The relative stabilites of the following carbocations is :
`H_(2)"CO CH"=CHoverset(+)CH_(2)H_(2)C=underset("OMe")underset("| ")"C "-overset(+)CH_(2)CH_(3)OCH_(2)overset(+)CH_(2)CH_(3)Ooverset(+)CH_(2)`

Options

A. `IgtIIgtIIIgtIV`
B. `IgtIVgtIIgtIII`
C. `IIgtIIIgtIVgtI`
D. `IIIgtIgtIIgtIV`

Answer

To determine the relative stabilities of the given carbocations, we need to analyze each structure based on the effects of substituents on the carbocation. The stability of carbocations can be influenced by the presence of electron-donating groups, which can stabilize the positive charge through inductive or resonance effects.

### Step-by-Step Solution:

1. **Identify the Carbocations**:
- Let's label the carbocations as follows:
- **Carbocation 1**: H₂C=CH-CH₂⁺
- **Carbocation 2**: H₂C=CH-CH₂-OMe
- **Carbocation 3**: H₂C-CH₂-CH₂⁺ (with an electronegative atom nearby)
- **Carbocation 4**: H₂C-CH₂-CH₂-OMe⁺

2. **Analyze Carbocation 1**:
- This carbocation has a double bond adjacent to the positively charged carbon. The double bond can stabilize the positive charge through resonance. Therefore, Carbocation 1 is relatively stable.

3. **Analyze Carbocation 2**:
- This carbocation has an OMe group (methoxy group) attached. The methoxy group has a +M (mesomeric) effect, which can donate electron density towards the positively charged carbon. This resonance stabilization makes Carbocation 2 more stable than Carbocation 1.

4. **Analyze Carbocation 3**:
- This carbocation has an electronegative atom (oxygen) nearby. The electronegative oxygen will pull electron density away from the carbocation, making it less stable. Therefore, Carbocation 3 is less stable.

5. **Analyze Carbocation 4**:
- Similar to Carbocation 2, this carbocation has an OMe group. The lone pair of electrons on the oxygen can participate in resonance with the positive charge, providing stabilization. Thus, Carbocation 4 is more stable than Carbocation 3 but less stable than Carbocation 1.

6. **Rank the Stabilities**:
- Based on the above analysis, we can rank the carbocations from most stable to least stable:
- **Most Stable**: Carbocation 1 (due to resonance with the double bond)
- **Second Most Stable**: Carbocation 4 (due to resonance with the OMe group)
- **Third Most Stable**: Carbocation 2 (due to +M effect of OMe but less than Carbocation 4)
- **Least Stable**: Carbocation 3 (due to the electron-withdrawing effect of oxygen)

7. **Final Order**:
- The final order of stability is: **1 > 4 > 2 > 3**.