The reaction given is:
${ CH3CH2CH2Br + NaCN \rightarrow CH3CH2CH2CN + NaBr }$
This is an example of a nucleophilic substitution reaction, specifically SN2 (bimolecular nucleophilic substitution). In such reactions, the choice of solvent can significantly impact the reaction rate.
- Nature of the Solvent: SN2 reactions are favored by polar aprotic solvents. Aprotic solvents do not have any hydrogen atom connected directly to an electronegative atom and therefore cannot participate in hydrogen bonding. Examples include acetone, DMSO, and N, N'-dimethylformamide (DMF). Polar aprotic solvents increase nucleophile strength, enhancing the reaction rate.
- Comparison of Solvent Options:
- Ethanol and Methanol: These are protic solvents that participate in hydrogen bonding. They reduce the effectiveness of the nucleophile (CN-), thus slowing the reaction rate.
- Water: Another protic solvent similar to alcohols, further reducing the nucleophilicity of CN-.
- N, N'-Dimethylformamide (DMF): A polar aprotic solvent which does not hinder the nucleophile, thereby accelerating the reaction.
From the analysis above, the reaction will be the fastest in N, N'-dimethylformamide (DMF), the correct choice.
Conclusion: Given the role of different solvents in an SN2 reaction, the reaction proceeds fastest in DMF due to its aprotic nature, allowing the cyanide ion to attack the electrophile efficiently without being hindered by hydrogen bonding.