Which of the following set of statements regarding the `S_N1` reaction shown by alkyl halide is correct here?
1. the `S_N1` reaction on the chiral starting material end up with racemization of the product
2. The more stable the carbocation intermediate the faster the `S_N1` reaction .
3. The added nucleophile plays no kinetic role in `S_N1` reaction
4. The `S_N1` reaction involves the inversion of configuration of the optically active substrate

Options

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

Answer

To solve the question regarding the `S_N1` reaction shown by alkyl halides, we will analyze each of the statements provided.

### Step-by-Step Solution:

1. **Understanding the `S_N1` Mechanism**:
- The `S_N1` (Substitution Nucleophilic Unimolecular) reaction involves two main steps:
- Formation of a carbocation intermediate after the leaving group departs.
- Nucleophilic attack on the carbocation.

2. **Analyzing Statement 1**:
- **Statement**: The `S_N1` reaction on the chiral starting material ends up with racemization of the product.
- **Explanation**: When a chiral alkyl halide undergoes an `S_N1` reaction, the planar carbocation can be attacked by the nucleophile from either side, leading to a mixture of both enantiomers (racemization).
- **Conclusion**: This statement is **correct**.

3. **Analyzing Statement 2**:
- **Statement**: The more stable the carbocation intermediate, the faster the `S_N1` reaction.
- **Explanation**: The rate of an `S_N1` reaction is directly related to the stability of the carbocation formed. Tertiary carbocations are more stable than secondary, which are more stable than primary. Thus, a more stable carbocation leads to a faster reaction.
- **Conclusion**: This statement is **correct**.

4. **Analyzing Statement 3**:
- **Statement**: The added nucleophile plays no kinetic role in `S_N1` reaction.
- **Explanation**: In an `S_N1` reaction, the rate-determining step is the formation of the carbocation, which depends solely on the concentration of the alkyl halide. The nucleophile's concentration does not affect the rate, as it attacks after the carbocation is formed.
- **Conclusion**: This statement is **correct**.

5. **Analyzing Statement 4**:
- **Statement**: The `S_N1` reaction involves the inversion of configuration of the optically active substrate.
- **Explanation**: Inversion of configuration is characteristic of `S_N2` reactions, not `S_N1`. In `S_N1`, due to the formation of a planar carbocation, the nucleophile can attack from either side, leading to racemization rather than strict inversion.
- **Conclusion**: This statement is **incorrect**.

### Final Answer:
The correct statements regarding the `S_N1` reaction are:
1. The `S_N1` reaction on the chiral starting material ends up with racemization of the product.
2. The more stable the carbocation intermediate, the faster the `S_N1` reaction.
3. The added nucleophile plays no kinetic role in `S_N1` reaction.

Thus, statements 1, 2, and 3 are correct, while statement 4 is incorrect.