How many of these carbocations are more stable than `(CH_(3))_(3)C^(+)`
`pH-overset(+)CH_(2),(Ph)_(2)overset(+)CH,(Ph)_(3)overset(+)C,(CH_(3))_(2)overset(+)CH,CH_(3)O-overset(+)CH_(2), Delta_(-)overset(+)CH_(2),square_(-)CH_2^(+) `

Answer

To determine how many of the given carbocations are more stable than `(CH₃)₃C⁺`, we need to analyze the stability of each carbocation based on the effects of substituents attached to them. The stability of carbocations can be influenced by hyperconjugation, inductive effects, and resonance effects.

### Step-by-Step Solution

1. **Identify the reference carbocation**: The reference carbocation is `(CH₃)₃C⁺` (tert-butyl carbocation). This carbocation is relatively stable due to hyperconjugation from the three methyl groups.

2. **Analyze the first carbocation: `pH-CH₂⁺`**:
- This carbocation has a phenyl group (pH) attached. The positive charge can be stabilized by resonance with the phenyl ring.
- **Conclusion**: More stable than `(CH₃)₃C⁺`.

3. **Analyze the second carbocation: `Ph₂CH⁺`**:
- This carbocation has two phenyl groups. The positive charge can be stabilized by resonance with both phenyl rings.
- **Conclusion**: More stable than `(CH₃)₃C⁺`.

4. **Analyze the third carbocation: `Ph₃C⁺`**:
- This carbocation has three phenyl groups. The positive charge is highly stabilized by resonance with all three phenyl rings.
- **Conclusion**: More stable than `(CH₃)₃C⁺`.

5. **Analyze the fourth carbocation: `(CH₃)₂CH⁺`**:
- This carbocation has two methyl groups and one hydrogen. It is less stable than `(CH₃)₃C⁺` because it has fewer electron-donating groups.
- **Conclusion**: Not more stable than `(CH₃)₃C⁺`.

6. **Analyze the fifth carbocation: `CH₃O-CH₂⁺`**:
- The `OCH₃` group has a -I (inductive) effect, which destabilizes the positive charge.
- **Conclusion**: Not more stable than `(CH₃)₃C⁺`.

7. **Analyze the sixth carbocation: `Δ⁻CH₂⁺`**:
- This carbocation has angle strain, which destabilizes it.
- **Conclusion**: Not more stable than `(CH₃)₃C⁺`.

8. **Analyze the seventh carbocation: `square⁻CH₂⁺`**:
- This carbocation exhibits "dancing resonance," which provides significant stabilization.
- **Conclusion**: More stable than `(CH₃)₃C⁺`.

### Summary of Stability
- More stable than `(CH₃)₃C⁺`:
1. `pH-CH₂⁺`
2. `Ph₂CH⁺`
3. `Ph₃C⁺`
4. `square⁻CH₂⁺`

- Not more stable than `(CH₃)₃C⁺`:
1. `(CH₃)₂CH⁺`
2. `CH₃O-CH₂⁺`
3. `Δ⁻CH₂⁺`

### Final Answer
**Total carbocations more stable than `(CH₃)₃C⁺`: 4**

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