Which of the following carbocation is most stable ?

Options

A. `(CH_3 )_3 C overset(+) CH_2`
B. `(CH_3)_3 overset(+) C`
C. `CH_3 CH_2 overset(+) C H_2`
D. `CH_(3) overset(+)CH CH_2 CH_3`

Explanation

To determine which carbocation is the most stable, we will analyze the given options based on the number of alpha hydrogens present. The stability of carbocations is generally increased with the number of alpha hydrogens, as they can help stabilize the positive charge through hyperconjugation.

### Step-by-step Solution:

1. **Identify the Carbocations:**
- **Option A:** \( \text{C}_3\text{H}_7^+ \) (with no alpha hydrogens)
- **Option B:** \( \text{C}_3\text{H}_9^+ \) (with three methyl groups attached)
- **Option C:** \( \text{C}_2\text{H}_5^+ \) (with two alpha hydrogens)
- **Option D:** \( \text{C}_4\text{H}_9^+ \) (with five alpha hydrogens)

2. **Count Alpha Hydrogens:**
- **Option A:** The carbocation has **0 alpha hydrogens**.
- **Option B:** The carbocation has **9 alpha hydrogens** (from three methyl groups).
- **Option C:** The carbocation has **2 alpha hydrogens** (from the two adjacent CH2 groups).
- **Option D:** The carbocation has **5 alpha hydrogens** (from the adjacent CH2 and CH3 groups).

3. **Stability Ranking:**
- The stability of carbocations increases with the number of alpha hydrogens:
- Option A: 0 alpha hydrogens → Least stable
- Option C: 2 alpha hydrogens → More stable than A
- Option D: 5 alpha hydrogens → More stable than C
- Option B: 9 alpha hydrogens → Most stable

4. **Conclusion:**
- **The most stable carbocation is Option B**, which has 9 alpha hydrogens.

### Summary of Stability:
- **Option A:** 0 alpha hydrogens (Least stable)
- **Option B:** 9 alpha hydrogens (Most stable)
- **Option C:** 2 alpha hydrogens
- **Option D:** 5 alpha hydrogens