Question

\(1,3,5,7-\) Cyclooctatetraene, \(\mathrm{C}_{8} \mathrm{H}_{8}\), has a heat of combustion of \(1095 \mathrm{kcal} ;\) it rapidly decolorizes cold aqueous \(\mathrm{KMnO}_{4}\), and reacts with \(\mathrm{Br}_{2} / \mathrm{CCl}_{4}\), to yield \(\mathrm{C}_{8} \mathrm{H}_{8} \mathrm{Br}_{8}\). (a) How should its structure be represented? (b) Upon what theoretical grounds might one have predicted its structure and properties? (c) Treatment of cyclooctatetraene with potassium metal has been found to yield a stable compound \(2 \mathrm{~K}^{+} \mathrm{C}_{8} \mathrm{H}_{8}{ }^{--}\) Of what significance is the formation of this salt? (d) Using models, suggest a possible shape (or shapes) for cyclooctatetraene. What shape would you predict for the \(\mathrm{C}_{8} \mathrm{H}_{8}^{--}\) anion?

Short answer

Cyclooctatetraene has a conjugated, planar structure with alternating carbon-carbon double bonds. Its structure and reactivity can be predicted based on its molecular formula and reactions with electrophiles. The formation of a stable anion when treated with potassium metal suggests strong electron delocalization within the molecule. Both the neutral molecule and anion adopt flat, eight-membered ring structures with alternating carbon-carbon single and double bonds, while the anion may experience slight curvature due to repulsion between negatively charged carbon atoms.

Step-by-step solution

(a) Structure Representation of Cyclooctatetraene

To determine the structure of cyclooctatetraene, we can use the fact that it reacts with \(\mathrm{Br}_{2}\) in \(\mathrm{CCl}_{4}\) to yield \(\mathrm{C}_{8} \mathrm{H}_{8} \mathrm{Br}_{8}\). This indicates that all double bonds are present on the cyclooctatetraene. Using this information, we can represent the structure as follows: ``` H H H H \ / \ / \ / C - C - C - C - C - C - / \ / \ / \ H H H H ``` Each carbon atom is bonded to two other carbon atoms and one hydrogen atom, resulting in a total of 8 carbon atoms and 8 hydrogen atoms in the molecule.

(b) Theoretical Predictions of Structure and Properties

Using the molecular formula \(\mathrm{C}_{8} \mathrm{H}_{8}\), we can determine that Cyclooctatetraene has 2 fewer hydrogen atoms than an alkane with 8 carbon atoms. Thus, it must have 4 fewer single bonds, which means it contains 4 double carbon-carbon bonds. From this, we can deduce that the structure of Cyclooctatetraene will likely resemble that of a conjugated diene. This indicates that the molecule should be planar and stabilized by resonance, which will give it a higher heat of combustion than expected for a non-conjugated system. Additionally, since Cyclooctatetraene contains double bonds, it should be susceptible to reactions with electrophiles like \(\mathrm{KMnO}_{4}\) and \(\mathrm{Br}_{2}\), providing further support for the structure reported in part (a).

(c) Significance of Salt Formation with Potassium Metal

The formation of a stable compound \(2\mathrm{K}^{+}\mathrm{C}_{8}\mathrm{H}_{8}^{--}\) when Cyclooctatetraene is treated with potassium metal indicates that the molecule has the ability to accept electrons and form an anionic species. This suggests that the molecule's 4 double bonds are readily accessible for electron donation, which hints at strong electron delocalization throughout the structure. The presence of a stable anionic salt also indicates that the structure of Cyclooctatetraene is likely planar and stabilized by resonance.

(d) Possible Shapes of Cyclooctatetraene and Its Anion

As discussed earlier, the structure of Cyclooctatetraene suggests a planar, conjugated system with alternating double bonds. Therefore, its possible shape can be envisioned as a flat, eight-membered ring with adjacent carbon atoms connected by double and single bonds. The \(\mathrm{C}_{8} \mathrm{H}_{8}^{--}\) anion, formed by accepting electrons from the potassium metal, is likely to adopt a similar structure to Cyclooctatetraene. However, the anion might experience slight curvature in the structure, as the extra electrons will cause some repulsion between the negatively charged carbon atoms. This would result in a less planar, somewhat puckered shape for the anion, still maintaining the alternating pattern of single and double carbon-carbon bonds.

Key concepts

Alkene Reactions

Alkenes, organic compounds with carbon-carbon double bonds, play a significant role in chemical reactions due to their electrophilic nature. In the context of cyclooctatetraene, the molecule's reaction with potassium permanganate (KMnO₄) and bromine (Br₂) illustrates typical alkene behavior.

For instance, the addition of Br₂ to alkenes is a classic example of a halogenation reaction, where the bromine molecule becomes attached across the double bond. Such reactions are useful not only for adding functional groups to a molecule but also for inferring the presence of double bonds. Cyclooctatetraene's rapid decolorization of KMnO₄ demonstrates its ability to undergo oxidation reactions, which is characteristic of alkenes. This provides a valuable clue about the location of double bonds within the molecule.

Conjugated Diene

A conjugated diene is a system where double bonds are separated by a single bond, allowing for greater electron delocalization across the pi bonds. Cyclooctatetraene has four double bonds, suggesting it should have the properties of a conjugated diene.

This conjugation confers additional stability to the molecule, known as conjugation energy. The extra stability arises due to the overlapping p orbitals, which allows electrons to delocalize over several adjacent atoms. This structure inherently impacts the molecule's reactivity and can lead to unique reactions, such as the Diels-Alder reaction.

In the case of cyclooctatetraene, however, despite initial assumptions of having a planar, conjugated structure, the molecule fails to exhibit typical conjugated diene stability—this is due to the ring strain present in an eight-membered ring that prohibits effective conjugation.

Resonance Stabilization

Resonance stabilization is a concept used to describe the delocalization of electrons in molecular structures with conjugated systems. Molecules with resonance stabilization generally have lower energies and greater stability than those without.

The formation of the stable ion 2 K⁺C₈H₈²⁻ when potassium reacts with cyclooctatetraene suggests some degree of delocalization and resonance stabilization. Potassium donates electrons to cyclooctatetraene, resulting in a dianion. In many conjugated systems, the charge would be delocalized over the molecule, but cyclooctatetraene's unique structure – which is not planar due to angle strain – limits this stabilization.

Nevertheless, the formation of the stable dianion hints at the unusual molecular orbitals of cyclooctatetraene, which allow for some degree of electron delocalization despite the molecule's non-planarity.