The carbocation `(CH_(3))_(3)C^(+)` is stabilized primarily by

Options

A. hyperconjugation
B. tautomerism
C. resonance
D. conjugation

Answer

To determine how the carbocation `(CH₃)₃C⁺` is stabilized, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Structure of the Carbocation**:
The given carbocation is `(CH₃)₃C⁺`, which can be represented as:
```
CH₃
|
CH₃ - C⁺ - CH₃
```
Here, the central carbon atom carries a positive charge and is bonded to three methyl groups (CH₃).

2. **Understand Carbocation Stability**:
The stability of carbocations is influenced by various factors, including hyperconjugation, resonance, and inductive effects. Among these, hyperconjugation plays a significant role in stabilizing carbocations.

3. **Count the Alpha Hydrogens**:
Alpha hydrogens are the hydrogens attached to the carbon atoms adjacent to the positively charged carbon. In this case, each of the three methyl groups contributes three alpha hydrogens:
- From each CH₃ group, we have 3 alpha hydrogens.
- Total alpha hydrogens = 3 (from first CH₃) + 3 (from second CH₃) + 3 (from third CH₃) = 9 alpha hydrogens.

4. **Explain Hyperconjugation**:
Hyperconjugation occurs when the sigma bonds (C-H) of the adjacent methyl groups can donate electron density to the empty p-orbital of the positively charged carbon. This delocalization of charge helps to stabilize the carbocation.

5. **Evaluate Other Stabilization Effects**:
- **Tautomerism**: This does not apply to this carbocation, as there are no keto-enol forms present.
- **Resonance**: There are no double bonds or conjugated systems in this structure to allow for resonance stabilization.
- **Conjugation**: Similar to resonance, there are no double bonds present that would allow for conjugation.

6. **Conclusion**:
Since hyperconjugation is the primary stabilizing factor for the carbocation `(CH₃)₃C⁺`, the correct answer is hyperconjugation.

### Final Answer:
The carbocation `(CH₃)₃C⁺` is stabilized primarily by **hyperconjugation**.