How many optically active isomers of 2,3-Dichlorobutandioic acid are possible ?

Explanation

To determine how many optically active isomers of 2,3-Dichlorobutanedioic acid are possible, we can follow these steps:

### Step 1: Draw the Structure
Start by drawing the structure of 2,3-Dichlorobutanedioic acid. The molecular formula indicates that we have a butane backbone with two carboxylic acid groups (–COOH) and two chlorine substituents on the second and third carbon atoms.

### Step 2: Identify Chiral Centers
Identify the chiral centers in the molecule. A chiral center is a carbon atom that is attached to four different groups. In 2,3-Dichlorobutanedioic acid, the second and third carbon atoms are chiral centers because they each have different substituents (–COOH, –Cl, –H, and the rest of the carbon chain).

### Step 3: Assign the Configuration
Using the Cahn-Ingold-Prelog (CIP) priority rules, assign the configurations (R or S) to each chiral center:
- For the second carbon (C2), assign priorities: Cl > COOH > H > the rest of the carbon chain. Depending on the arrangement, this could be either R or S.
- For the third carbon (C3), assign priorities similarly.

### Step 4: Determine Optical Activity
Next, determine the optical activity of the isomers:
- If a molecule has a plane of symmetry, it is optically inactive.
- If it does not have a plane of symmetry, it is optically active.

### Step 5: Count the Isomers
Count the total number of stereoisomers. For a compound with 'n' chiral centers, the maximum number of stereoisomers is given by the formula \(2^n\). In this case, with 2 chiral centers, the maximum number of stereoisomers is \(2^2 = 4\).

### Step 6: Identify the Optically Active Isomers
Out of the total isomers, identify which ones are optically active.
- You will find that some of the isomers will be enantiomers (mirror images) and will be optically active.
- Check for any meso compounds that may be present, which would be optically inactive due to internal symmetry.

### Conclusion
After analyzing the configurations and symmetry, you will find that there are 2 optically active isomers of 2,3-Dichlorobutanedioic acid.

### Final Answer
**There are 2 optically active isomers of 2,3-Dichlorobutanedioic acid.**

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