Why is it incorrect to say that the dihedral angle shown is 120° or even 109°?

Verified step by step guidance

1. Step 1: Understand the concept of dihedral angle. A dihedral angle is the angle between two planes formed by four atoms or groups in a molecule. It is measured by looking at the spatial relationship between two substituents on adjacent carbons in a molecule.
2. Step 2: Analyze the image provided. The molecule shown is a staggered conformation of a substituted ethane derivative. The dihedral angle in question is between the bromine atom (Br) and the methyl group (CH₃) as viewed along the C-C bond axis.
3. Step 3: Recognize the geometry of the molecule. The molecule adopts a tetrahedral geometry around each carbon atom due to sp³ hybridization. The bond angles in a tetrahedral geometry are approximately 109.5°, not 120°.
4. Step 4: Clarify why 120° is incorrect. A dihedral angle of 120° would imply a planar geometry, which is characteristic of sp² hybridization (e.g., trigonal planar structures). However, the molecule in the image is clearly staggered and tetrahedral, not planar.
5. Step 5: Explain why 109° is also incorrect. While the bond angles in a tetrahedral geometry are close to 109.5°, the dihedral angle specifically refers to the spatial relationship between substituents on adjacent carbons. In the staggered conformation shown, the dihedral angle between Br and CH₃ is 180°, not 109°.

Key Concepts

Dihedral Angle

The dihedral angle is the angle between two intersecting planes, specifically the angle formed by two bonds in a molecule. In organic chemistry, it is crucial for understanding the spatial arrangement of atoms and the conformational stability of molecules. The dihedral angle can influence steric interactions and the overall energy of a molecule.

Hybridization

Hybridization is the concept of mixing atomic orbitals to form new hybrid orbitals that can accommodate bonding in molecules. For example, sp3 hybridization leads to tetrahedral geometry with bond angles of approximately 109.5°, while sp2 hybridization results in trigonal planar geometry with bond angles of about 120°. Understanding hybridization helps explain the geometry and angles in molecular structures.

Steric Strain

Steric strain occurs when atoms in a molecule are forced closer together than their preferred distance, leading to increased energy and instability. This strain can affect the dihedral angles between bonds, as certain conformations may be energetically unfavorable. Recognizing steric strain is essential for predicting the most stable conformations of a molecule.