Consider the reaction :
`CH_(3)CH_(2)CH_(2)Br+NaCNrarrCH_(3)CH_(2)CH_(2)CN+NaBr`
This reaction will be the fastest in :

Options

A. ethanol
B. methanol
C. `N,N'`-dimethylformamide (DMF)
D. water

Explanation

To determine the fastest solvent for the reaction:

\[ \text{CH}_3\text{CH}_2\text{CH}_2\text{Br} + \text{NaCN} \rightarrow \text{CH}_3\text{CH}_2\text{CH}_2\text{CN} + \text{NaBr} \]

we need to analyze the nature of the reaction and the characteristics of the solvents provided.

### Step-by-Step Solution:

1. **Identify the Type of Reaction**:
The given reaction is a nucleophilic substitution reaction where NaCN acts as a nucleophile and attacks the alkyl halide (bromopropane). This is an SN2 reaction, which is bimolecular and involves a single transition state.

**Hint**: Look for the characteristics of SN2 reactions, which involve a nucleophile attacking an electrophile.

2. **Understand the Role of Solvent**:
The solvent can significantly affect the rate of an SN2 reaction. SN2 reactions are generally favored in polar aprotic solvents, as they stabilize the nucleophile without forming strong hydrogen bonds that would hinder its reactivity.

**Hint**: Recall that polar protic solvents can hinder nucleophilic attacks due to hydrogen bonding.

3. **Evaluate the Given Solvents**:
- **Ethanol (C2H5OH)**: This is a polar protic solvent. It can form hydrogen bonds, which can stabilize the nucleophile (CN⁻) but also hinder its reactivity.
- **Methanol (CH3OH)**: Similar to ethanol, methanol is also a polar protic solvent and will have the same effect.
- **N,N-Dimethylformamide (DMF)**: This is a polar aprotic solvent. It does not form strong hydrogen bonds with the nucleophile, allowing it to remain reactive.
- **Water (H2O)**: Water is a polar protic solvent and will also hinder the nucleophile due to hydrogen bonding.

**Hint**: Identify which solvents are polar protic and which are polar aprotic.

4. **Conclusion**:
Among the options, N,N-Dimethylformamide (DMF) is the only polar aprotic solvent. Therefore, the reaction will be fastest in DMF because it allows the nucleophile to remain reactive without the interference of hydrogen bonding.

**Final Answer**: The reaction will be fastest in **N,N-Dimethylformamide (DMF)**.