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

Answer

To determine the fastest reaction for the given nucleophilic substitution of `CH3CH2CH2Br` with `NaCN`, we need to analyze the reaction conditions and the nature of the solvents provided in the options.

### Step-by-step Solution:

1. **Identify the Type of Reaction**:
The reaction `CH3CH2CH2Br + NaCN → CH3CH2CH2CN + NaBr` is a nucleophilic substitution reaction. The alkyl halide `CH3CH2CH2Br` is a primary alkyl halide.

**Hint**: Recognize the type of reaction and the structure of the alkyl halide to determine the mechanism.

2. **Determine the Mechanism**:
Primary alkyl halides typically undergo nucleophilic substitution via the SN2 mechanism. This mechanism involves a single concerted step where the nucleophile attacks the carbon atom from the opposite side of the leaving group.

**Hint**: Recall that SN2 reactions are favored by primary alkyl halides due to less steric hindrance.

3. **Consider the Solvent Effects**:
The SN2 mechanism is favored by polar aprotic solvents. These solvents do not have hydrogen atoms directly bonded to electronegative atoms, which allows for better solvation of the nucleophile and enhances its reactivity.

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

4. **Analyze the Given Options**:
- **Ethanol**: A polar protic solvent (contains -OH group).
- **Methanol**: A polar protic solvent (contains -OH group).
- **N,N-Dimethylformamide (DMF)**: A polar aprotic solvent (does not have hydrogen directly bonded to electronegative atoms).
- **Water**: A polar protic solvent (contains -OH group).

**Hint**: Classify each solvent based on its ability to participate in hydrogen bonding.

5. **Select the Best Solvent**:
Since the SN2 mechanism is favored by polar aprotic solvents, the best choice among the options is N,N-Dimethylformamide (DMF), as it is a polar aprotic solvent that will enhance the rate of the reaction.

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