26 BOND RESONANCE ENERGIES ESTIMATES OF AVERAGE BOND ENERGIES AND RESONANCE ENERGIES OF HYDROCARBONS BY GEO. GLOCKLER Received 8th March, 1951 Average bond energies of hydrocarbons are estimated on the basis that the heat of sublimation of carbon L(C) = 169-7 kcal. It is assumed that the experi- mental values of the CC- and the CH- distances of the three molecules ethane, ethylene and acetylene yield a relation between these distances which also holds for all other hydrocarbon molecules. It means that carbon-carbon bonds of relatively high average bond energy associate with carbon-hydrogen bonds of relatively high average bond energy. These average bond energies are used to calculate resonance energies. It is emphasized that these latter quantities depend on the reference state chosen.The method of calculating resonance energies from heats of hydrogenation is analyzed and i t is found that this pro- cedure must be amplified by also considering the resonance energies and other effects which tend to change the average bond energies of the intermediate struc- tures. The hydrogenation of butadiene t o butene and butane and of benzene to I : 3-cyclohexadiene, cyclohexene and cyclohexane are discussed as examples. Introduction.-The heat of sublimation of carbon L(C) is still in This dispute as can be seen from an excellent review by Springall-l Springall, Research, 1950~ 3, 260.GEO. GLOCKLER 27 quantity is necessary for the calculation of average bond energies of hydro- carbon molecules and the latter quantities are needed to calculate reson- ance energies.There are now three experimental determinations 2* 3 9 * of L ( C ) which check satisfactorily' and the value L ( C ) = 7-36 eV (169.7 kcal.) is adopted here. For comparison the average bond energies of hydro- carbons based on L(C) = 5.888 eV (135.8 kcal.) are also given in Table I. In order to make the calculations described below' it is assumed that the experimental values for the internuclear CC- and CH- distances (R(CC) and R(CH)) for acetylene, ethylene and ethane can be used to establish a general relation between R(CC) and R(CH) for hydrocarbon molecules. It means that CC- bonds of relatively high CC- average bond energy associate with CH- bonds of relatively high CH- average bond energy. Methane and its radicals, the nonnal paraffins, I-olefins, di-olefins and benzene are considered in detail as examples.Similar studies have been made earlier by Skinner,G Roberts and Skinner and Glockler.* The system of bond energies used here (based on L(C) = 169.7 kcal.) fits better into a larger scheme involving CC, CN, CO, NO, 00 and NN bonds, than thc similar set based on L(C) = 135-8 kcaL8 Methyl Radical .-The bond dissociation energy of methane (D(CH,-H)) is known to be IOI kcal.99 lo The heat of formation of TABLE I.-HEATS OF FORMATION Q,, ATOMIC HEATS OF FORMATION Qa, AND INTERNUCLEAR DISTANCES R(CC) AND R(CH) ESTIMATED cc- BOND ENERGIES B(CC), AND CH- BOND ENERGIES %(CH), Qj kcal. - 54'33 - 54'33 - 204.1 - 187.6 - 14-52 - 14.52 - 24.00 - 2 4-00 0'00 0'00 I 6.52 16-52 15-99 15-99 - 128.8 - 107.4 Q, kcal.388-3 320'5 (135.4) 84-0 531'5 463'5 1304'2 I 100-4 169.8 135.8 665'9 598.0 392'4 358.4 (92'3) 80.0 I 1.207 1-207] 1.316 1.316 1'353 1.353 1'39 1'39 1'545 1'545 ( 1'5 4 7) (1'547) - - - 181.5 118.9 84.0 125.0 77'5 I 16.4 85.1 84.9 67.9 84-5 67.7 (135.4) - I - R(CH) A 1.060 1-060 - - 1-071 1-071 1.075 1.075 - - 1'100 1'100 1.092 1.092 1.131 1.131 &CH) kcal . 103.4 100.8 - - 101.6 96.5 98.3 96.9 88.4 98.1 89.6 80.0 101'0 I - (92'3) Rcmarks U b a b b a b ac bc a b b ad bd U U (a) Based on L(C) = 169.7 kcal. (b) Based on L ( C ) = 135.8 kcal. ; D(H2) = 103-2 kcal. ( c ) B(CC in diamond) = +L(C). (d) The value B(CH, radical) is obtained by extrapolation. Brewer, Gilles and Jenkins, J . Chem. Physics, 1948, 16, 797. Simpson, Thorn and Winslow, A .E.C.General Chemistry Report A NL-4264 Marshall and Norton, J . Amer. Chem. Soc., 1950, 72, 2166. Hagstrum, Physic. Rev., 1947, 72, 947. Skinner, Trans. Faraduy Soc., 1945, 41, 645. Roberts and Skinner, Trans. Faraday Soc., 1949. 45, 339. Glockler, J . Chem. Physics, 1948, 16, 842 ; 1951, 19, 124. Anderson and Kistiakowsky, J . Chem. Physics, 1943, 11, 6. (Argonne Nat. Laboratory, 1949). lo Kistiakowsky and Van AItsdalen, J . Chem. Physics, 1944, 12, 469.28 BOND RESONANCE ENERGIES methane (Qf = 15-98 k~a1.l~) yields Qa(CH4) = 392-4 kcal. (Table I). The heat of atomization of methyl radical must then be Qa(CH,) = Qa(CH4) - D(CH, - H) = 291-4 kcal., whence B(CH in CH,I = 97.1 kcal., (L(C) = 169.7 kcal. ; Table 11) These values lead to the CC- bond dissociation energy of ethane : D(CH, - CH,) = 83-5 kcal.while Szwarc la gives 80 f 6 kcal. based on the work of Rice and Do01ey.l~ Methylene Radical .-The CC- bond dissociation energy of ethylene into two CH, radicals is less than 160 kcal.l2. l4 Using D(CH, - CH,) = 150 kcal. yields the set D(CH,-H), D(CH,-H), D(CH-H) and D(CH) of Table 11. B(CH in CH,) and B(CH in CH,) are more nearly equal in the set based on L(C) = 169.7 kcal. This equality may be expected since in both structures the carbon atom used sp3 hybridization. It is also seen that B(CH in CH,) = 95-4 kcal. is nearer to B(CH in C2H4) = 104.8 kcal. than when L(C) = 135.8 kcal. is taken as a base. This feature is also expected since the carbon atom uses spz hybridization in both the CH,- radical and in C,H, (Walsh 15).The bond dissociation energies based on L ( C ) = 135.8 kcal. show erratic behaviour, as for example D(CH-€3) =76-3 kcal. would be less than the bond dissociation energy of CH- radical (80 kcal.). The first set in Table I1 seems to be the more acceptable. Hence the average CH- bond energy in methylene radical is estimated to be 95-4 kcal. and the CH- bond dissociation energy of CH, is taken to be 98.5 kcal. - - TABLE II.-AVERAGE BOND ENERGIES AND BOND DISSOCIATION Energies of Methane and its Radicals (kcal.) ; based on D(CH,-H) = IOI kcal. ; D(CzH4) = 150 kcal. ; assuming L(C) = 169.7 or 135.8 kcal. CH4 CH, . CH, . CH I &CH) 98.1 97'1 95'4 92'3 89.6 85.8 78.4 80.0 Qa 392'4 291.4 190.8 92'3 358'4 257'4 156.8 80.0 D(R-H) 101'0 100.6 98.5 92'3 101'0 100.6 76.8 80-0 11 Bichowsky and Rossini, The Thermochemistry of the Chemical Substances l2 Szwarc, Chem.Rev., 1950, 47, 75. l3 Rice and Dooley, J . Amer. Chem. Soc., 1933, 55, 4245. l4 Price, Physic. Rev., 1934, 45, 843 ; 1935, 47, 444. 15 Walsh, J . Chem. Soc., 1948, 398. (Reinhold Publishing Corp. New York, 1936).GEO. GLOCKLER 29 Methine Radical (CH, X217).-The heat of dissociation of CH(217) radical is given by Herzberg l6 as D(CH) = 3-47 eV (80.0 kcal.) based on the work of Shidei.17 This value depends on the interpretation of a missing line in the spectrum of CH as indicating a predissociation. It might, however, be a perturbation. In that case D(CH) = 4-00 eV (92.3 kcal.) obtained by extrapolation of a B(CH) against R(CH) curve (from the data of Table I) is a good estimate, considering also the fact that a linear Birge-Sponer extrapolation yields 5-31 eV (122.5 kcal.).16 The value D(CH) = 92-3 kcal.also fits better into the sequence HF, OH, NH and CH (Table 111, column 4). The values B(OH in H,O) and B(OH) are from Dwyer and Oldenbergla D(HF) is 145.6 or 132.6 kcal. depending on D(FJ being 60 or 40 kcal.ls. a. D(NH) is 96.9 or 78.4 kca1.l6- 21 The larger value fits the sequence given in column 4 of Table 111. The value of B(CH in C,H,) is related to the dissociation of acetylene into CH radicals or with the breaking of the CC- bond : C,H, + ZC + zH ZC + zH + 2CH C,H, -+ zCH - 388.3 or - 320-5 kcal. 184.6 or 160.0 kcal. - 203.7 or - 160.5 kcal. whereas Szwarc la mentions < 187 (?) kcal. The higher value (based on L(C) = 169.7 kcal.and D(CH) = 92.3 kcal.) is nearer to the questionable figure which was obtained by Price l4 and Hilgendorff 2 2 from a Rydberg series in acetylene. It is based on the interpretation of a diffuse band at 1520 as a predissociation. TABLE 111.-AVERAGE BOND ENERGIES g(MH) OF MH- BONDS M = F, 0, N and C ~~ 132.6 109-2 92-7 89.6 135'0 78.4 80.0 100'1 145.6 109.2 98-1 145.0 96.9 92-2 100'2 100'1 Remarks D(F,) = 34 or 60 kcal. Ref. (18) D(N2) = 225.1 or 272.1 kcal. L(C) = 135.8 or 169.7 kcal. D(F,) = 34 or 60 kcal. Ref. (18) Ref. (16) Ref. (IS), (21) Paraffins.-The heat of atomization of the normal paraffins a t oo K) based on Q, values from Selected Vulues 2s is given by Q~.(C,Hanca) = 112~20 + 276.64n ; n > 4 (kcal.), where 276.64 kcal. = increment per CH,- group.The bonds of the end methyl groups are stronger than the bonds within the carbon chain. The end CC- bond energy B(CC of CH,) = 83.8 kcal. from propane on. The next CC- bond energy is 83-5 kcal. from butane upwards and the other CC- bond energies are all equal to 83.3 kcal. The CH- bond energies 1 6 Herzberg, Molecular Spectra and Molecular Structuve, I . Spectra of Diatomic Molecules, 2nd edn. (D. Van Nostrand Co. Inc., New York, 1950). 1' Shidei, Japan J . Physics, 1936, 11, 23. la Dwyer and Oldenberg, J . Chem. Physics, 1944, 12, 351. so Eucken and Wicke, Naturwiss., 1950, 10, 233. 21 Glockler, J . Chem. Physics, 1948, 16, 602. 2z Hilgendorff, 2. Physik, 1935, 95, 781. 23 Selected Values of Properties of Hydrocarbons (Nat. Bur. Stand., Cir.461, Simon, FZuorine Chemistry, Vol. I (Academic Press Inc., New York, 1g50), Chap. 10. 1947).30 BOND RESONANCE ENERGIES are : B(CH in CH,) = 96.8 and B(CH next to CH,) = 96-73 kcal. The CH- bond energy of the CH- bond on the third and fourth carbon atom are 96-70 and 96.68 kcal. respectively. These values will reproduce the Q,, values satisfactorily. Ethane.-The heat of formation is 16-52 kcal.2, yielding Qa = 665.9 kcal. It is of interest to point out that the distances mentioned in Table I fit the moment of inertia of the Ethyl Radical.-Anderson and Van Artsdalen give 98 & 2 kcal. for D(C,H,-H) as an upper limit and the values summarized by Szwarc 1, range from 97 to 102 kcal. From Qa(C2Hs) = 665-7 kcal. and adopting D(C,H5-H) = 97 kcal. yields Qa(CaH5) = 568.7 kcal.and B(CH in C2H5) = 96.8 kcal. if B(CC in C,HJ = B(CC in CZH,) = 84-5 kcal. g(CH in C,H,) = 96-9 kcal. and hence B(CH in CZH,) and D(C2H5-H) are nearly the same showing that there is very little reorganization involved when an ethane molecule loses one hydrogen atom and becomes an ethyl radical. Olefins .-Q,, (propene) = 810.5 kcal. whereas a propene molecule which has ethylene and ethane-like bonds would have Q,, = 802.6 kcal. Hence some of the bonds have been strengthened. It is assumed that the single bond located near the double bond is mostly affected by hyper- conjugation.26 In order to obtain an estimate of this effect it is assumed that the ethylene portion of the molecule is as in ethylene (2B(CH as in CaH,) and B(C = C as in C,H,) = 2 x 101.6 + 125-0 kcal.) and that the remainder of the heat of atomization (482.3 kcal.) is distributed over the CC- single bond and the attendant CH- bonds.The estimated average bond energies in propene are : B(HC=) = 101.6, B(C=C) = 125.0, B(C-C) = 89-2, B(=CH-) = 99.7 and B(CH in CH,) = 97-8 kcal. The corresponding internuclear distances are : R(HC=) = 1.071, R(C=C) = 1.353, B(C-C) = 1-52, R(=CH-) = 1.082 and R(CH in CH,) = 1-094 A. The CH- bond on the middle carbon atom is taken to have the average bond energy of B(=CH) and B(CH in CH,). The I-butene molecule is treated in a similar manner with the as- sumption that the propene-end of the mclecule is a s in propene itself. Labelling the CC- double bond CCI ", the CC- single bond adjacent to the double bond " CC I1 " and the CC- single bond of the CH,- group " CC I11 " it is found that : - CH I : zB(CH as in C2H4) CC I : B(C=C as in C2H,) = 125.07 ,, cc 11 : ~(c-c as in propane) = 89.21 ,, CH I I1 : B(CH near C=C) = 99.68 ,, CH I1 I11 : 2g(CH betw.C-C) = 194.65 ,, CH I11 : 3B(CH of CH,) = 290.60 ,, = 203.19 kcal. CC I11 : B(C-C of CH,) = 84-53 Y ? ~~ Q,, (actual) = 1086.78 ; 1086.93 ,, The normal increment of Qa of the I-olefins is reached between I-hexene and I-heptene. Di-o1efins.-The heat of formation of butadiene at oo K is 30-2 kcaL2' whence Q,, = 958.5 kcal. If the molecule had ethylene-ethane-like bonds, its Q,, would be 939.5 kcal. The middle single CC- bond is known to be shorter (1-46 %i compared to 1-55 A) and hence stronger than usual. It will be assumed that the two end portions of the molecule are " ethylene like " and that all of the change in bond energy is located in the middle 24 Smith, J .Chem. Physics, 1947, 17, 139. 25 Anderson and Artsdalen, J . Cliem. Physics, 1944. 12, 479. 26 Mulliken, Riecke and Brown, J . Amer. Chem. SOC., 1941, 63, 41. Aston, Szasz, Wooley and Brickwedde, J. Chem. Physics, 1946, 14, 67.GEO. GLOCKLER 31 CC- bond. The attendant CH- bonds are expected to be affected to a degree as determined by the CC bonds which emanate from the carbon atom to which they are attached. In the manner indicated with I-butene it is found that 4B(CH as in C,H,) = 406.374 kcal. ; R = 1.071 8, 2B(C=C as in C2H4) = 250.143 kcal. ; R = 1-353 B(C-C, middle) = I O O - ~ O Z kcal. ; R = 1-457 A zB(CH, middle) = 201-065 kcal.; E? = 1-077 Qa (base) 939'53 kcal. Qa (actual) Butadiene . 958.51 kcal. Butene . . 1086.77 ,, Butane . . 1218.51 ,, 1222.23 Qa = 958.48 kcal. ; 958.514 kcal. It should be noted that the bond distance of the single CC- bond has been determined from the bond energy data used here and is an inde- pendent check on the electron diffraction value cited above (1.46 When on the other hand, the system of bond energies based on L(C) = 13543 kcal. is used to make the same calculation then it is found that 4B(CH as in C,H4) = 386.08 kcal. ; R = 1.017 8, zB(C=C as in C,H,) = 154.98 kcal. ; R = 1-353 A B(C-C, middle) = 86.37 kcal. ; R = 1.288 A zB(CH, middle) = 195.25 kcal. ; R = 1.068 A Qa = 822-78 kcal. ; The single CC- bond distance is now calculated to be 1-288A which would make this bond even shorter than a C=C bond and it does not check the electron diffraction value (1.46 A).Hence this point is taken as a piece of circumstantial evidence against L(C) = 135.8 kcal. Resonance and hyperconjugation.-By resonance energy is meant the usual strengthening of the bonds of a molecule due to the fact that the actual total energy of atomization of the molecule is found to be greater than the same quantity when calculated on the basis of some preconceived notion regarding the bonds in a given structure. This hypothetical molecule is then used as the base for calculating the resonance energy of the molecule. For example, it will be assumed here that the basic forms of butadiene, butene and butane have ethylene-like double CC- bonds and ethane-like single CC- bonds. From this point of view it is necessary to include all forms of reorganization energy such as hyperconjugation, near-bond effect, Van der Waals' interaction, London dispersion effect, inductive effect, etc., etc.The three molecules mentioned show the following differences between their Qa (actual) and Qa (ethylene-ethane- like) values : 822.67 kcal. n 18-98 kcsl. 5-89 I, - 3'72 9 , If butadiene is referred to a " butene-like " base then the dii'ference is 958.51 - 945.08 = 13-43 kcal. This quantity differs markedly from 3.5 kcal. given by Wheland 29 and obtained as the difference of twice the heat of hydrogenation of butene to butane and the observed heat of hydrogenation of butadiene to butane. In this case, this difference or resonance energy of butadiene is referred 28 Schomaker and Pauling, J .Amer. Chem. Soc., 1939, 61, 1769. 29 Wheland, The Theory of Resonance (John Wiley and Sons, Inc., New York, 1944).32 BOND RESONANCE ENERGIES to a butene-like base, rather than to a common " ethylene-ethane-like " reference structure. Since butene does not show resonance, i.e., there is only one basic structure, it is quite proper to use it as a resonance reference. However, it seems better to employ a common base such as ethylene- ethane-like bonds. It is true that then aEZ the effects which weaken or strengthen bonds will be involved along with resonance. However, in a large enough molecule it may well happen that the other effects besides the possibility for resonance may produce numerically as large changes in bond energy as does resonance.A detailed study of the hydrogenation of butadiene to butene and butane shows that the following relationships exist. Each molecule is referred to an ethylene-ethane-like base. Let QO1, QOZ, Qos = energy of atomization of butadiene, butene and butane Q1, Q2, Qs = actual energy of atomization of these molecules (based REi, RE2, RE3 = resonance energy or hyperconjugation energy or It is proposed to study first the hydrogenation of butadiene and butene, assuming them to be ethylene-ethane-like. The processes, buta- diene + H2 --f butene, and butene + H, + butane, are alike in the sense that the same bond changes occur. respectively referred to an ethylene-ethane base. on L(C) = 169.7 kcal.).near bond effect, etc., for these molecules. BUTADIENE : Qol = 939.53 kcal. 2 X 101.59 99'24 99'24 2 X 101.59 H H 125.07 84-53 125.07 H2- b C C F - H, BUTENE : Qot = 1080.88 kcal. 2 X 101.59 99-24 2 X 96-87 3 x 96.87 H H2 125.07 84'53 84'53 Q o a - Q o i = (2 x 96-87 - 99-24} + (84.53 - 125.07) H, b C C d - H , and and similarly + (3 x 96.87 - 2 x 101.59) = 141-37 kcal., BUTANE : Qo3 = 1222-23 kcal. 3 x 96.87 2 x 96-87 2 x 96-87 3 X 96-87 H Z H, Ha= C- C- C C HS 84'57 84'57 84'57 so that Qos - Qo2 = (3 x 96-87 - 2 x 101.59) + (84.53 - 125.07) + (2 x 96-87 - 99-22) = 141-37 kcal. These differences refer to the hydrogenation of butadiene to butene and butene to butane by hydrogen atoms C4Ht + 2H + C,H,* + 141.37 kcal. C4H$ + ZH -+ C,H,$ + 141-37 kcal. C,H$ + H, + C,H,* + 38-18 kcal.C4H$ + H, + C4H,*, + 38-18 kcal. The hydrogenations by molecular hydrogen are (0" K) C,H,* etc. represent the ethylene-ethane-like molecules. It is seen that or Q02 - QOI = Q o S - Qos, * ' (1) ~ ( Q o s - Q o z ) = Qos - Qol,GEO. GLOCKLER 33 i.e. twice the last step of hydrogenation equals the total hydrogenation from butadiene to butane, which is obviously true €or the starred struc- tures. If the bond energies of the real molecules and the basic reference structures are different either by resonance or otherwise, then the following relations exist where BEi are the resonance energies or other bond energy changing effects. (3) The differences in the Q's now refer to the hydrogenation of the actual molecule?, and it is seen that twice the diflerence in hydrogenation energy of the last step from butene to butane minus the total hydrogenation energy from butadiene to butane equals the resonance energy of butadiene (RE,) only if RE, = RE3 = 0.Qi = Qw + REi, * (2) Putting eqn. ( 2 ) into (I) yields 2(Ra - Q2) - (Qs - Qi) = 2(RE3 - BE,) - (RE3 - RE,). - The real molecules are represented as follows : BUTADIENE : Q1 = 958.50 kcal. 2 X 101.59 100.53 100.53 2 X 101.59 H H H , ~ C ~ C - C - C C - - - - - - - - H , 125.07 roo-go 125.07 BUTENE : Qa = 1086.77 kcal. 2 X 101.59 99.68 2 x 97'33 3 x 96-87 H H, H 2 C- G-------C- C H3 125.07 89.21 84.53 BUTANE : Q3 = 1218*51 kcal. 3 X 96.75 2 X 96.73 2 X 96-73 3 X 96-75 Ha Ha 83'77 83-51 83'77 H3=C--C-C- The hydrogenations (at oo K) are and The experimental values 3 O are 26.72 and 30.45 kcal.respectively (at 82' C). The usual calculation for the resonance energy of butadiene (using the values at oo K) is RE, = 2 x 28.48 - 53-53 = 3-43 kcal. This difference is, however, a(Q3 - Q2) - (a3 - $21) = 2VE3 - RE,) - (RE3 - J w 9 or 3-43 = z(- 3-72 - 5.89) - (- 3-72 - 18-98). Hence the resonance energy of butadiene referred to an ethylene-ethane base is 18.9 kcal. and on a butene base it is 958.50 - 945.07 = 13-43 kcal. The three resonance or strengthening or weakening effects of butadiene. butene and butane when referred to the ethylene-ethane base are 18.9, 5-9 and - 3-7 kcal. It is seen that the resonance energy 18.9 kcal, is only about three times the second value (5-9 kcal.). The latter effect 3O Kistiakowsky, Ruhoff, Smith and Vaughan, J .Amer. Chem. SOL, 1936, B 58, 146.34 BOND RESONANCE ENERGIES is due to some other influence than resonance and the impression is gained that the changes brought about in bond energies due to resonance effects and other features such a s hyperconjugation, etc., are only different in degree and not in kind. After all, were it possible to solve the wave equation without approximations, the concepts of resonance, Van der Waals' forces, etc. would not be needed. Benzene .-The average bond energies of benzene fit into general B(CC) against R(CC) and B(CH) against B(CH) curves based on the data of Table I using L(C) = 169.7 kcal. This is not the case for L(C) = 135.8 kcal. It is conceivable that several of these curves may be necessary for different kinds of bonds.The ordinary heat of formation 23 is 24 kcal. a t 0" K leading to Q,, = 1304.2 kcal. If the structure were Kekulk-like then this value would be 1224.2 kcal. The difference is the resonance energy of benzene of 80 kcal. The difference from the accepted value (39 k~al.~o. 3 l ) is due to the use of another set of bond energies (based on L(C) = 125.0 kcal.) 31 and because the heats of hydrogenation in steps from benzene to cyclohexane are to be interpreted in a manner analogous to the butadiene case mentioned above. I n the present instance there are three stages : Again Qoi refers to the ethylene-ethane base and Qi to the actual molecules. The quantities BEi represent the resonance energies of the molecules or any effect that causes them to be different from their basic reference structure.Since the steps of hydrogenation of the base struc- ture refer to the additions and subtractions of the same kind of bonds - C6H6 --f C6H8 4 C6Hlo -+ C6H12. Q02 - R o i = Qos - 9 o a = Qo4 - Qosj - (4) or 3(!?04 - Q03) = 9 0 4 - Qo1J which is obvious if all steps are alike. Qi of eqn. (2) where i(C6H6) = I, i(C6H8) = 2, i(C6H10) = 3 and i(C6H1,) = 4 yields 3@4 - Q3) - (94 - Qi) = 3(RE4 - RE31 - (RE4 - RE,). ( 5 ) The left side of eqn. (5) refers to three times the heat of hydrogenation of cyclohexene to cyclohexane minus the heat of hydrogenation of benzene to cyclohexane. This difference is only equal to the resonance energy of benzene (BE,) when RE, and RE4 are zero. The heats of hydrogenation of benzene at 355" K in steps are known : 8 2 Replacing the Qoi by the respective - oOK i 355OK I I I - 5-57 kcal.27'78 I J 28*59 I J - 5-5 kcal. 20-8 28.7 IS The corresponding heats of formation at 355°K are: Qr(C6H6) = - 19-10, Q,(C6H,) = - 24-67, Qt(C6Hlo) = 2-11 and Q,(C6Hlz) = 30.7 kcal. These values are known for benzene and cyclohexane at 0" K : Qf(c6H6) =- 24.0 and Qf(C6Hl,) = 20.7 kcal. The Q, values for C,H8 and C6H,, at 0" K were found by graphic interpolation to be : Q,(C6H8) = -29.5 and 9,(C6Hlo) =- 8.7 kcal. These data lead to the hydrogen- ation values at 0°K given above. On the usual basis it would be said 91Pauling, The Nature of the Chemical Bond (Cornell Univ. Press, Ithaca, 32 Kistiakowsky, Ruhoff, Smith and Vaughn, J . Chem. Physics, 1936, 58, N.Y., 1940). 137 and 146.GEO. GLOCKLER 35 that the resonance energy of benzene is 3 x 28-7 - (28.7 + 20.8 - 5.5) = 42.1 kcal., whereas this quantity equals the combination of RE-factors mentioned above. They can be found from the corresponding Qa values : Qa(C&) = kcal. and the similar values of their ethylene-ethane-like bases : g2(C,H6) = 1224-2, ax(C6H8) = 1372.6, Qg(C6HlO) = 1521.oandQ~(C,H,,) = 1669.5 kcal. The result is IZE(C,H,) = 80.0, RE(C,H,) =29-3, RE(C,H,,) = 4-9 and RE(C,H,,) = - 11.7 kcal. These values also yield 42-1 kcal. when placed in eqn. (5). In conclusion it should be said that no c l a h is made that the present set of bond energies is satisfactory in every respect. After all the heat of sublimation of carbon is not definitely settled. Even more important, the very definition of the term " average bond energy " is in question as pointed out recently by Szwarc and Evans.33 The main thesis of the present remarks is to emphasize that some acceptable system of bond energies must be invented if resonance energies are to be calculated and that the method involving heats of hydragenation must be applied properly. 1304'2J Qo(C6Ha) = 1401.9, Qa(C6H10) = 1525.9 and Qa(c~H12) = 1657.9 Financial support was received from ONR Contract N8 onr 79400. Department of Chemistry and Chemical Engiwerifig, Iowa City, Iowa. The State University of Iowa, 33 Szwarc and Evans, J . Chem. Physics, 1950, 18, 618.