Among the isomers of Dimethylcyclohexanes, the chiral ones are

Options

A. 1, 2-trans and 1,3-cis
B. 1, 2-cis and 1,3-trans
C. 1, 3-trans and 1, 4-trans
D. 1, 2-trans and 1, 3-trans

Answer

To determine the chiral isomers of dimethylcyclohexane, we need to analyze the different isomers of dimethylcyclohexane and identify which ones lack a plane of symmetry or a center of symmetry.

### Step-by-Step Solution:

1. **Identify the Isomers of Dimethylcyclohexane**:
Dimethylcyclohexane can have several isomers based on the position and orientation of the two methyl groups (CH₃). The possible isomers include:
- 1,2-cis
- 1,2-trans
- 1,3-cis
- 1,3-trans
- 1,4-cis
- 1,4-trans

2. **Draw the Structures**:
For each isomer, draw the cyclohexane ring and place the methyl groups according to the specified positions and orientations.

3. **Analyze Chirality**:
- **1,2-trans Dimethylcyclohexane**: This structure does not have a plane of symmetry, hence it is chiral.
- **1,3-cis Dimethylcyclohexane**: This structure has a plane of symmetry, making it achiral.
- **1,2-cis Dimethylcyclohexane**: This structure also has a plane of symmetry, making it achiral.
- **1,3-trans Dimethylcyclohexane**: This structure does not have a plane of symmetry, hence it is chiral.
- **1,4-cis Dimethylcyclohexane**: This structure has an inversion center, making it achiral.
- **1,4-trans Dimethylcyclohexane**: This structure has an inversion center, making it achiral.

4. **Conclusion**:
The chiral isomers of dimethylcyclohexane are:
- 1,2-trans
- 1,3-trans

### Final Answer:
The chiral isomers of dimethylcyclohexane are 1,2-trans and 1,3-trans.

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