In which of the following pairs A is more stable than B?

Options

A.
B.
C.
D. `{:(A,B),(Ph_(3)C^(.),(CH_3)_(3)C^(.)):}`

Answer

To determine which of the following pairs has A being more stable than B, we will analyze each option based on the stability of free radicals and the effects of hybridization, resonance, and steric factors.

### Step-by-Step Solution:

1. **Analyze Option A: Cyclohexane vs. Methyl-substituted Cyclohexane**
- **A**: Cyclohexane (C6H12)
- **B**: Methyl-substituted Cyclohexane (C6H11-CH3)
- In this case, we are comparing a secondary free radical (methyl-substituted) with a tertiary free radical (if we assume the methyl group is on a carbon that makes it tertiary).
- Tertiary radicals are more stable than secondary radicals due to hyperconjugation and inductive effects.
- **Conclusion**: B is more stable than A.

2. **Analyze Option B: Three-membered Ring vs. Six-membered Ring**
- **A**: Three-membered ring (less stable due to angle strain)
- **B**: Six-membered ring (more stable due to less strain)
- Six-membered rings are generally more stable than three-membered rings due to less angle strain and torsional strain.
- **Conclusion**: B is more stable than A.

3. **Analyze Option C: Cyclohexane Radical vs. SP2 Hybridized Radical**
- **A**: Cyclohexane radical (sp3 hybridized)
- **B**: SP2 hybridized radical
- SP2 hybridized radicals are less stable than sp3 hybridized radicals due to the increased s-character in sp2 (33% vs. 25% in sp3), leading to higher energy and less stability.
- **Conclusion**: B is more stable than A.

4. **Analyze Option D: Phenyl Radical vs. Tertiary Carbon Radical**
- **A**: Phenyl radical (C6H5-CH)
- **B**: Tertiary carbon radical (C(CH3)3)
- The phenyl radical is stabilized by resonance from the three benzene rings, which provides significant stabilization.
- The tertiary carbon radical is stabilized by hyperconjugation but lacks the resonance stabilization that the phenyl radical has.
- **Conclusion**: A is more stable than B due to resonance stabilization.

### Final Conclusion:
The only pair where A is more stable than B is in option D.