How many positional isomers are possible for dimethylcyclohexane?

Options

A. 3
B. 4
C. 5
D. 6

Explanation

To determine the number of positional isomers for dimethylcyclohexane, we need to follow these steps:

### Step 1: Understand the Structure of Cyclohexane
Cyclohexane is a six-membered carbon ring (C6H12). When we add two methyl (–CH3) groups to this structure, we need to consider their positions on the cyclohexane ring.

### Step 2: Identify Possible Positions for Methyl Groups
In dimethylcyclohexane, the two methyl groups can be attached to different carbon atoms in the cyclohexane ring. The positions can be classified as follows:
- 1,1-Dimethyl (both methyl groups on the same carbon)
- 1,2-Dimethyl (methyl groups on adjacent carbons)
- 1,3-Dimethyl (methyl groups separated by one carbon)
- 1,4-Dimethyl (methyl groups separated by two carbons)
- 1,5-Dimethyl (methyl groups on opposite sides of the ring)

### Step 3: Count the Unique Positional Isomers
1. **1,1-Dimethylcyclohexane**: Both methyl groups on the same carbon.
2. **1,2-Dimethylcyclohexane**: Methyl groups on adjacent carbons.
3. **1,3-Dimethylcyclohexane**: Methyl groups separated by one carbon.
4. **1,4-Dimethylcyclohexane**: Methyl groups separated by two carbons.
5. **1,5-Dimethylcyclohexane**: Methyl groups on opposite sides of the ring.

However, due to the symmetry of the cyclohexane ring, some of these arrangements will be identical.

### Step 4: Identify Distinct Isomers
After analyzing the positions:
- **1,2-Dimethylcyclohexane** has two distinct orientations (cis and trans).
- **1,3-Dimethylcyclohexane** also has two distinct orientations (cis and trans).
- **1,4-Dimethylcyclohexane** has one orientation.

Thus, the distinct positional isomers are:
1. 1,1-Dimethylcyclohexane
2. 1,2-Dimethylcyclohexane (cis and trans)
3. 1,3-Dimethylcyclohexane (cis and trans)
4. 1,4-Dimethylcyclohexane

### Conclusion
In total, there are **5 distinct positional isomers** for dimethylcyclohexane.

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