Which of the following is most stable ?

Options

A. `Ph_(3)C^(+)`
B. `Ph_(2)CH^(+)`
C. `PhCH_(2)^(+)`
D. Troplium cation.

Explanation

To determine which of the given compounds is the most stable, we will analyze the stability of each carbocation based on the number of resonance structures and the extent of resonance stabilization.

### Step-by-Step Solution:

1. **Identify the Compounds**:
- The first compound has a carbocation with 3 phenyl rings attached.
- The second compound has a carbocation with 2 phenyl rings and 1 hydrogen.
- The third compound has a carbocation with 1 phenyl ring and 1 CH2 group.
- The fourth compound is a tropilium ion.

2. **Analyze the First Compound**:
- The first compound has a carbocation stabilized by resonance from 3 phenyl rings.
- Each phenyl ring can donate electron density through resonance, leading to significant stabilization of the positive charge.
- Therefore, the stability of the first compound is very high due to extensive resonance.

3. **Analyze the Second Compound**:
- The second compound has a carbocation with 2 phenyl rings and 1 hydrogen.
- While there is still resonance stabilization, it is less than that of the first compound because it has fewer phenyl groups contributing to the resonance.
- Thus, the stability of the second compound is lower than the first.

4. **Analyze the Third Compound**:
- The third compound has a carbocation with only 1 phenyl ring.
- This compound has some resonance stabilization, but it is significantly less than that of the first and second compounds.
- Therefore, its stability is the lowest among the first three compounds.

5. **Analyze the Fourth Compound (Tropilium Ion)**:
- The tropilium ion is a cyclic structure that has resonance stabilization within the ring.
- However, the resonance stabilization in the tropilium ion is not as extensive as that provided by 3 phenyl rings in the first compound.
- Therefore, while the tropilium ion is stable, it does not surpass the stability of the first compound.

6. **Conclusion**:
- Based on the analysis, the compound with the carbocation having 3 phenyl rings is the most stable due to the highest degree of resonance stabilization.

### Final Answer:
The compound with the carbocation having 3 phenyl rings is the most stable.