Total number of position isomers of dimethyl cyclohexane.

Options

A. `2`
B. `3`
C. `4`
D. `5`

Explanation

To determine the total number of position isomers of dimethylcyclohexane, we can follow these steps:

### Step 1: Understand the Structure
Dimethylcyclohexane consists of a cyclohexane ring with two methyl (−CH₃) groups attached to it. The position of these methyl groups on the cyclohexane ring will determine the different isomers.

### Step 2: Identify Possible Positions
The cyclohexane ring has six carbon atoms. We can label them as C1, C2, C3, C4, C5, and C6. When considering position isomers, we need to place the two methyl groups on different carbon atoms.

### Step 3: List the Possible Isomers
1. **1,1-Dimethylcyclohexane**: Both methyl groups are on the same carbon (C1).
2. **1,2-Dimethylcyclohexane**: One methyl group on C1 and the other on C2.
3. **1,3-Dimethylcyclohexane**: One methyl group on C1 and the other on C3.
4. **1,4-Dimethylcyclohexane**: One methyl group on C1 and the other on C4.
5. **1,5-Dimethylcyclohexane**: One methyl group on C1 and the other on C5.
6. **1,6-Dimethylcyclohexane**: One methyl group on C1 and the other on C6.
7. **2,2-Dimethylcyclohexane**: Both methyl groups are on C2.
8. **2,3-Dimethylcyclohexane**: One methyl group on C2 and the other on C3.
9. **2,4-Dimethylcyclohexane**: One methyl group on C2 and the other on C4.
10. **2,5-Dimethylcyclohexane**: One methyl group on C2 and the other on C5.
11. **2,6-Dimethylcyclohexane**: One methyl group on C2 and the other on C6.
12. **3,3-Dimethylcyclohexane**: Both methyl groups are on C3.
13. **3,4-Dimethylcyclohexane**: One methyl group on C3 and the other on C4.
14. **3,5-Dimethylcyclohexane**: One methyl group on C3 and the other on C5.
15. **3,6-Dimethylcyclohexane**: One methyl group on C3 and the other on C6.
16. **4,4-Dimethylcyclohexane**: Both methyl groups are on C4.
17. **4,5-Dimethylcyclohexane**: One methyl group on C4 and the other on C5.
18. **4,6-Dimethylcyclohexane**: One methyl group on C4 and the other on C6.
19. **5,5-Dimethylcyclohexane**: Both methyl groups are on C5.
20. **5,6-Dimethylcyclohexane**: One methyl group on C5 and the other on C6.
21. **6,6-Dimethylcyclohexane**: Both methyl groups are on C6.

### Step 4: Count the Unique Isomers
After listing all possible combinations, we can eliminate duplicates and symmetrical structures. The unique position isomers of dimethylcyclohexane are:
1. 1,1-Dimethylcyclohexane
2. 1,2-Dimethylcyclohexane
3. 1,3-Dimethylcyclohexane
4. 1,4-Dimethylcyclohexane
5. 1,5-Dimethylcyclohexane
6. 1,6-Dimethylcyclohexane
7. 2,2-Dimethylcyclohexane
8. 2,3-Dimethylcyclohexane
9. 2,4-Dimethylcyclohexane
10. 2,5-Dimethylcyclohexane
11. 2,6-Dimethylcyclohexane
12. 3,3-Dimethylcyclohexane
13. 3,4-Dimethylcyclohexane
14. 3,5-Dimethylcyclohexane
15. 3,6-Dimethylcyclohexane
16. 4,4-Dimethylcyclohexane
17. 4,5-Dimethylcyclohexane
18. 4,6-Dimethylcyclohexane
19. 5,5-Dimethylcyclohexane
20. 5,6-Dimethylcyclohexane
21. 6,6-Dimethylcyclohexane

### Final Count
After careful consideration, the total number of unique position isomers of dimethylcyclohexane is **10**.