(a) How do the following heats of hydrogenation $\left(\Delta H_h, \mathrm{~kJ} / \mathrm{mol}\right)$ 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 $\left(\Delta H_h=-336.8 \mathrm{~kJ} / \mathrm{mol}\right)$ ? Draw a conclusion about the relative reactivities of the two compounds.
In computing the first column of Table 10-1, we assume that in the absence of any orbital interactions each double bond should contribute $-119.7 \mathrm{~kJ} / \mathrm{mol}$ to the total $\Delta H_h$ of the compound, since this is the $\Delta H_h$ of an isolated $\mathrm{C}=\mathrm{C}$ (in cyclohexane). Any difference between such a calculated $\Delta H_h$ value and the observed value is the delocalization energy. Since $\Delta H_h$ for 1,4-cyclohexadiene is $7.5 \mathrm{~kJ} / \mathrm{mol}$ less than that for 1,3-cyclohexadiene, conjugation stabilizes the 1,3-isomer. [Remember that the smaller (more negative) the energy, the more stable the structure.]
(a) 1,3,5-Cyclohexatriene should behave as a typical triene and have $\Delta H_h=-359.1 \mathrm{~kJ} / \mathrm{mol}$. The observed $\Delta H_h$ for benzene is $-208.4 \mathrm{~kJ} / \mathrm{mol}$. Benzene is not $1,3,5$-cyclohexatriene; in fact, the latter does not exist.
(b) See Table 10-1.
(c) The delocalization energy of benzene $(-150.7 \mathrm{~kJ} / \mathrm{mol})$ is much smaller than that of $1,3,5$-hexatriene $(-22.3 \mathrm{~kJ} / \mathrm{mol})$. Three conjugated double bonds engender a large negative delocalization energy only when they are in a ring. Since the ground-state enthalpy of benzene is much smaller in absolute value than that of the triene, the $\Delta H^{\ddagger}$ for addition of $\mathrm{H}_2$ to benzene is much greater, and benzene reacts much slower. Benzene is less reactive than open-chain trienes towards all electrophilic addition reactions.