Which of the following statements regarding `1,2`-dimethyl cyclo-pentane and `1,3`-dimethyl cyclopentane is/are correct?

Options

A. In both, cis form is meso, while trans from is resolvable
B. In both, trans form is meso, while cis form is resolvable
C. In both cis and trans forms are meso.
D. In both, cis and trans forms are resolvable.

Answer

To analyze the statements regarding `1,2`-dimethylcyclopentane and `1,3`-dimethylcyclopentane, we will follow these steps:

### Step 1: Understand the Structures
1. **Draw the structures of both compounds**:
- **1,2-Dimethylcyclopentane**: This compound has two methyl groups attached to the first and second carbon of the cyclopentane ring.
- **1,3-Dimethylcyclopentane**: This compound has two methyl groups attached to the first and third carbon of the cyclopentane ring.

### Step 2: Identify the Isomer Types
2. **Determine the types of isomers**:
- **1,2-Dimethylcyclopentane** can exist in two forms:
- **Cis form**: Both methyl groups are on the same side of the ring.
- **Trans form**: Methyl groups are on opposite sides of the ring.
- **1,3-Dimethylcyclopentane** also has cis and trans forms.

### Step 3: Analyze Symmetry
3. **Check for symmetry**:
- **1,2-Dimethylcyclopentane**: The cis form has a plane of symmetry, making it a meso compound. The trans form does not have a plane of symmetry and is optically active.
- **1,3-Dimethylcyclopentane**: The cis form also has a plane of symmetry, making it a meso compound. The trans form is optically active as well.

### Step 4: Determine Optical Activity
4. **Assess optical activity**:
- **1,2-Dimethylcyclopentane**: The cis form is not optically active (meso), while the trans form is optically active.
- **1,3-Dimethylcyclopentane**: Both cis and trans forms are meso and optically active.

### Step 5: Evaluate Statements
5. **Evaluate the correctness of the statements**:
- **Statement 1**: Correct - The cis form of both compounds is meso.
- **Statement 2**: Incorrect - The trans form of 1,2-dimethylcyclopentane is not meso.
- **Statement 3**: Incorrect - The cis form of 1,3-dimethylcyclopentane is meso.
- **Statement 4**: Incorrect - The trans form of 1,3-dimethylcyclopentane is not meso.

### Conclusion
Based on the analysis, the only correct statement is that the cis form of both compounds is meso.

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