neighboring libraries and to other scientists known to be interested in the dissertation topic. Unfortunately, the process is somewhat haphazard; and, since the dissertations are not abstracted by Chemical Abstracts, they cannot be readily located and retrieved except by persons who happen to be on the mailing list or who happen to learn about the existence of the dissertation through the grapevine and write for it. For example, one of us (ELE) was in possession of the dissertation of H. van Kamp (3) but not of that of J. J. Engelsman (1), which latter he obtained only in 1994 through a lucky accident.
21.34 ± 0.10 kcal mol{1 (89.3 ± 0.4 kJ mol{1). Using this value one obtains the heat of combustion of gaseous cyclotetradecane as –(2,183.5 ± 0.3 + 21.34 ± 0.1) or – 2,204.8 ± 0.4 kcal mol{1. [The same value, –9,225.0 ± 2.5 kJ mol{1 or –2,204.8 ± 0.6 kcal mol{1, is given in van Kamp’s dissertation (3).] Although neither the heat of sublimation nor the gas phase value of the heat of combustion was published in a primary journal, one of us (ELE) obtained a copy of van Kamp’s dissertation (3) and included the value in a table (8) of heats of combustion of cycloalkanes per methylene group. The tabulated value is –9,225.0/14 = 658.9 kJ mol{1 (157.5 kcal mol{1). Since this is very close to the standard increment per CH 2 group in a long-chain alkane—that is, cyclotetradecane has a “normal” heat of combustion, equivalent to that of a hypothetical acyclic compound consisting of 14 methylene groups3—it was concluded that C 14H28 is “strain free”. A similar conclusion (strain of 0.2 ± 0.2 kJ mol{1) was arrived at in the thesis of van Kamp (3), which also contains a figure (reproduced here as Figure 1) showing the heat of combustion of gaseous cycloalkanes as a function of size. The curve shows the well-known and well-understood trend: 5and 7-membered rings are more strained than 6-membered rings; medium-sized (8- to 11-membered) rings show appreciable strain, which ebbs as the rings become large (12-membered and beyond).4 Unfortunately, when the heat of sublimation of cyclotetradecane was determined again in 1964 (6), an entirely different value of 32.21 kcal mol{1 (134.8 kJ mol{1) was found. With this value, using the same authors’ data for the solid (see above), the heat of combustion of C 14H 28 in the vapor state is calculated to be –(2,184.2 + 32.2) or –2,216.4 kcal mol{1 (–9,273.4 kJ mol{1). The authors did not refer to the value available in reference 8, nor did they attempt to calculate the strain per CH2 in cyclotetradecane based on their value, which would amount to –2,216.4/14 = –158.3 kcal mol {1 or –662.4 kJ mol {1 , about the same as in cycloundecane and 0.8 kcal mol{1 (3.3 kJ mol{1) greater than that calculated in the previous paragraph (8). (While this may not strike the reader as a huge discrepancy, the resulting “increase” in total strain in cyclotetradecane, 11.6 kcal mol {1 or 48.4 kJ mol{1, is appreciable. The 1964 value of –∆Hcomb/n is indicated in Figure 1 by an X; it causes an appreciable spike!) The 1964 value subsequently found its way into the TRC Tables (10). When one of us (ELE) used these tables in a recent text (11) he noted the discrepancy.5 Others evidently did, too: the heat of sublimation of C14H28 was redetermined in 1992 (2) to be 23.5 kcal mol {1 (98.3 kJ mol{1), much closer to the 1955 value of 21.34 kcal mol{1
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Figure 1. Strain per CH2 group for a cyclane (CH2) n as function of n (total strain divided by n). From reference 3. The point marked x is calculated from reference 7. Regarding cycloheptadecane, see footnote 4.
(89.3 kJ mol{1) than to the 1964 value of 32.2 kcal mol{1. With the new value and using the value for the heat of combustion of the solid of –2,183.5 kcal mol{1 (5), the heat of combustion of gaseous C14H28 is –2,207.0 kcal mol{1 (–9,234.4 kJ mol{1), the total strain is 3.4 kcal mol{1 (14.2 kJ mol{1), and the strain per CH 2 is 0.2 kcal mol{1 (1.0 kJ mol {1 ), similar to that for cyclododecane and cyclotridecane (8).6 The conclusion reached in 1957 (3) on the basis of the value of the heat of sublimation given in reference 1, namely that the strain in C14H28 is negligible, was very nearly correct!
trans-Stilbene The heat of combustion of trans-stilbene is of particular interest in connection with the equilibrium between trans-stilbene and cis-stilbene, which plays an important role in photochemistry (12). (Strictly speaking, it is the free energy difference that is needed. However, see text and reference 13—the difference in entropy between the stereoisomers is small.) The difference in heat of combustion (or of formation) of the stilbenes has been determined in three ways: by determination of the position of equilibrium as a function of temperature (13, 14), as the difference of the heats of combustion in the gaseous state (15), and as the difference in heats of hydrogenation (16) in the liquid phase.7 The heats of combustion of solid trans-stilbene and liquid cis-stilbene were determined early on by Coops and Hoijtink (17) and are –7,404.1 ± 0.7 kJ mol{1 (–1,769.6 ± 0.2 kcal mol{1) for the cis and –7,361.1 ± 0.5 kJ mol{1 (–1,759.3 ± 0.1 kcal mol{1) for the trans isomer. [For reasons that are not clear to us these values are reported elsewhere (18) as –1,770.46 and –1,760.18 kcal mol{1.
3 It may be questioned whether a linear acyclic hydrocarbon is “strainless” and thus whether the –157.4 kcal mol–1 (–658.6 kJ mol–1 ) value is appropriate. It has been argued (9) that, since straight-chain alkanes exist to some extent in the higher-energy gauche form, the desired heat of combustion per CH2 of the more stable anti conformer should be taken as –157.6 kcal mol–1 (–659.4 kJ mol–1). The effect of this change is to increase the calculated strain per CH2 group by 0.20 kcal mol–1 (0.84 kJ mol–1). 4 The apparent slight negative strain of cycloheptadecane is probably an artifact of experimental error (van Kamp, H., personal communication). 5 The original footnote e to Table 11.4 (which was changed in proof when the corrected value from reference 2 was substituted) read “This value cannot be correct.”
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Other values reported for the heat of combustion of crystalline trans-stilbene are –1,758.80 kcal mol{1 (19) and –1,759.28 kcal mol {1 (20)]. The heat of vaporization of the cis isomer is 15.8 ± 0.3 kcal mol{1 or 66.1 ± 1.26 kJ mol{1 (21), giving the heat of combustion of gaseous cisstilbene as –7,470.2 ± 2.0 kJ mol{1 or –1,785.4 ± 0.4 kcal mol{1. Since JJE’s early value for the heat of sublimation of trans-stilbene (1) was not published in the journal literature, when the heat of isomerization of the stilbenes was computed (15), a later value of 95.4 ± 3.0 kJ mol{1 (22.8 ± 0.7 kcal mol{1) (22) was used (23), giving the heat of combustion of gaseous trans-stilbene as –7,456.5 ± 3.5 kJ mol {1 (–1,782.1 ± 0.8 kcal mol{1 ) and the difference in heats of combustion of the stilbenes as ∆H° = {13.7 ± 5.5 kJ mol{1 or –3.3 ± 1.3 kcal mol{1 (cis trans). This value was in fair agreement with a value of {2.3 ± 0.3 kcal mol {1 (in toluene) or {2.9 ± 0.3 kcal mol{1 (in methylcyclohexane) (–9.6 ± 1.3 or –12.1 ± 1.3 kJ mol{1) determined by measuring the temperature dependence of the equilibrium of the stilbenes (14), but disagreed with a value determined by difference in heats of hydrogenation (16) of –5.7 ± 0.2 kcal mol{1 (–23.9 ± 0.8 kJ mol{1). Thus in 1986 there were two determinations favoring the lower absolute value of the enthalpy difference between the stilbenes and one determination favoring the higher. But this situation changed in 1987 when the equilibrium cis-stilbene trans-stilbene was redetermined (13), the result being ∆H° = –4.59 ± 0.09 kcal mol{1 (–19.2 ± 0.4 kJ mol{1), ∆S° = –1.05 ± 0.24 cal mol{1 K{1 (–4.4 ± 1.0 J mol{1K{1),8 giving a calculated value for ∆G°300 of –4.28 ± 0.16 kcal mol{1 (–17.9 ± 0.7 kJ mol{1). At this point, then, it appeared that, contrary to the earlier conclusion (15), the higher value (around 5 kcal mol{1 or 21 kJ mol{1) was the correct one; however, the discrepant heat-of-combustion data were a matter of concern, especially since the work of Coops and his school—who determined these heats, albeit in the condensed phase— was generally very accurate. Interestingly, however, when one takes the 1955 value (1) for the heat of sublimation of trans-stilbene, 20.68 ± 0.08 kcal mol{1 (86.53 ± 0.33 kJ mol{1), the heat of combustion of gaseous trans-stilbene becomes {7,447.6 ± 0.8 kJ mol{1 or {1,780.0 ± 0.2 kcal mol{1 and the difference in heats of combustion of the stilbenes becomes –22.8 ± 2.8 kJ mol{1 or {5.4 ± 0.7 kcal mol{1, in better agreement with the most recent and presumably most accurate value derived from equilibrium measurements (13). Thus it now appears virtually certain that the higher value for the difference ({19.2 kJ mol{1 or {4.6 kcal mol{1) is the correct one; earlier measurements went astray presumably because of the difficulty of measuring heats of sublimation (1) or because of the presence of impurities in the samples used for equilibrium measurements (14; cf. 13). The best value is probably between 4.5 and 5.0 kcal mol{1 (18.8 and 20.9 kJ mol{1) in view of reference 13; values given elsewhere are 16.2 kJ mol{1 ° (3.87 kcal mol{1) (18) and ∆G300(?) = 22.8 kJ mol{1 (5.5 6 Setting aside the point made in footnote 3, this is probably a maximum value. The strain for C14H28 given in reference 2 ranges from 1.1 to 3.2 kcal mol–1 (4.6–13.4 kJ mol–1 ), depending on exactly what data one uses. This corresponds to a strain per CH2 group of 0.08–0.23 kcal mol–1 (0.33–0.96 kJ mol–1 ). 7 The heats of hydrogenation were determined in the (neat) liquid (cis) or solid (trans) phase and were corrected to the liquid phase using the heat of fusion of trans-stilbene. If one converts the raw data to the vapor phase using the heats of vaporization and sublimation given in this paper, an unreasonably large difference of nearly 8 kcal mol{1 (33.5 kJ mol {1) results.
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Research: Science & Education kcal mol{1) (24). The value for the heat of sublimation of trans-stilbene (1) may be slightly too low, making the calculated enthalpy difference of 5.4 kcal mol{1 (22.8 kJ mol{1) slightly too high. Summary The fact that the values for the heats of sublimation of cyclotetradecane (21.34 ± 0.10 kcal mol{1 or 89.3 ± 0.4 kJ mol{1) and of trans-stilbene (20.68 ± 0.08 kcal mol{1 or 86.5 ± 0.3 kJ mol{1) determined by one of us in 1955 (1) were not published in the journal literature caused confusion and uncertainty which, in the case of cyclotetradecane, was alleviated only in 1992 and in the case of trans-stilbene has existed until this day. We believe these problems are now settled. Acknowledgment We are indebted to Gus Somsen, Vrije Universiteit, Amsterdam, for furnishing a copy of the thesis of JJE (ref 1) to ELE and for facilitating the contact between the two authors. We thank Harmen van Kamp for permission to use the unpublished Figure 3 from his doctoral dissertation. 8
That the entropy of cis-stilbene is higher than that of the trans isomer is reasonable: the trans isomer, to preserve maximum pi orbital overlap, retains a nearly planar conformation. In contrast, the cis isomer, for steric reasons, must have one of the benzene rings tilted; under these circumstances, there is considerable opportunity for rotation (libration) of the benzene rings. Reference 14, in contrast, reports ∆G ° = –2.7 kcal mol{1, which in conjunction with the same authors’ value for ∆H° (see text) would require that the entropy of trans-stilbene be appreciably higher than that of the cis isomer.
Literature Cited 1. Engelsman, J. J. An Application of a Thermistor Manometer for the Determination of Heats of Sublimation of Slightly Volatile Compounds; Doctoral Dissertation, Vrije Universiteit: Amsterdam, The Netherlands, 1955. 2. Chickos, J. S.; Hesse, D. G.; Panshin, S. Y.; Rogers, D. W.; Saunders, M.; Uffer, P. M.; Liebman, J. F. J. Org. Chem. 1992, 57, 1897. 3. van Kamp, Harmen Energetische Grootheden van Cyclanen; Doctoral Dissertation, Vrije Universiteit: Amsterdam, The Netherlands, 1957. 4. Kaarsemaker, S.; Coops, J. Recl. Trav. Chim. Pays-Bas 1952, 71, 261. 5. Coops, J.; van Kamp, H.; Lambregts, W. A.; Visser, B. J.; Dekker, H. Recl. Trav. Chim. Pays-Bas 1960, 79, 1226. 6. Frisch, M. A.; Bautista, R. G.; Margrave, J. L.; Parsons, C. G.; Wotiz, J. H. J. Am. Chem. Soc. 1964, 86, 335. 7. cf. Eliel, E. L.; Wilen, S. H. Stereochemistry of Organic Compounds; WileyInterscience: New York, 1994; pp 675–678. 8. Eliel, E. L. Stereochemistry of Carbon Compounds; McGraw-Hill: New York, 1962; p 189, Table 7-1. 9. Schleyer, P. v. R.; Williams, J. E.; Blanchard, K. R. J. Am. Chem. Soc. 1970, 92, 2377. 10. TRC Thermodynamic Tables, Hydrocarbons,; Thermodynamics Research Center, The Texas A&M University System: College Station, TX, 1991; Vol. VII, p n-1960. 11. Reference 7, Table 11.4. 12. cf. reference 8, pp 583–584. 13. Saltiel, J.; Ganapathy, S.; Werking, D. J. Phys. Chem. 1987, 91, 2755. 14. Fischer, G; Muszkat, K. A.; Fischer, E. J. Chem. Soc. B 1968, 1156. 15. Eliel, E. L.; Brunet, E. J. Org. Chem. 1986, 51, 1902. The calculations in this paper are slightly in error (by 0.8 kcal mol–1 ). 16. Williams, R. B. J. Am. Chem. Soc. 1942, 64, 1395. 17. Coops, J.; Hoijtink, G. J. Recl. Trav. Chim. Pays-Bas 1950, 69, 358. 18. Pedley, J. B; Naylor, R. D.; Kirby, S. P. Thermochemical Data of Organic Compounds, 2nd ed.; Chapman and Hall: New York, 1986. 19. Richardson, J. W.; Parks, G. S. J. Am. Chem. Soc. 1939, 61, 3543. 20. Marantz, S.; Armstrong, G. T. J. Chem. Eng. Data 1968, 13, 118. 21. Brackman, D. S.; Plesch, P. H. J. Chem. Soc. 1952, 2188. 22. Burgess, J.; Kemmitt, R. D. W.; Morton, N.; Mortimer, C. T.; Wilkinson, M. P. J. Organomet. Chem. 1980, 191, 477. 23. Morawetz, E. (J. Chem. Thermodyn. 1972, 4, 455) has reported an even larger value of 23.71 ± 0.19 kcal mol –1 (99.20 ± 0.80 kJ mol –1). 24. Hnyk, D.; Procházka, M.; Juˇska, L. Coll. Czech. Chem. Com. 1985, 50, 2884.
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