Which one of the following alkyl bromides undergoes most rapid solvolysis in methanol solution to give corresponding methyl ether?

Options

A.
B.
C.
D.

Answer

To determine which alkyl bromide undergoes the most rapid solvolysis in methanol solution to give the corresponding methyl ether, we need to analyze the structure of the alkyl bromides and their reactivity in nucleophilic substitution reactions.

### Step-by-Step Solution:

1. **Understanding Solvolysis**:
- Solvolysis is a type of nucleophilic substitution reaction where the solvent (in this case, methanol) acts as the nucleophile. The reaction will lead to the formation of a methyl ether.

2. **Identify the Alkyl Bromides**:
- Assume we have the following alkyl bromides to consider:
- A: 1-bromopropane (primary)
- B: 2-bromopropane (secondary)
- C: 2-bromo-2-methylpropane (tertiary)
- D: 1-bromo-2-methylpropane (secondary)

3. **Mechanism of Reaction**:
- The solvolysis reaction can proceed via two mechanisms: SN1 and SN2.
- SN1 mechanism is favored for tertiary carbocations due to their stability, while SN2 is favored for primary carbocations due to less steric hindrance.

4. **Carbocation Stability**:
- Tertiary carbocations are more stable than secondary, which are more stable than primary.
- In this case, 2-bromo-2-methylpropane (C) will form a tertiary carbocation upon losing the bromide ion, making it more favorable for solvolysis.

5. **Comparing Reactivity**:
- 1-bromopropane (A) will undergo SN2, which is slower due to the backside attack being hindered.
- 2-bromopropane (B) and 1-bromo-2-methylpropane (D) will also undergo SN2, but they are secondary and have more steric hindrance compared to the tertiary.
- 2-bromo-2-methylpropane (C) will undergo SN1, allowing it to react faster due to the stability of the tertiary carbocation.

6. **Conclusion**:
- Among the given alkyl bromides, 2-bromo-2-methylpropane (C) will undergo the most rapid solvolysis in methanol to give the corresponding methyl ether due to the formation of a stable tertiary carbocation.

### Final Answer:
The alkyl bromide that undergoes the most rapid solvolysis in methanol solution to give the corresponding methyl ether is **2-bromo-2-methylpropane (C)**.

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