the incorrect statement with respect to `S_(N^(1) " and " S_(N^(2))` mechanisms for alkyl halide is :

Options

A. A strong nucleophile is an aprotic solvent increases the rate or favours `S_N2` reaction.
B. Competing reaction for `S_N2` reaction is rearrangement
C. `S_N1` reaction can be catalysed by some Lewis acid
D. A weak nucleophice and a protic solvent increases the rate of `S_N1` reaction

Answer

To determine the incorrect statement regarding the SN1 and SN2 mechanisms for alkyl halides, we will analyze the characteristics of each mechanism step by step.

### Step-by-Step Solution:

1. **Understanding SN1 Mechanism**:
- The SN1 reaction occurs in two steps. The first step involves the formation of a carbocation after the leaving group (e.g., Br) departs.
- The second step involves the nucleophile attacking the carbocation, leading to the formation of the product.
- This mechanism typically results in a racemic mixture due to the planar nature of the carbocation, allowing the nucleophile to attack from either side.

**Hint**: Remember that SN1 reactions are characterized by carbocation formation and can lead to racemic mixtures.

2. **Understanding SN2 Mechanism**:
- The SN2 reaction is a one-step process where the nucleophile attacks the carbon atom from the opposite side of the leaving group.
- This simultaneous bond formation and breaking leads to a transition state and results in inversion of configuration at the carbon center.

**Hint**: In SN2 reactions, the nucleophile attacks from the opposite side of the leaving group, causing inversion of configuration.

3. **Comparing Nucleophiles**:
- In SN1 reactions, a weak nucleophile can suffice, as the rate-determining step is the formation of the carbocation.
- In contrast, SN2 reactions require a strong nucleophile to effectively attack the substrate.

**Hint**: Recall that SN1 can use weak nucleophiles, while SN2 requires strong nucleophiles.

4. **Solvent Effects**:
- SN1 reactions are favored by polar protic solvents, which stabilize the carbocation and the leaving group.
- SN2 reactions are favored by polar aprotic solvents, which do not solvate the nucleophile as strongly, allowing it to remain reactive.

**Hint**: Identify the solvent types that favor each mechanism: polar protic for SN1 and polar aprotic for SN2.

5. **Identifying Incorrect Statement**:
- Now, we analyze the statements provided:
- A strong nucleophile in a polar aprotic solvent increases the rate of SN2 reaction. (Correct)
- Competing reaction for SN2 reaction is rearrangement. (Incorrect, as SN2 does not involve rearrangement)
- SN1 reaction can be catalyzed by some Lewis acid. (Correct)
- A weak nucleophile in a polar aprotic solvent increases the rate of SN1 reaction. (Correct)

**Conclusion**: The incorrect statement is that the competing reaction for SN2 is rearrangement, as SN2 does not involve rearrangement.

**Final Answer**: The incorrect statement is: "Competing reaction for SN2 reaction is rearrangement."