Stability order of following carbocation :
`"(i) "{:(" "CH_(2)-CH_(3)),(" "|),(CH_(3)-C^(+)),(" "|),(" "CH_(3)):} " (ii) " {:(" "CH_(3)),(" "|),(CH_(3)-C^(+)),(" "|),(" "H):} " (iii) " {:(" "CH_(3)),(" "|),(CH_(3)-C^(+)),(" "|),(" "CH_(3)):} " (iv) " Ph-CH^(+)- ulul(CH_(3))`

Options

A. a. i gt ii gt iii gt iv
B. b. iv gt iii gt i gt ii
C. c. iv gt iii gt ii gt i
D. d. iii gt iv gt ii gt i

Answer

To determine the stability order of the given carbocations, we will analyze each carbocation based on hyperconjugation and resonance effects.

### Step-by-Step Solution:

1. **Identify the Carbocations**:
- (i) CH3-CH2-C^(+)-CH3
- (ii) CH3-CH-C^(+)-H
- (iii) CH3-C^(+)-CH3
- (iv) Ph-CH^(+)-CH3

2. **Draw the Structures**:
- For (i): The structure is CH3-CH2-C^(+)-CH3 (2-butyl carbocation).
- For (ii): The structure is CH3-CH-C^(+)-H (isopropyl carbocation).
- For (iii): The structure is CH3-C^(+)-CH3 (tert-butyl carbocation).
- For (iv): The structure is Ph-CH^(+)-CH3 (benzyl carbocation).

3. **Analyze Each Carbocation**:
- **(i) CH3-CH2-C^(+)-CH3**:
- This carbocation has 6 alpha hydrogens (3 from each CH3 group) contributing to stability via hyperconjugation.
- **(ii) CH3-CH-C^(+)-H**:
- This carbocation has 6 alpha hydrogens (3 from CH3 and 3 from CH) contributing to stability via hyperconjugation.
- **(iii) CH3-C^(+)-CH3**:
- This carbocation has 9 alpha hydrogens (3 from each CH3 group) contributing to stability via hyperconjugation.
- **(iv) Ph-CH^(+)-CH3**:
- This carbocation is stabilized by resonance due to the phenyl group, which can delocalize the positive charge. It has 3 alpha hydrogens from CH3 and 1 from the CH adjacent to the carbocation, totaling 4 alpha hydrogens, but the resonance effect greatly enhances its stability.

4. **Stability Order**:
- The stability of carbocations generally follows the order: tertiary > secondary > primary > methyl.
- However, resonance plays a significant role in stabilizing the benzyl carbocation.
- Therefore, the stability order based on the analysis is:
- (iv) Ph-CH^(+)-CH3 > (iii) CH3-C^(+)-CH3 > (i) CH3-CH2-C^(+)-CH3 = (ii) CH3-CH-C^(+)-H

5. **Final Stability Order**:
- The final order of stability is:
- (iv) > (iii) > (i) = (ii)