Which of the following represents a gauche conformer of $C_2{H}_6$ (ethane) or $C_2{H}_5{F}_2$ (2-fluoroethanol)?

• A. A Newman projection of butane where the two methyl groups are separated by a dihedral angle of $60°$
• B. A Newman projection of ethane where all hydrogens are staggered
• C. A Newman projection of butane where the two methyl groups are eclipsed
• D. A Newman projection of butane where the two methyl groups are separated by a dihedral angle of $180°$

Answer: (A)

Verified step by step guidance

1. Understand the concept of conformers and dihedral angles: Conformers are different spatial arrangements of atoms that result from rotation about a single bond. The dihedral angle is the angle between substituents on adjacent carbons when viewed along the bond axis.
2. Recall that a gauche conformer specifically refers to a staggered conformation where two substituents (often bulky groups) are separated by a dihedral angle of approximately 60°.
3. Analyze the Newman projections given: Identify the dihedral angles between the key substituents (e.g., methyl groups in butane) in each projection. For example, a dihedral angle of 60° corresponds to a gauche conformation, 180° corresponds to anti, and 0° corresponds to eclipsed.
4. Apply this knowledge to the molecules mentioned: For ethane (C2H6), all hydrogens staggered means a dihedral angle of 60° between hydrogens, but since all substituents are identical and small, the term gauche is not typically used. For 2-fluoroethanol or butane, the gauche conformation is meaningful when bulky groups are 60° apart.
5. Conclude that the Newman projection of butane where the two methyl groups are separated by a dihedral angle of 60° represents the gauche conformer, as this matches the definition of gauche conformation.