The number of stereoisomers of butane -`2,3`-diol is

Options

A. four
B. two
C. six
D. three

Answer

To determine the number of stereoisomers of butane-2,3-diol, we will follow these steps:

### Step 1: Identify the Structure of Butane-2,3-diol
Butane-2,3-diol has four carbon atoms (butane) with hydroxyl (OH) groups attached to the second and third carbon atoms. The structure can be represented as follows:

```
CH3
|
CH3-CH-CH-CH2
| |
OH OH
```

### Step 2: Identify Chiral Carbons
A chiral carbon is defined as a carbon atom that is bonded to four different groups. We need to analyze each carbon in the structure:

- **C1 (CH3)**: This carbon is attached to three hydrogen atoms and one carbon (C2). It is not chiral.
- **C2 (CH)**: This carbon is attached to one hydroxyl group (OH), one hydrogen atom (H), one carbon (C1), and one carbon (C3). It has four different groups attached, so it is chiral.
- **C3 (CH)**: This carbon is attached to one hydroxyl group (OH), one hydrogen atom (H), one carbon (C2), and one carbon (C4). It also has four different groups attached, so it is chiral.
- **C4 (CH2)**: This carbon is attached to two hydrogen atoms and one carbon (C3). It is not chiral.

### Step 3: Count the Number of Chiral Carbons
From the analysis, we have identified that there are **2 chiral carbons** (C2 and C3).

### Step 4: Calculate the Number of Stereoisomers
The formula to calculate the number of stereoisomers is given by:
\[ \text{Number of stereoisomers} = 2^n \]
where \( n \) is the number of chiral carbons.

Substituting the value of \( n \):
\[ \text{Number of stereoisomers} = 2^2 = 4 \]

### Conclusion
Thus, the total number of stereoisomers of butane-2,3-diol is **4**.

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