The numer of optically active stereoisomers of tartaric acid, (HOOC.CHOH.CHOH.COOH) is

Options

A. 4
B. 2
C. 1
D. 3

Answer

To determine the number of optically active stereoisomers of tartaric acid (HOOC.CHOH.CHOH.COOH), we will follow these steps:

### Step 1: Identify the Structure of Tartaric Acid
Tartaric acid has the following structure:
```
HOOC
|
CHOH
|
CHOH
|
COOH
```
This structure contains two hydroxyl (OH) groups and two carboxylic acid (COOH) groups.

### Step 2: Identify Chiral Carbon Atoms
A chiral carbon atom is defined as a carbon atom that is bonded to four different groups. In the structure of tartaric acid, we need to identify the carbon atoms:

1. The first carbon (C1) is attached to:
- COOH
- OH
- H
- CHOH (the second carbon)

Since all four groups are different, C1 is a chiral carbon.

2. The second carbon (C2) is attached to:
- COOH
- OH
- H
- C1 (the first carbon)

Again, all four groups are different, so C2 is also a chiral carbon.

3. The third carbon (C3) is part of the COOH group and is attached to:
- OH
- H
- C2 (the second carbon)
- Another COOH group

However, C3 is not chiral because it is part of the COOH group and does not have four different groups.

### Step 3: Count the Chiral Centers
From the analysis, we find that there are **two chiral carbon atoms** (C1 and C2).

### Step 4: Calculate the Number of Optically Active Stereoisomers
The number of optically active stereoisomers can be calculated using the formula:
\[ \text{Number of stereoisomers} = 2^n \]
where \( n \) is the number of chiral centers.

In this case, \( n = 2 \):
\[ \text{Number of stereoisomers} = 2^2 = 4 \]

### Step 5: Determine the Number of Optically Active Isomers
Since tartaric acid has two chiral centers, it can exist in multiple stereoisomeric forms. However, not all stereoisomers are optically active. Tartaric acid has a meso form, which is achiral. Therefore, the number of optically active stereoisomers is:
\[ \text{Optically active stereoisomers} = 4 - 1 = 3 \]

### Conclusion
The number of optically active stereoisomers of tartaric acid is **3**.

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