A tertiary butyl carbocation is more stable than a secondary butyl carbocation because of which of the following ?

Options

A. `"-I effect of" -CH_3` groups
B. `"+R effect of" -CH_3` groups
C. `"-R effect of" -CH_3` groups
D. Hyperconjugation

Answer

To determine why a tertiary butyl carbocation is more stable than a secondary butyl carbocation, we can analyze the structures and the factors affecting their stability.

### Step-by-Step Solution:

1. **Identify the Structures**:
- The **tertiary butyl carbocation** (C4H9+) has the structure:
```
CH3
|
CH3-C^+
|
CH3
```
- The **secondary butyl carbocation** (C4H9+) has the structure:
```
CH3
|
CH3-CH^+-CH2
```

2. **Understand Carbocation Stability**:
- Carbocations are positively charged species that are stabilized by surrounding groups. The stability of carbocations increases with the number of alkyl groups attached to the positively charged carbon atom.

3. **Factors Affecting Stability**:
- **Hyperconjugation**: This is the primary factor contributing to the stability of carbocations. It involves the interaction of the σ-bonds (C-H or C-C) with the empty p-orbital of the carbocation. More alkyl groups lead to more hyperconjugation.
- **Inductive Effect**: Alkyl groups are electron-donating and can help stabilize the positive charge through the inductive effect, but this effect is less significant compared to hyperconjugation.

4. **Count the Number of Hyperconjugation Structures**:
- For the **tertiary butyl carbocation**:
- It has 9 possible hyperconjugation structures due to the three methyl (CH3) groups providing 3 alpha hydrogens each.
- For the **secondary butyl carbocation**:
- It has only 5 possible hyperconjugation structures due to the two methyl groups providing 3 alpha hydrogens and the ethyl group providing 2 alpha hydrogens.

5. **Conclusion**:
- Since the tertiary butyl carbocation has more hyperconjugation structures (9) compared to the secondary butyl carbocation (5), it is more stable. Thus, the stability of the tertiary butyl carbocation is primarily due to hyperconjugation.

### Final Answer:
The tertiary butyl carbocation is more stable than the secondary butyl carbocation because of **hyperconjugation**.

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