The stable conformer `(s)` of trans`-1-4-` dimethyl] cyclohexane is/are:

Options

A. `1-` axial -`4-` equatorial form
B. `1-` axial `-4-` axial form
C. `1-` equatorial `-4-` axial from
D. `1-` equatorial`-4-` equatorial from

Answer

To determine the stable conformers of trans-1,4-dimethylcyclohexane, we will analyze the different possible arrangements of the methyl groups on the cyclohexane ring.

### Step-by-Step Solution:

1. **Understanding the Structure**:
- Trans-1,4-dimethylcyclohexane has two methyl groups located at the 1st and 4th carbon atoms of the cyclohexane ring. The term "trans" indicates that the methyl groups are on opposite sides of the ring.

2. **Drawing the Cyclohexane Ring**:
- Draw the cyclohexane ring in a chair conformation. Label the carbon atoms from 1 to 6.

3. **Positioning the Methyl Groups**:
- For the trans arrangement, we can place one methyl group at the 1st carbon and the other at the 4th carbon. There are two possible configurations:
- Methyl at C1 is axial and methyl at C4 is equatorial.
- Methyl at C1 is equatorial and methyl at C4 is axial.

4. **Analyzing the Conformers**:
- **Conformer 1**: Methyl at C1 (axial) and methyl at C4 (equatorial).
- In this arrangement, there is 1,3-diaxial interaction with axial hydrogens, leading to steric repulsion. This conformer is unstable.

- **Conformer 2**: Methyl at C1 (equatorial) and methyl at C4 (axial).
- Here, there is also steric hindrance due to the axial methyl group interacting with other axial hydrogens, making this conformer unstable as well.

- **Conformer 3**: Both methyl groups in equatorial positions.
- If both methyl groups are equatorial, there are no steric interactions or repulsions between them or with axial hydrogens. This arrangement is the most stable.

5. **Conclusion**:
- The most stable conformer of trans-1,4-dimethylcyclohexane is when both methyl groups are in equatorial positions.

### Final Answer:
The stable conformer of trans-1,4-dimethylcyclohexane is the one where both methyl groups are in equatorial positions.

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