A schematic analysis of the reaction of the enantiomer with racemic mixture is shows below:
`{:(d,+,"d and l",rarr,(d)-(d)),("The(+)-form of",,"A racemic mixture of",,+),("chiral molecules",,"other molecules with",,(d)-(l)),(,,50%(d) and 50%(l),,):}`
The products (d-d) and (d-l) are clearly neither identical nor enantiomers (non-superimposable mirror images) as the diastereomers, stereoisomers that are not mirror images' . The formation of diasteromers allows the separation of enantiomers (called resolution) which is not easy as enantiomers have identical physical properties. One general with naturally occurring chiral molecule to form a pair of diastereomers. These can be separated easily as they have different physical properties. If the original chemical reaction can be reversed, the enantiomers can be isolated.
How many diastereomers are possible among all the possible stereoisomers of 2,3-dibromopentane ?

Options

A. (a) 2
B. (b) 1
C. (c) 3
D. (d) 4

Explanation

To determine the number of diastereomers possible among all the stereoisomers of 2,3-dibromopentane, we can follow these steps:

### Step 1: Identify the Stereocenters
2,3-dibromopentane has two stereocenters at the 2nd and 3rd carbon atoms. Each stereocenter can have two configurations: R (rectus) or S (sinister).

### Step 2: Calculate Total Stereoisomers
The total number of stereoisomers for a compound with 'n' stereocenters is given by the formula \(2^n\). Here, \(n = 2\) (since there are two stereocenters).
\[ \text{Total Stereoisomers} = 2^2 = 4 \]

### Step 3: List the Stereoisomers
The four stereoisomers of 2,3-dibromopentane can be represented as follows:
1. (2R, 3R)
2. (2R, 3S)
3. (2S, 3R)
4. (2S, 3S)

### Step 4: Identify Enantiomers
Enantiomers are pairs of stereoisomers that are non-superimposable mirror images of each other. From the list above:
- (2R, 3R) and (2S, 3S) are enantiomers.
- (2R, 3S) and (2S, 3R) are enantiomers.

### Step 5: Identify Diastereomers
Diastereomers are stereoisomers that are not mirror images. From the stereoisomers listed:
- (2R, 3R) and (2R, 3S) are diastereomers.
- (2R, 3R) and (2S, 3R) are diastereomers.
- (2R, 3S) and (2S, 3S) are diastereomers.
- (2S, 3R) and (2S, 3S) are diastereomers.

### Step 6: Count the Diastereomers
From the analysis, we can see that:
- (2R, 3R) is a diastereomer to (2R, 3S) and (2S, 3R), and (2S, 3S).
- (2R, 3S) is a diastereomer to (2R, 3R) and (2S, 3S).
- (2S, 3R) is a diastereomer to (2R, 3R) and (2S, 3S).
- (2S, 3S) is a diastereomer to (2R, 3R) and (2R, 3S).

Thus, the total number of diastereomers is 4.

### Final Answer
The number of diastereomers possible among all the possible stereoisomers of 2,3-dibromopentane is **4**.

---