Among the following, the compound that undergoes the fastest `S_N1` reaction is:

Options

A.
B.
C.
D. `CH_(3)CH_(2)-OTs`

Explanation

To determine which compound undergoes the fastest \( S_N1 \) reaction, we need to analyze the stability of the carbocations formed from the given compounds. The \( S_N1 \) reaction mechanism involves the formation of a carbocation intermediate, and the rate of the reaction is influenced by the stability of this carbocation.

Here's a step-by-step solution:

### Step 1: Identify the Compounds
We have four compounds with different structures. Each compound has a leaving group (OTs) that will depart to form a carbocation.

### Step 2: Determine the Carbocation Formed
For each compound, we need to draw the carbocation that will be formed after the leaving group departs.

1. **Compound A**: When the OTs group leaves, it forms a primary carbocation.
2. **Compound B**: The leaving of the OTs group results in a secondary carbocation.
3. **Compound C**: The OTs group leaves, forming a tertiary carbocation.
4. **Compound D**: The leaving of the OTs group leads to a resonance-stabilized carbocation.

### Step 3: Analyze Carbocation Stability
The stability of carbocations can be ranked as follows:
- Tertiary (3°) > Secondary (2°) > Primary (1°) > Methyl (0°)

Additionally, resonance stabilization can significantly enhance carbocation stability.

- **Compound A**: Primary carbocation (least stable).
- **Compound B**: Secondary carbocation (more stable than primary).
- **Compound C**: Tertiary carbocation (most stable).
- **Compound D**: Resonance-stabilized carbocation (can be very stable depending on the structure).

### Step 4: Compare the Stability
From the analysis:
- Compound C has the most stable carbocation (tertiary).
- Compound D may also be stable due to resonance, but the stability of a tertiary carbocation generally surpasses that of a resonance-stabilized carbocation unless the resonance is exceptionally strong.

### Conclusion
Based on the stability of the carbocations formed, **Compound C** undergoes the fastest \( S_N1 \) reaction because it forms the most stable tertiary carbocation.

### Final Answer
The compound that undergoes the fastest \( S_N1 \) reaction is **Compound C**.

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