Animated Solution for Chemistry - s and p-Block Elements: The $C-C$ bond length is maximum in

Carbon is a fascinating element, capable of bonding with itself in various ways to form entirely different materials known as allotropes. From the ultra-hard diamond to the soft, slippery graphite, and the futuristic soccer-ball-shaped fullerenes, the secret to their distinct properties lies in their atomic arrangement and hybridization.

In this problem, we are asked to determine which of these allotropes possesses the maximum $C-C$ bond length. To solve this, we must dive into the microscopic world of chemical bonding, specifically looking at hybridization and bond order.

The Strength of $s{p}^3$ Hybridization

Let's start with diamond. Imagine a massive, rigid, three-dimensional network. In this structure, every single carbon atom undergoes $s{p}^3$ hybridization. This means it uses one $s$ orbital and three $p$ orbitals to form four identical hybrid orbitals, which point towards the corners of a regular tetrahedron.

Because each carbon atom is bonded to four others, all the bonds in diamond are pure single bonds. Single bonds have a bond order of 1, meaning the electron density pulling the two nuclei together is relatively low compared to double or triple bonds. Consequently, the atoms settle at a comfortable distance from each other. The experimental $C-C$ bond length in diamond is exactly $154\text{ pm}$.

The Elegance of Resonance

Now, let's shift our focus to graphite. Unlike the 3D network of diamond, graphite consists of flat, two-dimensional layers of carbon atoms arranged in a hexagonal honeycomb lattice. Here, each carbon atom is $s{p}^2$ hybridized, bonding to only three other carbon atoms.

What happens to the fourth valence electron? It resides in an unhybridized $p$ orbital perpendicular to the layer. These $p$ orbitals overlap sideways to form an extensive, delocalized $\pi$-electron cloud across the entire layer. This phenomenon, known as resonance, gives every $C-C$ bond in graphite a partial double bond character.

Because double bonds are stronger and pull the atoms closer together than single bonds, the partial double bond character in graphite shrinks the bond length. The $C-C$ bond length within the layers of graphite is $141.5\text{ pm}$.

The Molecular Soccer Ball

Finally, we look at Buckminsterfullerene, or $C_{60}$. This molecule is shaped like a truncated icosahedron, resembling a microscopic soccer ball made of 20 hexagons and 12 pentagons.

Like in graphite, the carbon atoms in $C_{60}$ are $s{p}^2$ hybridized. However, the bonds are not perfectly uniform. The structure contains distinct single and double bonds. The bonds that fuse two hexagons together have more double-bond character and are shorter, measuring $138.3\text{ pm}$. The bonds that fuse a pentagon and a hexagon have more single-bond character and are longer, measuring $143.5\text{ pm}$.

Let's compare the data we've gathered: - Diamond: $154\text{ pm}$ (Pure $s{p}^3$ single bonds) - Fullerene ($C_{60}$): $143.5\text{ pm}$ and $138.3\text{ pm}$ ($s{p}^2$ alternating bonds) - Graphite: $141.5\text{ pm}$ ($s{p}^2$ partial double bonds)

It is abundantly clear that the pure single bonds in diamond are the longest. The increased $s$-character in the $s{p}^2$ hybridized orbitals of graphite and fullerene, combined with their $\pi$-bonding, pulls the carbon atoms closer together. Therefore, the maximum $C-C$ bond length is found in diamond.