Which of the following statements are correct ?

Options

A. Polar protic solvents (e.g, `MeOH, EtOH`) form H-bonding to nucleophile and stabilise it, thus rate of `SN^2` reaction is decreased.
B. Polar aprotic solvents (e.g., `DMSO, DMF`) raise the energy of the nucleophile and thus the rate of `SN^2` is increased.

C. Reactivity of nucleophile in the presence of crown ether (solvent) is increased for `SN^1` and `SN^2` reactions.
D. Reactivity nucleophile in the presence of crown ether (solvent) is decreased for `SN^(1)` and `SN^(2)` reactions.

Answer

To determine which statements are correct regarding the effects of different solvents on nucleophiles and reaction rates in SN1 and SN2 mechanisms, we will analyze each statement step by step.

### Step-by-Step Solution:

1. **Statement 1 Analysis**:
- **Statement**: "The polar protic solvents example, here we have the methanol, ethanol form hydrogen bonding to nucleophile and stabilise it, thus the rate of SN2 reaction is decreased."
- **Explanation**: Polar protic solvents like methanol and ethanol can form hydrogen bonds with nucleophiles. This hydrogen bonding stabilizes the nucleophile, making it less reactive. As a result, the availability of the nucleophile to participate in the SN2 reaction is reduced, leading to a decrease in the rate of the reaction.
- **Conclusion**: This statement is **correct**.

2. **Statement 2 Analysis**:
- **Statement**: "The polar aprotic solvents, example DMSO, DMF raise the energy of the nucleophile, thus the rate of SN2 is increased."
- **Explanation**: Polar aprotic solvents like DMSO and DMF do not form hydrogen bonds with nucleophiles. Instead, they solvate cations effectively while leaving the nucleophile free and more reactive. This results in an increase in the nucleophile's energy and enhances its reactivity, thereby increasing the rate of SN2 reactions.
- **Conclusion**: This statement is **correct**.

3. **Statement 3 Analysis**:
- **Statement**: "Reactivity of nucleophile in the presence of the crown ether solvent is increased for SN1 and SN2."
- **Explanation**: Crown ethers are complexing agents that can stabilize cations and enhance the nucleophilicity of anions by providing a favorable environment for the nucleophile. This increased reactivity leads to a higher rate of both SN1 and SN2 reactions.
- **Conclusion**: This statement is **correct**.

4. **Statement 4 Analysis**:
- **Statement**: "In presence of crown ether it is decreased."
- **Explanation**: This statement contradicts the previous analysis. Crown ethers do not decrease the reactivity of nucleophiles; instead, they enhance it. Therefore, this statement is incorrect.
- **Conclusion**: This statement is **incorrect**.

### Final Conclusion:
- The correct statements are:
- Statement 1: Correct
- Statement 2: Correct
- Statement 3: Correct
- Statement 4: Incorrect

### Summary of Correct Options:
- The correct options are **1, 2, and 3**.