The most stable carbonium ion among the following is

Options

A. `C_(6)H_(5)overset(+)CHC_(6)H_(5)`
B. `C_(6)H_(5)overset(+)CH_(2)`
C. `CH_(3)overset(+)CH_(2)`
D. `C_(6)H_(5)CH_(2)overset(+)CH_(2)`

Explanation

To determine the most stable carbonium ion (carbocation) from the given options, we will analyze the stability of each structure based on resonance and inductive effects.

### Step-by-Step Solution:

1. **Identify the Structures**:
- The first structure has two phenyl groups attached to a carbon atom with a positive charge (C6H5-CH^+-C6H5).
- The second structure has one phenyl group and a positive charge on a carbon atom adjacent to a CH2 group (C6H5-CH^+-CH2).
- The third structure has a positive charge on a carbon atom adjacent to two hydrogen atoms (CH3-CH^+-CH2).
- The fourth structure has a positive charge on a carbon atom adjacent to two CH2 groups (C6H5-CH2-CH^+-CH2).

2. **Analyze Resonance Effects**:
- In the first structure, the positive charge can be delocalized over the two phenyl groups through resonance. This delocalization stabilizes the positive charge significantly.
- In the second structure, the positive charge is only partially stabilized by the single phenyl group. There is some resonance, but it is less effective than in the first structure.
- The third structure has no resonance stabilization as the positive charge is not adjacent to any electron-donating groups. It is only stabilized by the inductive effect from the CH3 group.
- The fourth structure has no resonance stabilization either, as the positive charge is not in direct conjugation with any phenyl group.

3. **Evaluate Inductive Effects**:
- The third structure (CH3-CH^+-CH2) has a +I effect from the CH3 group, which provides some stabilization.
- The fourth structure (C6H5-CH2-CH^+-CH2) has no significant stabilization due to the lack of resonance.

4. **Rank the Stability**:
- The first structure is the most stable due to extensive resonance stabilization.
- The second structure is less stable than the first but more stable than the third and fourth due to some resonance.
- The third structure is more stable than the fourth due to the +I effect from the CH3 group.
- The fourth structure is the least stable due to the absence of resonance and inductive effects.

5. **Conclusion**:
- The most stable carbonium ion among the given options is the first structure (C6H5-CH^+-C6H5) due to the resonance stabilization provided by the two phenyl groups.

### Final Answer:
The most stable carbonium ion among the following is the first structure (C6H5-CH^+-C6H5).

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