The Shapes of Carbon Compounds

Before we dive into reactions, we must understand the architecture of the molecules themselves. The shape of a carbon compound is not arbitrary; it is a direct consequence of how carbon uses its atomic orbitals to form bonds. This is the foundation upon which all of organic chemistry is built.

You already know that carbon is tetravalent — it forms four covalent bonds. But how it forms these bonds, and the geometry that results, is determined by hybridisation. This is the mixing of one s orbital and a certain number of p orbitals to create a set of equivalent hybrid orbitals. The number of hybrid orbitals formed always equals the number of atomic orbitals that mixed.

The three most important hybridisation states for carbon are sp³, sp², and sp. Each gives a distinct shape and set of bond properties.

Hybridisation and Molecular Shapes

The textbook uses three classic examples to illustrate this:

• Methane (CH₄): Carbon uses sp³ hybridisation. One s orbital and three p orbitals mix to give four equivalent sp³ hybrid orbitals. These orbitals point towards the corners of a regular tetrahedron, with a bond angle of $109.5^\circ$. This is the tetrahedral geometry.
• Ethene (C₂H₄): Each carbon uses sp² hybridisation. One s orbital mixes with two p orbitals, leaving one p orbital unhybridised. This gives three equivalent sp² hybrid orbitals that lie in a plane at $120^\circ$ angles. The unhybridised p orbitals on the two carbons overlap sideways to form a pi ($\pi$) bond. The overall shape around each carbon is trigonal planar.
• Ethyne (C₂H₂): Each carbon uses sp hybridisation. One s orbital mixes with one p orbital, leaving two p orbitals unhybridised. This gives two equivalent sp hybrid orbitals that lie on a straight line at $180^\circ$. The two sets of unhybridised p orbitals overlap sideways to form two pi ($\pi$) bonds. The shape around each carbon is linear.

The Influence of s-Character on Bond Properties

The key insight is that these hybrid orbitals are not identical in composition. The s-character — the percentage of the s orbital in the hybrid — changes across the series.

• An sp³ hybrid orbital has $\frac{1}{4}$ or 25% s-character.
• An sp² hybrid orbital has $\frac{1}{3}$ or 33.3% s-character.
• An sp hybrid orbital has $\frac{1}{2}$ or 50% s-character.

This difference in s-character has a profound effect on the properties of the bonds these orbitals form. The s orbital is closer to the nucleus than the p orbitals. Therefore, an orbital with more s-character is held more tightly by the nucleus.

This leads to two direct consequences for the bonds formed:

1. Bond Length and Bond Enthalpy (Strength)

Because an sp hybrid orbital is held closer to the nucleus, it can form a shorter, stronger bond. The sp³ hybrid orbital, with the least s-character, forms the longest, weakest bond.

The sp hybrid orbital forms the shortest and strongest bonds. The sp² hybrid orbital is intermediate in both s-character and bond properties. The sp³ hybrid orbital forms the longest and weakest bonds.

2. Electronegativity of Carbon

The electronegativity of a carbon atom is not a fixed value; it changes with its hybridisation state. Since an sp-hybridised carbon holds its electrons closer to the nucleus, it attracts bonding electrons more strongly. This makes it more electronegative than an sp²-hybridised carbon, which in turn is more electronegative than an sp³-hybridised carbon.