a. The heats of combustion (ΔHc) and heats of hydrogenation (ΔHH2) for addition of 1 mol of H2

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A. The heats of combustion (ΔHc) and heats of hydrogenation...

a. The heats of combustion $\left(\Delta H_{\mathrm{c}}\right)$ and heats of hydrogenation $\left(\Delta H_{\mathrm{H}_{2}}\right)$ for addition of $1 \mathrm{~mol}$ of $\mathrm{H}_{2}$ and the estimated stabilization energy (SE) for benzene and cyclooctatetraene (in $\mathrm{kcal} / \mathrm{mol}$ ) are given below. The $\Delta H_{\mathrm{c}}$ and $\Delta H_{\mathrm{H}_{2}}$ are also given for [16]annulene. Compare the stabilization energy of [16] annulene with benzene and cyclooctatetraene on a per $\mathrm{CH}$ basis. $$ \begin{array}{llcc} \hline & \text { Benzene } & \text { Cyclooctatetraene } & \text { [16]Annulene } \\ \hline \Delta H_{\mathrm{c}} & 781 & 1086 & 2182 \\ \Delta H_{\mathrm{H}_{2}} & -5.16 & 25.6 & 28.0 \\ \mathrm{SE} & 36 & 4 & ? \\ \hline \end{array} $$ b. The enthalpies of the reaction of the cyclooctatetraene and [16]annulene dianions with water have been measured. $$ \begin{aligned} &2 \mathrm{Na}^{+}\left(\mathrm{C}_{n} \mathrm{H}_{n}\right)^{2-}+2 \mathrm{H}_{2} \mathrm{O}_{(1)} \rightarrow \mathrm{C}_{n} \mathrm{H}_{\mathrm{n}+2}+2 \mathrm{NaOH} \\ &\Delta H=-33.33 \mathrm{kcal} / \mathrm{mol} \text { for cyclooctatetraene } \\ &\Delta H=-10.9 \mathrm{kcal} / \mathrm{mol} \text { for }[16] \text { annulene. } \end{aligned} $$ Using these data and the enthalpy of the reaction of sodium with water: $$ 2 \mathrm{Na}_{\text {(s) }}+2 \mathrm{H}_{2} \mathrm{O}_{\text {(1) }} \rightarrow 2 \mathrm{NaOH}_{\text {(aq) }}+\mathrm{H}_{2} \Delta H=-88.2 \mathrm{kcal} / \mathrm{mol} $$ calculate $\Delta H$ for the reaction: $$ 2 \mathrm{Na}_{(\mathrm{s})}+\mathrm{C}_{n} \mathrm{H}_{n} \rightarrow 2 \mathrm{Na}^{+}+\left(\mathrm{C}_{n} \mathrm{H}_{n}\right)^{2-} $$ Why might the reaction of $\left[\mathrm{C}_{16} \mathrm{H}_{16}\right]^{2-}$ with water be less exothermic than for $\left[\mathrm{C}_{8} \mathrm{H}_{8}\right]^{2-}$ ? How do you interpret the difference in the heat of reaction of the two hydrocarbons to form the respective dianions?

a. The heats of combustion $\left(\Delta H_{\mathrm{c}}\right)$ and heats of hydrogenation $\left(\Delta H_{\mathrm{H}_{2}}\right)$ for addition of $1 \mathrm{~mol}$ of $\mathrm{H}_{2}$ and the estimated stabilization energy (SE) for benzene and cyclooctatetraene (in $\mathrm{kcal} / \mathrm{mol}$ ) are given below. The $\Delta H_{\mathrm{c}}$ and $\Delta H_{\mathrm{H}_{2}}$ are also given for [16]annulene. Compare the stabilization energy of [16] annulene with benzene and cyclooctatetraene on a per $\mathrm{CH}$ basis.
$$
\begin{array}{llcc}
\hline & \text { Benzene } & \text { Cyclooctatetraene } & \text { [16]Annulene } \\
\hline \Delta H_{\mathrm{c}} & 781 & 1086 & 2182 \\
\Delta H_{\mathrm{H}_{2}} & -5.16 & 25.6 & 28.0 \\
\mathrm{SE} & 36 & 4 & ? \\
\hline
\end{array}
$$
b. The enthalpies of the reaction of the cyclooctatetraene and [16]annulene dianions with water have been measured.
$$
\begin{aligned}
&2 \mathrm{Na}^{+}\left(\mathrm{C}_{n} \mathrm{H}_{n}\right)^{2-}+2 \mathrm{H}_{2} \mathrm{O}_{(1)} \rightarrow \mathrm{C}_{n} \mathrm{H}_{\mathrm{n}+2}+2 \mathrm{NaOH} \\
&\Delta H=-33.33 \mathrm{kcal} / \mathrm{mol} \text { for cyclooctatetraene } \\
&\Delta H=-10.9 \mathrm{kcal} / \mathrm{mol} \text { for }[16] \text { annulene. }
\end{aligned}
$$
Using these data and the enthalpy of the reaction of sodium with water:
$$
2 \mathrm{Na}_{\text {(s) }}+2 \mathrm{H}_{2} \mathrm{O}_{\text {(1) }} \rightarrow 2 \mathrm{NaOH}_{\text {(aq) }}+\mathrm{H}_{2} \Delta H=-88.2 \mathrm{kcal} / \mathrm{mol}
$$
calculate $\Delta H$ for the reaction:
$$
2 \mathrm{Na}_{(\mathrm{s})}+\mathrm{C}_{n} \mathrm{H}_{n} \rightarrow 2 \mathrm{Na}^{+}+\left(\mathrm{C}_{n} \mathrm{H}_{n}\right)^{2-}
$$
Why might the reaction of $\left[\mathrm{C}_{16} \mathrm{H}_{16}\right]^{2-}$ with water be less exothermic than for $\left[\mathrm{C}_{8} \mathrm{H}_{8}\right]^{2-}$ ? How do you interpret the difference in the heat of reaction of the two hydrocarbons to form the respective dianions?

Key Concepts

Thermodynamic Cycles and Hess's Law

Thermodynamic cycles, employing Hess's Law, allow for the calculation of reaction enthalpies by combining known reaction steps. In this context, enthalpies from separate reactions involving dianions and water, together with the reaction of sodium with water, are used to indirectly determine the enthalpy change of forming dianions. This approach is essential when direct measurement of a reaction is challenging.

Aromaticity

Aromaticity is a concept in organic chemistry referring to the enhanced stability of cyclic, conjugated molecules that meet specific criteria (planarity, cyclic, conjugation, and following Huckel’s 4n+2 rule). Aromatic compounds, such as benzene, exhibit unusual stability because of the delocalization of ?-electrons. This concept is central to understanding differences in stabilization energy among various cyclic conjugated systems.

Dianion Reaction Energetics

The reaction energetics for dianions in aqueous solutions are influenced by factors such as electronic structure and solvation effects. Differences in the enthalpies of reaction for the formation of two different hydrocarbon dianions indicate variations in their intrinsic stabilization and the degree to which solvation stabilizes the ion. A less exothermic reaction for one dianion compared to another may suggest diminished resonance stabilization or stronger solvation influences, impacting the net energy change observed.

Heat of Hydrogenation

Heat of hydrogenation is the energy change observed when hydrogen is added to unsaturated compounds, effectively converting double bonds into single bonds. This measurement allows for estimation of stabilization energies relative to hypothetical non-delocalized structures. By comparing the measured heat with the expected value if no resonance stabilization were present, one can assess the extra stability provided by delocalization or aromaticity.

Heat of Combustion

Heat of combustion is the energy released when a compound undergoes complete oxidation in oxygen. It reflects the overall stability of the compound, where lower combustion energies per CH unit indicate a more stable (often aromatic) system. In the context of comparing different unsaturated cyclic hydrocarbons, the heat of combustion can be used to infer relative stabilization by assessing the release of energy upon total oxidation.

Stabilization Energy

Stabilization energy quantifies the extra stability of a molecule due to electron delocalization, as seen in aromatic systems. It is estimated by comparing the experimental energies (such as heats of hydrogenation or combustion) with those of hypothetical localized structures. On a per CH basis, this value normalizes differences across molecules of varying sizes, enabling a fair comparison of aromatic or antiaromatic character.

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