Problem 15 - Advanced Organic Chemistry. Part A. Structure and Mechanisms

Question

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?

Step-by-Step Solution

Answer

[16]Annulene has a higher stabilization per CH unit than benzene and cyclooctatetraene. [16]Annulene's reaction is less exothermic due to greater structural stability.

Step 1: Calculate SE for [16]Annulene

Benzene has a stabilization energy (SE) of 36 kcal/mol with 6 CH units, giving an SE per CH of 6. Cyclooctatetraene has SE of 4 kcal/mol with 8 CH units, giving an SE per CH of 0.5. For [16]annulene, dividing the total combustion heat by the number of CH units: \[ \text{SE per CH for [16]annulene} = \frac{2182}{16} \approx 136.375 \text{ kcal/mol} \]

Step 2: Heat of Reaction with Water for Cyclooctatetraene

The enthalpy of the overall reaction is given by: \[ 2\text{Na}^+ \left(\text{C}_n\text{H}_n\right)^{2-} + 2\text{H}_2\text{O} \rightarrow \text{C}_n\text{H}_{n+2} + 2\text{NaOH} \] For cyclooctatetraene, \( \Delta H = -33.33 \text{kcal/mol} \). Subtracting \( 2 \times (\Delta H \text{ for Na with } \text{H}_2\text{O}) = 2 \times (-88.2) \) gives: \[ \Delta H = -33.33 + 176.4 = 143.07 \text{ kcal/mol} \]

Step 3: Heat of Reaction with Water for [16]Annulene

For [16]annulene, \( \Delta H = -10.9 \text{kcal/mol} \). Subtracting \( 2 \times (\Delta H \text{ for Na with } \text{H}_2\text{O}) \), we have: \[ \Delta H = -10.9 + 176.4 = 165.5 \text{ kcal/mol} \]

Step 4: Calculate \( \Delta H \) for \([16]\)Annulene Reduction

The reaction being considered is: \[ 2\text{Na}_{(s)} + \text{C}_n\text{H}_n \rightarrow 2\text{Na}^+ + \left(\text{C}_n\text{H}_n\right)^{2-} \] Given \( \Delta H \) for sodium with water, subtract this from calculated total \( \Delta H \) from step 3. For reduction of [16]annulene: \[ \Delta H = 165.5 - (-88.2) = 253.7 \text{ kcal/mol} \]

Step 5: Interpretation

The less exothermic reaction of \([16]\)annulene dianion with water compared to cyclooctatetraene suggests higher stability due to resonance or structural factors, leading to oxidative preference. The difference in heat reactions suggests [16]annulene potentially has a greater electronic delocalized configuration providing added stabilization, making its reduction less favorable energetically.

Key Concepts

Heats of Combustion

Understanding the heats of combustion is vital in assessing the energy released when a compound undergoes complete combustion with oxygen. Usually measured in kilocalories per mole (kcal/mol), it's a key indicator of the energy stability and potential energy content of a substance.

When a molecule combusts, it converts chemical energy into thermal energy. A higher heat of combustion indicates a higher energy content in the molecule, which typically means it is less stable compared to lower energy compounds. In the case of benzene, cyclooctatetraene, and [16]annulene, their heats of combustion (\(\Delta H_{c}\)) are measured to be 781 kcal/mol, 1086 kcal/mol, and 2182 kcal/mol respectively.

• Benzene has a relatively low heat of combustion, indicating it is quite stable due to its known aromatic nature.
• Cyclooctatetraene displays a higher heat of combustion, reflecting less stability compared to benzene.
• [16]annulene shows the highest among the three, denoting even less stability.

The comparisons help in determining which molecule is more prone to energetic changes and stability issues.

Heats of Hydrogenation

Heats of hydrogenation highlight the enthalpy change when hydrogen is added to a compound, such as when converting unsaturated hydrocarbons to saturated ones. Lower heats of hydrogenation suggest a more stable molecule due to less energy released during hydrogenation.

Examining benzene, cyclooctatetraene, and [16]annulene, their heats of hydrogenation (\(\Delta H_{\mathrm{H}_{2}}\)) are -5.16 kcal/mol, 25.6 kcal/mol, and 28.0 kcal/mol respectively. Benzene's low value is indicative of aromatic stability, a result of a delocalized pi-electron cloud that doesn't easily release energy when hydrogenated.

• Benzene’s negative \(\Delta H_{\mathrm{H}_{2}}\) confirms its stability and resistance to hydrogenation.
• Cyclooctatetraene shows a positive \(\Delta H_{\mathrm{H}_{2}}\), suggesting an easier, more energy-releasing hydrogenation, due to its non-aromatic behavior.
• [16]annulene, despite being larger, has a similar meaning to its heat of hydrogenation as cyclooctatetraene, indicating it does not achieve the same stability as benzene.

This idea helps students compare how different structural features affect molecular stability across these species.

Annulenes

Annulenes are cyclic hydrocarbons with alternating single and double bonds. They are intriguing because their potential for aromatic stability varies based on the number of π-electrons. According to Hückel's rule, only those with 4n+2 π-electrons can exhibit aromatic stability.

Benzene, a classic example of aromaticity, fits this rule with 6 π-electrons. Cyclooctatetraene, on the other hand, with 8 π-electrons, doesn't comply with Hückel's rule, resulting in a structure that's not aromatic and conformations that struggle with antiaromatic instability.

• Benzene's aromaticity greatly aids its stability, as seen by its heat measurements.
• Cyclooctatetraene's propensity to puckering further implies inadequate stability.
• [16]annulene's compliance with Hückel's rule (16 π-electrons) positions it closer to aromaticity but still not achieving full aromatic characteristics like benzene.

Understanding the trends in annulenes helps students recognize the delicate balance of forces determining aromatic stability in cyclic hydrocarbons.

Cyclooctatetraene

Cyclooctatetraene (COT) is a fascinating molecule due to its structure and reactivity. Although you might anticipate aromatic characteristics due to its eight conjugated double bonds, its typical non-planar “tub” conformation alters this expectation.

The conformation of cyclooctatetraene prevents it from achieving the aromatic stability seen in planar anulenes. Its adoption of a non-planar shape prevents the delocalization needed for aromaticity: hence COT exhibits neither the stability associated with aromatic systems, nor significant antiaromaticity since it's not forced to be planar.

• The molecule behaves like a typical polyene rather than an aromatic compound.
• Heats and chemical reactions imply reactivity similar to non-aromatic compounds.
• The shape contributes significantly to its energy profile and stability estimations.

The structural uniqueness of cyclooctatetraene serves as an ideal example to illustrate how confinement to a particular shape can impact electron flow and thus the chemical characteristics of a compound.