Question

In a buckyball, three of the bonds around each hexagon are so-called double bonds. They result from adjacent atoms sharing a state that does not participate in the \(s p^{2}\) bonding. Which state is it, and is this extra bond a \(\sigma\) -bond or a \(\pi\) -bond? Explain.

Short answer

The shared state that does not participate in \(s p^{2}\) bonding is the p electron state of the carbon atom. The extra bond is a \(\pi\) bond formed by the parallel overlap of p orbitals of adjacent carbon atoms.

Step-by-step solution

Understanding Bonding in Buckyball

A buckyball or fullerene is made up of 60 carbon atoms arranged in a structure of 20 hexagons and 12 pentagons, having a soccer ball shape. Each carbon atom is \(s p^{2}\) hybridized and forms 3 sigma bonds with 3 neighboring carbon atoms, one in each of three, and leaves one p orbital for forming \(\pi\) bond

Identify double bonds

When hexagonal structures are formed, there are three bonds that can be classified as double bonds. This is because in addition to \(\sigma\) bonds formed by \(s p^{2}\) hybridization, the carbon atoms are also forming \(\pi\) bonds by sharing their unpaired p electrons.

Determine bond type

The extra bond according to the problem, is not participating in \(s p^{2}\) hybridization. This means that it is not a \(\sigma\) bond. The unparticipated bond making the bond 'double' is a \(\pi\) bond, formed by the parallel overlap of p orbitals, and this contributes to the structure of hexagon in buckyballs.

Key concepts

Understanding sp2 Hybridization

When we dive into the intricate world of chemistry, particularly the structure of molecules like the fascinating 'buckyball,' we encounter the concept of sp² hybridization. This term refers to the mixing of one s orbital and two p orbitals from the same atom to form three new, equivalent orbitals known as sp² hybrid orbitals.

Each carbon atom has an electron configuration that, when energized, leads to the promotion of an electron into a higher energy state, thus resulting in the hybridization process. In buckyballs, every carbon atom undergoes sp² hybridization, creating three hybrid orbitals that form sigma bonds with neighboring carbon atoms. The remaining unhybridized p orbital is essential for pi bonding, which is crucial for the formation of double bonds in the buckyball structure.

Understanding sp² hybridization is fundamental because it contributes to the unique shape and properties of molecules. The geometric consequence of this hybridization is a trigonal planar arrangement, promoting the formation of strong and stable chemical bonds.

Delving into the Nature of Pi Bonds

Proceeding to pi bonds, these result from the side-to-side overlap of adjacent unhybridized p orbitals. In a buckyball, once the sigma bonds are formed through sp² hybridization, each carbon atom still has one unhybridized p orbital. These p orbitals extend above and below the plane of the atoms that are sigma bonded.

The pi bonds form when these lobes overlap with those from neighboring carbon atoms. This creates a region of electron density that does not lie along the line of the internuclear axis, which is the characteristic of the pi bond compared to the sigma bond. It's also important to note that pi bonds are generally weaker than sigma bonds and provide less overlap, but they are pivotal in conferring stability and unique chemical properties to the structure of the buckyball.

Sigma Bonds: The Backbone of Molecular Structure

Switching our focus to sigma bonds, they are the most common type of covalent bond formed between two atoms. Characterized by head-to-head orbital overlap, they allow the sharing of electrons along the axis connecting two atomic nuclei.

In the context of a buckyball, every carbon atom uses its three sp² hybrid orbitals to form sigma bonds with three different neighboring carbon atoms. This ensures a firm and robust connectivity within the molecule, contributing to its overall stability and strength. Unlike pi bonds, these are free to rotate, which makes them pivotal in contributing to the flexibility and multiple conformations that a molecule like buckyball can exhibit.

The Fullerene Structure: A Geodesic Sphere of Carbon

Lastly, exploring the fullerene structure opens up a fascinating realm of molecular geometry. Fullerenes are a class of carbon allotropes, among which the buckyball, or C₆₀, is a quintessential example. It resembles a geodesic dome with a spheroidal shape resemblant of a soccer ball consisting of pentagons and hexagons.

The unique arrangement of 20 hexagons and 12 pentagons, each vertex being a carbon atom, is a testament to carbon's versatile bonding capabilities. The curvature of the buckyball's surface is made possible because of the seamless integration of pentagonal and hexagonal rings, with sp² hybridized carbon atoms at the vertices. The pi bonds, although they don't contribute to the spherical shape directly, play a key role in the electronic properties, making fullerenes potential candidates in various applications ranging from organic photovoltaics to drug delivery systems.

The understanding of fullerene structures not only epitomizes the beauty and intricacy of molecular architecture but also paves the way for innovative materials and technologies based on this extraordinary carbon assemblage.