Total number of optically inactive stereoimers of succinic acid are

Answer

To determine the total number of optically inactive stereoisomers of succinic acid, we will follow these steps:

### Step 1: Understand the Structure of Succinic Acid
Succinic acid (butanedioic acid) has the molecular formula C4H6O4. It has two carboxylic acid groups (-COOH) at both ends of a four-carbon chain.

### Step 2: Identify Chiral Centers
For a compound to have optical isomers, it must have chiral centers. A chiral center is typically a carbon atom that is bonded to four different groups. In the case of succinic acid, we need to consider its derivatives that can have chiral centers.

### Step 3: Draw the Structure of 2,3-Dihydroxy Succinic Acid
When we consider 2,3-dihydroxy succinic acid, we can visualize it as having two hydroxyl (-OH) groups attached to the second and third carbon atoms of the chain. This gives us two chiral centers.

### Step 4: Calculate the Total Number of Stereoisomers
The total number of stereoisomers can be calculated using the formula \(2^n\), where \(n\) is the number of chiral centers. In this case, since there are 2 chiral centers:
\[ \text{Total Stereoisomers} = 2^2 = 4 \]

### Step 5: Identify Optically Inactive Isomers
Among these stereoisomers, we need to identify which ones are optically inactive. A compound is optically inactive if it has a plane of symmetry or is a meso compound.

In the case of 2,3-dihydroxy succinic acid, one of the stereoisomers will be a meso compound, which is optically inactive due to its internal plane of symmetry. The other stereoisomers will be optically active.

### Conclusion
Thus, the total number of optically inactive stereoisomers of succinic acid is **1** (the meso compound).

### Summary of Steps:
1. Understand the structure of succinic acid.
2. Identify chiral centers in the derivative (2,3-dihydroxy succinic acid).
3. Calculate total stereoisomers using \(2^n\).
4. Identify optically inactive isomers (meso compounds).
5. Conclude the total number of optically inactive stereoisomers.