Which of the following carbocation is most stable?

Options

A. `(CH_3)_3C.overset(o+)CH_2`
B. `(CH_3)_3overset(o+)C`
C. `CH_3CH_2overset(o+)CH_2`
D. `CH_3overset(o+)CHCH_2CH_3`

Explanation

To determine which carbocation is the most stable among the given options, we will analyze the stability based on three main effects: resonance, hyperconjugation, and inductive effects. Here’s a step-by-step solution:

### Step 1: Understand Carbocation Stability
Carbocation stability is influenced by:
1. **Resonance Effect**: More resonance structures lead to greater stability.
2. **Hyperconjugation**: The more alkyl groups attached to the positively charged carbon, the greater the hyperconjugative effect, which stabilizes the carbocation.
3. **Inductive Effect**: Electron-donating groups increase stability.

### Step 2: Analyze Each Carbocation
We will evaluate each option based on the presence of hyperconjugative structures since resonance is not applicable here.

#### Option 1: CH3-CH2-C(+)-CH3
- No alpha hydrogens are present.
- **Hyperconjugative Structures**: 0

#### Option 2: (CH3)3C(+)
- Three alpha hydrogens are present from each of the three methyl groups.
- **Hyperconjugative Structures**: 3 (from each CH3) + 1 (original structure) = 10

#### Option 3: CH3-CH2-CH2-C(+)
- Two alpha hydrogens are present.
- **Hyperconjugative Structures**: 2 + 1 (original structure) = 3

#### Option 4: CH3-CH(+)-CH2-CH3
- Five alpha hydrogens are present (three from the first CH3 and two from the second CH2).
- **Hyperconjugative Structures**: 5 + 1 (original structure) = 6

### Step 3: Compare Stability
Now we can summarize the number of hyperconjugative structures for each option:
- Option 1: 0 structures (least stable)
- Option 2: 10 structures (most stable)
- Option 3: 3 structures
- Option 4: 6 structures

### Conclusion
The most stable carbocation is **Option 2: (CH3)3C(+)**, which has the highest number of hyperconjugative structures (10).