Which of the following is most stable carbocation.

Options

A. `CH_(3)-overset(+)(C)H_(2)`
B. `CH_(2)-overset(+)(C)H-CH_(3)`
C. `CH_(3)-underset(CH_(3))underset(|)overset(+)(C)-CH_(3)`
D. `(CH_(3)-CH_(2))_(3)overset(+)(C)`

Answer

To determine which of the given carbocations is the most stable, we can analyze the stability based on the number of alkyl groups attached to the positively charged carbon (carbocation) and the number of alpha hydrogens available for hyperconjugation.

### Step-by-Step Solution:

1. **Identify the Carbocations**:
- Let's denote the carbocations as A, B, C, and D based on the options provided in the question.

2. **Understand Carbocation Stability**:
- Carbocations are stabilized by electron-donating groups. Alkyl groups (like CH₃, C₂H₅, etc.) are electron-donating due to hyperconjugation. The more alkyl groups attached to the positively charged carbon, the more stable the carbocation.

3. **Count the Alkyl Groups**:
- For each carbocation, count the number of alkyl groups attached to the carbon with the positive charge.
- Carbocations with more alkyl groups are generally more stable.

4. **Determine Alpha Hydrogens**:
- The stability of a carbocation can also be assessed by counting the number of alpha hydrogens (hydrogens attached to the carbons adjacent to the carbocation).
- More alpha hydrogens mean more hyperconjugation, which stabilizes the carbocation.

5. **Calculate Alpha Hydrogens for Each Carbocation**:
- For each carbocation, identify the alpha carbons (the carbons adjacent to the carbocation) and count the hydrogens on these carbons.
- For example, if carbocation C has three alpha carbons each with three hydrogens, it has a total of 9 alpha hydrogens.
- If carbocation D has two alpha carbons with two hydrogens each, it has a total of 6 alpha hydrogens.

6. **Compare the Stability**:
- Compare the total number of alpha hydrogens and the number of alkyl groups for each carbocation.
- The carbocation with the highest number of alpha hydrogens and alkyl groups will be the most stable.

7. **Conclusion**:
- Based on the analysis, if carbocation C has 9 alpha hydrogens and carbocation D has 6 alpha hydrogens, then carbocation C is more stable due to the higher number of alpha hydrogens and alkyl groups.

### Final Answer:
- The most stable carbocation is **Option C**.