How many optically active stereoisomers are possible for butane-2, 3-diol ?

Answer

To determine the number of optically active stereoisomers for butane-2,3-diol, we can follow these steps:

### Step 1: Understand the Structure of Butane-2,3-diol
Butane-2,3-diol has the following structure:

- The molecular formula is C4H10O2.
- It contains two hydroxyl (-OH) groups located on the second and third carbon atoms of the butane chain.

### Step 2: Draw the Structure
The structural formula can be represented as follows:

```
CH3-CHOH-CHOH-CH3
```

### Step 3: Identify Chiral Centers
Chiral centers are carbon atoms that have four different substituents. In butane-2,3-diol, the second and third carbon atoms are chiral centers because they each have:
- One hydroxyl group (-OH)
- One hydrogen atom (H)
- One methyl group (CH3)
- One carbon chain (the rest of the butane)

### Step 4: Count the Stereoisomers
The formula to calculate the number of stereoisomers is \(2^n\), where \(n\) is the number of chiral centers. In butane-2,3-diol, there are 2 chiral centers:

\[ n = 2 \quad \Rightarrow \quad \text{Number of stereoisomers} = 2^2 = 4 \]

### Step 5: Determine Optical Activity
Among the 4 stereoisomers, we need to check for optical activity. The stereoisomers can be categorized as:
- Two enantiomers (D and L forms) that are optically active.
- One meso form, which is superimposable on its mirror image and is optically inactive due to the presence of a plane of symmetry.

### Conclusion
Thus, the total number of optically active stereoisomers for butane-2,3-diol is 2 (the D and L forms), while the meso form is optically inactive.

### Final Answer
**The number of optically active stereoisomers for butane-2,3-diol is 2.**

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