The dihedral angle between the two methyl groups in gauche conformation of n-butane is

Options

A. `120^(@)`
B. `180^(@)`
C. `45^(@)`
D. `60^(@)`

Answer

To determine the dihedral angle between the two methyl groups in the gauche conformation of n-butane, follow these steps:

### Step 1: Understand the Structure of n-Butane
n-Butane has the molecular formula C4H10 and consists of a straight chain of four carbon atoms. The structure can be represented as:
\[ \text{CH}_3 - \text{CH}_2 - \text{CH}_2 - \text{CH}_3 \]

### Step 2: Identify the Conformations
n-Butane can adopt different conformations due to rotation around the carbon-carbon single bonds. The two main conformations are:
- Staggered conformation
- Eclipsed conformation

In the staggered conformation, the groups attached to the carbon atoms are positioned as far apart as possible, while in the eclipsed conformation, they are aligned with each other.

### Step 3: Define the Gauche Conformation
The gauche conformation is a specific type of staggered conformation where two bulky groups (in this case, the two methyl groups, CH3) are adjacent to each other.

### Step 4: Determine the Dihedral Angle
In the gauche conformation of n-butane, the dihedral angle between the two methyl groups is measured. The dihedral angle is defined as the angle between the planes formed by the two sets of atoms.

For the gauche conformation:
- The dihedral angle between the two methyl groups (CH3) is 60 degrees.

### Step 5: Conclusion
Thus, the dihedral angle between the two methyl groups in the gauche conformation of n-butane is **60 degrees**.

---