Some pairs of ions are given below. In which pair, first ion is more stable than second ?

Options

A. `CH_(3)-overset(o+)(CH)-CH_(3) and CH_(3) - overset(o+)(CH) - OCH_(3)`
B. `CH_(3)-CH_(2)-overset(o+)(CH)-CH_(3) and CH_(3) = CH -CH_(2) - overset(o+)(CH)`
C.
D. `{:(CH_(3)-CH-CH_(3)),(" |"),(CH_(3)-underset(o+)(C)-CH_(3)):}`
`{:(CH_(3)-N-CH_(3)),(" |"),(CH_(3)-underset(o+)(C)-CH_(3)):}`

Answer

To determine which pair of ions has the first ion more stable than the second, we need to analyze the stability of carbocations based on hyperconjugation and resonance effects.

### Step-by-step Solution:

1. **Understanding Carbocation Stability**:
- Carbocation stability is influenced by hyperconjugation and resonance. Hyperconjugation involves the donation of electron density from adjacent C-H bonds to the positively charged carbon, while resonance involves the delocalization of charge through pi bonds or lone pairs.

2. **Analyzing the Given Options**:
- We will evaluate each option to determine the stability of the carbocations based on the number of alpha hydrogens and the presence of resonance.

3. **Option A**:
- First ion: Carbocation with 6 alpha hydrogens and a +M effect from OCH3.
- Second ion: A carbocation with fewer stabilizing factors.
- **Conclusion**: The second ion is more stable due to the +M effect from OCH3, which stabilizes the positive charge better than hyperconjugation alone.

4. **Option B**:
- First ion: Carbocation with 5 alpha hydrogens.
- Second ion: A carbocation with only 2 alpha hydrogens and no resonance.
- **Conclusion**: The first ion is more stable due to having more alpha hydrogens contributing to hyperconjugation.

5. **Option C**:
- First ion: Carbocation with 1 alpha hydrogen.
- Second ion: A carbocation with resonance stabilization.
- **Conclusion**: The second ion is more stable due to resonance, which is more effective than hyperconjugation.

6. **Option D**:
- First ion: Carbocation with 7 alpha hydrogens and a +M effect from nitrogen.
- Second ion: A carbocation with 6 alpha hydrogens and a +M effect.
- **Conclusion**: The first ion is more stable due to the higher number of alpha hydrogens and the resonance stabilization from nitrogen.

### Final Conclusion:
The pair in which the first ion is more stable than the second is **Option B**.

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