Which statements is/are correct about the conformer of cis and trans 1,1,3,5-tertramethyl cyclohexane ?

Options

A. (a) cis isomer is more stable than trans isomer.
B. (b) trans isomer is more stable than cis isomer.
C. (c) There are two 1,3-Me/H diaxial interactions in cis isomer.
D. (d) There are two 1,3-Me/H and one 1,3-Me/Me diaxial interaction in trans isomer.

Answer

To determine the correct statements about the conformers of cis and trans 1,1,3,5-tetramethylcyclohexane, we will analyze the stability and interactions of the conformers step by step.

### Step 1: Understand the Structure of 1,1,3,5-Tetramethylcyclohexane
1. Draw the cyclohexane ring, which consists of six carbon atoms connected in a hexagonal shape.
2. Identify the positions of the four methyl groups: two at position 1 (1,1-dimethyl) and one each at positions 3 and 5.

### Step 2: Determine the Configurations
1. For the **cis isomer**, both methyl groups at position 1 will be on the same side of the cyclohexane ring.
- Possible configurations for the methyl groups at positions 3 and 5 can be either axial or equatorial.
2. For the **trans isomer**, the methyl groups at position 1 will be on opposite sides of the ring.
- The configurations can be either 3A-5E (3 axial, 5 equatorial) or 3E-5A (3 equatorial, 5 axial).

### Step 3: Analyze Stability
1. **Cis Isomer Stability**:
- In the cis configuration, if both methyl groups at positions 3 and 5 are in equatorial positions, the steric hindrance is minimized, making this configuration more stable.
- If both are axial, there would be steric hindrance due to 1,3-diaxial interactions, making it less stable.

2. **Trans Isomer Stability**:
- In the trans configuration, having one methyl group axial and the other equatorial (3A-5E or 3E-5A) reduces steric hindrance. However, if both are axial, it leads to increased steric repulsion, making it less stable.

### Step 4: Evaluate the Given Statements
1. **Option A**: "Cis isomer is more stable than trans isomer."
- This statement is **correct** because the cis isomer can have both methyl groups in equatorial positions, minimizing steric hindrance.

2. **Option B**: "Trans isomer is more stable than cis isomer."
- This statement is **incorrect** as explained above.

3. **Option C**: "There are 2, 1,3-MeH-diaxial interactions in cis isomer."
- This statement is **correct** because in the cis configuration with axial methyl groups, there are indeed 1,3-diaxial interactions between the methyl and hydrogen atoms.

4. **Option D**: "There are 2, 1,3-methyl-hydrogen and 1,1,3-methyl-methyl-diaxial interactions in trans isomer."
- This statement is **correct** because in the trans configuration, there will be interactions between the axial methyl groups and hydrogen atoms, as well as between the axial methyl groups themselves.

### Conclusion
The correct statements about the conformers of cis and trans 1,1,3,5-tetramethylcyclohexane are A, C, and D.