The central carbon atom of an allene is a member of two double bonds, and it has an interesting orbital arrangement that holds the two ends of the molecule at right angles to each other. (a) Draw an orbital diagram of allene, showing why the two ends are perpendicular. (b) Draw the two enantiomers of penta-2,3-diene. A model may be helpful.

Verified step by step guidance

1. Identify the hybridization of the central carbon atom in allene. The central carbon is sp hybridized, allowing it to form two pi bonds with the adjacent carbons.
2. Visualize the orbital arrangement: The central carbon uses two sp hybrid orbitals to form sigma bonds with the adjacent carbons, and two p orbitals to form pi bonds.
3. Understand the geometry: The two pi bonds are perpendicular to each other because they involve p orbitals that are orthogonal, leading to the perpendicular arrangement of the ends of the molecule.
4. For part (b), recognize that penta-2,3-diene has a similar structure to allene, with two double bonds and a central carbon. The presence of different substituents (e.g., H and D) on the terminal carbons can lead to chirality.
5. Draw the two enantiomers of penta-2,3-diene by arranging the substituents on the terminal carbons in such a way that they are non-superimposable mirror images of each other.

Key Concepts

Hybridization

Hybridization is the concept of mixing atomic orbitals to form new hybrid orbitals that can accommodate bonding. In the case of allene, the central carbon atom undergoes sp2 hybridization, allowing it to form two pi bonds with adjacent carbon atoms. This arrangement leads to a planar structure around the central carbon, while the terminal carbons are oriented at right angles due to the perpendicular nature of the p orbitals involved in the pi bonding.

Molecular Geometry

Molecular geometry refers to the three-dimensional arrangement of atoms in a molecule. In allene, the unique arrangement of the sp2 hybridized central carbon and the terminal carbons results in a linear geometry for the central part and a perpendicular orientation for the terminal groups. This geometry is crucial for understanding the molecule's reactivity and interactions with other compounds.

Stereoisomerism

Stereoisomerism is a form of isomerism where molecules have the same molecular formula but differ in the spatial arrangement of atoms. In the case of penta-2,3-diene, the presence of double bonds allows for the formation of enantiomers, which are non-superimposable mirror images. Understanding stereoisomerism is essential for predicting the behavior and properties of organic compounds, especially in reactions involving chiral centers.