How may optical isomers are possible for
`CH_(3)overset(H)overset("|")underset(OH)underset("| ")"C "overset(H)overset("|")underset(OH)underset("| ")"C "-CO_(2)H`

Answer

To determine the number of optical isomers for the compound \( CH_3C(OH)(C(OH)COOH) \), we need to identify the chiral centers in the molecule and then apply the formula for calculating optical isomers based on the number of chiral centers.

### Step-by-Step Solution:

1. **Identify the Structure**:
The given compound can be represented as:
\[ CH_3 - C(OH) - C(OH) - COOH \]
Here, we have two carbon atoms that are connected to hydroxyl (OH) groups and one carbon atom that is part of the carboxylic acid (COOH).

2. **Locate Chiral Centers**:
A chiral center is a carbon atom that is attached to four different groups. In this compound:
- The first carbon (attached to \( CH_3 \), \( OH \), \( H \), and the second carbon) is a chiral center.
- The second carbon (attached to \( OH \), \( COOH \), \( H \), and the first carbon) is also a chiral center.

Thus, we have **two chiral centers** in this compound.

3. **Calculate the Number of Optical Isomers**:
The formula to calculate the number of optical isomers (enantiomers) based on the number of chiral centers \( n \) is:
\[ \text{Number of optical isomers} = 2^n \]
Here, \( n = 2 \):
\[ \text{Number of optical isomers} = 2^2 = 4 \]

4. **Conclusion**:
Therefore, the total number of optical isomers possible for the compound is **4**.