An organic compound `(C_8H_10O_2)` rotates plane-polarized light. It produces pink colour with neutral `FeCl_3` solution. What is the total number of all the possible isomers for this compound?

Explanation

To determine the total number of possible isomers for the organic compound \( C_8H_{10}O_2 \) that rotates plane-polarized light and produces a pink color with neutral \( FeCl_3 \) solution, we can follow these steps:

### Step 1: Analyze the Molecular Formula
The given molecular formula is \( C_8H_{10}O_2 \). This indicates that the compound contains 8 carbon atoms, 10 hydrogen atoms, and 2 oxygen atoms.

### Step 2: Identify Functional Groups
The fact that the compound produces a pink color with neutral \( FeCl_3 \) suggests that it contains a phenolic group (a hydroxyl group attached to a benzene ring). Therefore, we can deduce that the compound likely has a phenolic structure.

### Step 3: Determine Chirality
Since the compound rotates plane-polarized light, it must be chiral. This means that there must be at least one chiral center in the molecule. A chiral center is typically a carbon atom bonded to four different substituents.

### Step 4: Construct Possible Structures
Given that we have a phenolic compound, we can start with a benzene ring (C6H5) and add substituents to it. The remaining part of the molecular formula \( C_8H_{10}O_2 \) suggests that we can add a hydroxyl group (-OH) and an alkyl group (like -CH3) to the benzene ring.

### Step 5: Identify Substituent Positions
The substituents can be placed in ortho, meta, or para positions relative to the hydroxyl group on the benzene ring. We can consider the following combinations:
1. **Ortho position**: -OH and -CH3
2. **Meta position**: -OH and -CH3
3. **Para position**: -OH and -CH3

### Step 6: Check for Chirality in Each Structure
For each of the above positions, we need to check if the resulting structure has a chiral center:
- **Ortho isomer**: This can be chiral if the substituents are different.
- **Meta isomer**: This can also be chiral if the substituents are different.
- **Para isomer**: This can be chiral if the substituents are different.

### Step 7: Count Isomers
Each chiral structure can exist in two enantiomeric forms (R and S configurations). Therefore, for each of the three positions (ortho, meta, para), we can have:
- 2 isomers for ortho
- 2 isomers for meta
- 2 isomers for para

### Step 8: Total Isomers Calculation
Adding these together gives us:
- Total isomers = 2 (ortho) + 2 (meta) + 2 (para) = 6

### Conclusion
Thus, the total number of all possible isomers for the compound \( C_8H_{10}O_2 \) is **6**.

---