Question

The allene molecule \(\left(\mathrm{H}_{2} \mathrm{C}=\mathrm{C}=\mathrm{CH}_{2}\right)\) is linear (the three \(\mathrm{C}\) atoms lie on a straight line). What are the hybridization states of the carbon atoms? Draw diagrams to show the formation of sigma bonds and pi bonds in allene.

Short answer

Central C: \(sp\); Terminal Cs: \(sp^2\); Carbon atoms are linear.

Step-by-step solution

Identify the Structure

The allene molecule is represented as \( ext{H}_2 ext{C}= ext{C}= ext{CH}_2\). It consists of three carbon atoms connected by double bonds, with hydrogen atoms at each end.

Determine Hybridization at Central Carbon

The central carbon in allene is connected to the two terminal carbons via double bonds. It uses \(sp\) hybridization. Each of its \(sp\) orbitals forms a sigma bond with the \(sp^2\) orbital of the two terminal carbon atoms. This leaves two \(p\) orbitals on the central carbon for pi bonds with the adjacent carbons.

Determine Hybridization at Terminal Carbons

Each terminal carbon is attached to two hydrogen atoms and the central carbon. They use \(sp^2\) hybridization. The three \(sp^2\) orbitals form sigma bonds: two with hydrogen atoms and one with the central carbon. There is one \(p\) orbital left to form a pi bond with a \(p\) orbital of the central carbon.

Formation of Sigma Bonds

The sigma bonds in the allene molecule are formed as follows: each \(sp^2\) hybrid orbital from the terminal carbons forms a sigma bond with the \(sp\) hybrid orbital from the central carbon, and also forms sigma bonds with hydrogen atoms using \(sp^2\) orbitals.

Formation of Pi Bonds

The unhybridized \(p\) orbitals on the central carbon form two pi bonds with the \(p\) orbitals on the terminal carbons. These pi bonds are perpendicular to each other, contributing to the linear shape along the carbon axis.

Key concepts

Hybridization

Understanding hybridization is essential to grasp the structure of molecules like allene. In chemistry, hybridization is the process by which atomic orbitals mix to form new hybrid orbitals. These hybrid orbitals are crucial as they shape the way atoms bond together.

In the allene molecule, we observe two types of hybridization:

• Central Carbon: This carbon is connected to two other carbon atoms with double bonds, assigning it an sp hybridization. This hybridization involves mixing one s orbital and one p orbital to form two equivalent sp hybrid orbitals, which lie 180 degrees apart, paramount for forming a linear setup.
• Terminal Carbons: These carbons exhibit sp² hybridization. Here, one s orbital and two p orbitals combine, which form three equivalent sp² orbitals, completing the bonding requirements with hydrogen atoms and the central carbon.

This hybridization configuration is at the heart of the molecular geometry of allene, setting the groundwork for sigma and pi bond formation.

Sigma bonds

Sigma bonds are the backbone of molecular structures, being the strongest type of covalent bond. They are formed by the direct, head-on overlap of atomic orbitals. In the allene molecule, sigma bonds are crucial for its stability and structure.

Each carbon in allene forms sigma bonds as follows:

• At the Central Carbon: It uses its two sp hybrid orbitals to form sigma bonds with the sp² orbitals of the terminal carbon atoms.
• At the Terminal Carbons: Besides forming sigma bonds with the central carbon, they use two other sp² orbitals to connect with hydrogen atoms. This overlap forms stable bonds, ensuring the molecule's overall linearity.

Sigma bonds represent the first overlap in any bond formation, providing the foundational skeleton on which pi bonds can build.

Pi bonds

Pi bonds complement sigma bonds by providing additional bonding in molecules with multiple bonding configurations, like allene. Unlike sigma bonds, pi bonds are formed by the side-to-side overlap of unhybridized p orbitals.

In allene, two pi bonds play a crucial role:

• Central Carbon's Role: The central carbon atom retains two p orbitals after hybridization. These p orbitals can form pi bonds with the p orbitals of the terminal carbons.
• Terminal Carbons' Contribution: Each terminal carbon, with a remaining p orbital, forms one pi bond with the central carbon. These pi bonds are vital for maintaining the molecule's linearity.

Pi bonds are pivotal in maintaining the rigidity of the molecule, especially in organic compounds containing multiple bonds like allene.

Linear geometry

Linear geometry in molecules refers to the arrangement where atoms align in a straight line. For the allene molecule, the linear structure is a defining feature and results from its particular hybridization and bond formation.

The main factors contributing to allene's linear geometry include:

• Hybridization Type: The central carbon's sp hybridization naturally aligns its sigma bonds at 180 degrees, creating a straight line.
• Pi Bond Formation: The pi bonds formed on the central carbon are perpendicular, which helps maintain the axes in a linear fashion along the molecule.

This linear geometry is supplemented by the symmetry we often see in allene, where the terminal hydrogens position themselves at the ends of this linear setup. Such molecular alignment is vital in discussions around the physical properties and reactivity of the allene molecule.