Delocalization energy of benzene

The delocalization energy of benzene is 2p (verify this). From information in Exereise 7-6 ealeulate yet another value for the size of the unit p based on the thermodynamic values of the enthalpy of fomiation of benzene. Does this value agree with the themiodynamic values in Problem 14 Does it agree with the spectroscopic value ... 

Ignoring O (see eqn (10-5.1)), the 7r-electron energy for the ground state will be 6a+80 which, when compared with the 71-electron energy of three ethylene molecules (6 a+60), shows that the delocalization energy of benzene is 2/ . 

Remembering that p is negative, we see that n bonding has stabilized the molecule by 8p. Energies expressed in units of / are not very informative, however, unless we can estimate the value of p. We shall next turn to the calculation of the delocalization energy of benzene in units of /i. Since the delocalization energy may be estimated experimentally, we shall then be able to evaluate p. It is not practicable to do this by computation. 

Experimentally, the delocalization energy of benzene is estimated in the following way. The actual enthalpy of formation of benzene can be determined by thermochemical measurements. The energy of the hypothetical molecule cyclohexatriene can be estimated by using the bond energies for C—C, C=C, and C—H found in other molecules such as ethane and ethylene. The difference between these energies is the experimental value of the delocalization energy. We then evaluate / , since... 

Radical anions of 2,3-dimethylpyrazine and 2,5-di-/-butyl-3-isopropylpyrazine have been prepared with metallic potassium in 1,2-dimethoxyethane, and their e.s.r. spectra examined (596a). Heats of hydrogenation of compounds containing isolated and conjugated C=N double bonds have been measured, and the empirical delocalization energy for pyrazine has been determined as 22.3 kcal/mol (93.3 kJ/mol) and corresponds to only 62% of the empirical delocalization energy of benzene (597). 

Problem 10.2 (a) How do the following heats of hydrogenation (AHh, kJ/mol) show that benzene is not the ordinary triene 1,3,5-cyclohexatriene Cyclohexene, -119.7 1,4-cyclohexadiene, 239.3 1,3-cyclohexadiene, -231.8 and benzene, 208.4. (b) Calculate the delocalization energy of benzene, (c) How does the delocalization energy of benzene compare to that of 1,3,5-hexatriene (AHh = - 336.8 kJ/mol) Draw a conclusion about the relative reactivities of the two compounds. 

Figure 13.13 combines all these numbers and shows graphically how this procedure yields the amount by which benzene is more stable than the hypothetical 1,3,5-cyclohexatriene, —32.9 kcal/mol (Fig. 13.13). This difference represents the amount of energy the special stabilization of benzene is worth. It is more than 30 kcal/mol and is called the resonance energy or delocalization energy of benzene.

Cyclohexene, a compound with one double bond with localized tt electrons, has an experimental LtP = -28.6 kcal/mol for its reaction with H2 to form cyclohexane. Therefore, the LhP of "cyclohexatriene," an unknown hypothetical compound with three double bonds with localized n electrons, would be three times that value (A// = 3 x -28.6 = -85.8) for the same reaction. Benzene, which has three double bonds with delocalized tt electrons, has an experimental LhP = -49.8 kcal/mol for its reaction with H2 to form cyclohexane. The difference in the energies of "cyclohexatriene" and benzene (36 kcal/mol) is the delocalization energy of benzene—the extra stability benzene has as a result of having delocalized electrons. 

The 7T electrons in graphite are probably the most extreme case of carbon electron delocalization known since there is an equal probability of finding a given it electron in any of three adjacent rings around each carbon atom. It would be expected that the stabilization energy" from this delocalization is very high since the delocalization energy" of benzene is known to be 36 kcal/mol. 

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