Which of the following are correct ?

Options

A. `CH_(3)-O-CH_(2)^(o+)"is more stable than" CH_(3)-CH_(2)^(o+)`
B. `(CH_(3))_(2)CH^(o+)"is less stable than"CH_(3)-CH_(2)-CH_(2)^(o+)`
C. `C_(2)=CH-CH_(2)^(o+)"is more stable than"CH_(3)-CH_(2)-CH_(2)^(o+)`
D. `CH_(2)=CH^(o+)"is more stable than" CH_(3)-CH_(2)^(o+)`

Explanation

To solve the question regarding the stability of various carbocations, we will analyze each statement provided in the question step by step.

### Step 1: Analyze Statement A
**Statement A:** CH3OCH2^+ is more stable than CH3CH2^+.

- **Explanation:** The carbocation CH3OCH2^+ has a positively charged carbon adjacent to an oxygen atom. The lone pairs on the oxygen can stabilize the positive charge through resonance. We can draw the resonance structure where the lone pair of oxygen can donate its electrons to the positively charged carbon, leading to a more stable configuration. In contrast, CH3CH2^+ does not have any such resonance stabilization.

- **Conclusion:** This statement is **correct**.

### Step 2: Analyze Statement B
**Statement B:** CH3C(CH3)^+ is less stable than CH3CH2CH2^+.

- **Explanation:** The carbocation CH3C(CH3)^+ is a secondary carbocation (2°), while CH3CH2CH2^+ is a primary carbocation (1°). Secondary carbocations are generally more stable than primary carbocations due to hyperconjugation and the inductive effect from surrounding alkyl groups. In this case, CH3C(CH3)^+ has more alpha hydrogens (6) compared to CH3CH2CH2^+ (2), which contributes to its stability.

- **Conclusion:** This statement is **incorrect**.

### Step 3: Analyze Statement C
**Statement C:** The structure with a double bond is more stable than the one without.

- **Explanation:** The presence of a double bond in a carbocation can lead to resonance stabilization. For instance, if we have a double bond adjacent to a positively charged carbon, the double bond can delocalize the positive charge, spreading it over multiple atoms. This delocalization increases stability compared to a carbocation without such unsaturation.

- **Conclusion:** This statement is **correct**.

### Step 4: Analyze Statement D
**Statement D:** CH2=CH^+ is more stable than CH3CH2^+.

- **Explanation:** The carbocation CH2=CH^+ is sp2 hybridized, while CH3CH2^+ is sp3 hybridized. The sp2 hybridized carbocation has more s-character (33%) compared to the sp3 hybridized carbocation (25%). Higher s-character means greater electronegativity, which makes the positive charge less stable. Therefore, CH2=CH^+ is less stable than CH3CH2^+.

- **Conclusion:** This statement is **incorrect**.

### Final Summary
From the analysis:
- **Correct Statements:** A and C
- **Incorrect Statements:** B and D