Which of the following is the most stable cation?

Options

A. `CH_(3)CH_(2)overset(+)(C)HCH_(3)`
B. `CH_(3)-overset(+)underset(CH_(3))(C)CH_(3)`
C. `CH_(3)CH_(2)CH_(2)overset(+)(C)H_(2)`
D. `CH_(3)^(+)`

Explanation

To determine which of the following cations is the most stable, we need to analyze the stability of different types of carbocations based on hyperconjugation and the degree of substitution. Here’s how we can approach the solution step-by-step:

### Step 1: Identify the Types of Carbocations
We need to identify the types of carbocations given in the options. Carbocations can be classified as:
- Primary (1°) carbocation: A carbon atom bonded to one carbon atom and three hydrogen atoms.
- Secondary (2°) carbocation: A carbon atom bonded to two carbon atoms and one hydrogen atom.
- Tertiary (3°) carbocation: A carbon atom bonded to three carbon atoms.

### Step 2: Understand Hyperconjugation
Hyperconjugation is the interaction of the electrons in a σ-bond (usually C-H or C-C) with an adjacent empty p-orbital (the positively charged carbon in a carbocation). The more hyperconjugation a carbocation can undergo, the more stable it is.

### Step 3: Calculate Hyperconjugation for Each Carbocation
1. **For the first carbocation (2°)**:
- Structure: CH3-CH2-CH^+-CH3
- Hyperconjugation: 5 (2 from CH3 and 3 from CH2)

2. **For the second carbocation (3°)**:
- Structure: CH3-C^+(CH3)-CH3
- Hyperconjugation: 9 (3 from each of the three CH3 groups)

3. **For the third carbocation (1°)**:
- Structure: CH3-CH2-CH2^+
- Hyperconjugation: 2 (only 2 from CH2)

4. **For the fourth carbocation (0°)**:
- Structure: CH3^+
- Hyperconjugation: 0 (no adjacent carbons)

### Step 4: Compare the Stability
Now, we compare the number of hyperconjugation interactions:
- 2° carbocation: 5 hyperconjugation
- 3° carbocation: 9 hyperconjugation
- 1° carbocation: 2 hyperconjugation
- 0° carbocation: 0 hyperconjugation

The stability order based on hyperconjugation is:
- Tertiary (3°) > Secondary (2°) > Primary (1°) > Methyl (0°)

### Step 5: Conclusion
The most stable cation among the options provided is the tertiary carbocation (3°) because it has the highest number of hyperconjugation interactions.

### Final Answer
The most stable cation is the **B part**, which is the tertiary carbocation.

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