The minimum torsional strain developed in butane is at dihedral angle (s)

Options

A. `0^(º), 108^(º)`
B. `120^(@), 240^(º)`
C. `60^(@), 180^(@), 300^(@)`
D. `60^(@), 120^(@), 180^(@)`

Answer

To determine the minimum torsional strain developed in butane, we need to analyze the molecular structure and the concept of dihedral angles. Here’s a step-by-step solution:

### Step 1: Understand Butane Structure
Butane (C₄H₁₀) consists of four carbon atoms connected in a straight chain. The structural formula can be represented as:
\[ \text{CH}_3 - \text{CH}_2 - \text{CH}_2 - \text{CH}_3 \]

### Step 2: Define Torsional Strain
Torsional strain arises from the repulsion between electrons in bonds that are eclipsed or close to each other. In butane, the torsional strain is influenced by the arrangement of hydrogen and methyl (CH₃) groups around the carbon-carbon bonds.

### Step 3: Dihedral Angles and Staggered vs. Eclipsed Conformations
- **Dihedral Angle**: The angle between the planes formed by two sets of atoms in a molecule. In butane, we can consider the dihedral angle between the hydrogen atoms or between a hydrogen and a methyl group on adjacent carbons.
- **Staggered Conformation**: When the groups on adjacent carbons are positioned as far apart as possible (e.g., 60° or 180°).
- **Eclipsed Conformation**: When the groups are aligned with each other (e.g., 0° or 120°).

### Step 4: Analyze Conformations
1. **Staggered Conformation**:
- At a dihedral angle of **60°**, the groups are staggered, resulting in lower torsional strain.
- At a dihedral angle of **180°**, the groups are in an anti-conformation, which also results in minimal repulsion and thus low torsional strain.
- At a dihedral angle of **300°**, the groups are again staggered, leading to low torsional strain.

2. **Eclipsed Conformation**:
- At **0°** and **120°**, the groups are eclipsed, leading to higher torsional strain due to increased electron repulsion.

### Step 5: Conclusion
The minimum torsional strain in butane occurs at staggered conformations, specifically at dihedral angles of **60°**, **180°**, and **300°**. Among these, the most stable conformation is at **180°**, where the methyl groups are opposite each other.

### Final Answer
The minimum torsional strain developed in butane is at dihedral angles of **60°**, **180°**, and **300°**.

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