Total number of position isomers of trimethyl cyclohexane are:

Options

A. 5
B. 6
C. 7
D. 8

Explanation

To determine the total number of position isomers of trimethylcyclohexane, we will follow these steps:

### Step 1: Understand the Structure
Trimethylcyclohexane consists of a cyclohexane ring with three methyl (–CH₃) groups attached to it. The cyclohexane ring has six carbon atoms, and we need to place the three methyl groups in different positions.

**Hint:** Remember that position isomers differ in the placement of substituents on the same carbon skeleton.

### Step 2: Identify Possible Positions
The six carbon atoms in cyclohexane can be numbered from 1 to 6. We need to consider the various ways to attach three methyl groups to these positions while ensuring that we account for symmetry (i.e., some arrangements will be equivalent due to the cyclic nature of the molecule).

**Hint:** Use a systematic approach to number the positions and visualize the placements.

### Step 3: List the Combinations
We can start placing the methyl groups in different combinations:

1. **1,1,2-Trimethylcyclohexane**: Two methyl groups on carbon 1 and one on carbon 2.
2. **1,1,3-Trimethylcyclohexane**: Two methyl groups on carbon 1 and one on carbon 3.
3. **1,1,4-Trimethylcyclohexane**: Two methyl groups on carbon 1 and one on carbon 4.
4. **1,2,2-Trimethylcyclohexane**: Two methyl groups on carbon 2 and one on carbon 1.
5. **1,2,3-Trimethylcyclohexane**: One methyl group on carbons 1, 2, and 3.
6. **1,2,4-Trimethylcyclohexane**: One methyl group on carbons 1, 2, and 4.
7. **1,3,5-Trimethylcyclohexane**: One methyl group on carbons 1, 3, and 5.

**Hint:** Keep track of which combinations are unique and which are equivalent due to symmetry.

### Step 4: Eliminate Equivalent Structures
After listing the combinations, we need to eliminate any duplicates that arise from the symmetry of the cyclohexane ring. For example, 1,2,3 is equivalent to 3,2,1 due to the cyclic structure.

### Step 5: Count Unique Isomers
From the combinations listed, we find that the unique position isomers are:
1. 1,1,2
2. 1,1,3
3. 1,1,4
4. 1,2,2
5. 1,2,3
6. 1,2,4
7. 1,3,5

Thus, the total number of unique position isomers of trimethylcyclohexane is **6**.

### Final Answer
The total number of position isomers of trimethylcyclohexane is **6**.

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