Arrange following carbocation in the decreasing order of stability
(i) `CH_3-overset(+)CH-CH_3`
(ii) `CH_3-overset(+)CH-O-CH_3`
(iii) `CH_3-overset(+)(CH)-CO-CH_3`

Options

A. `(iii) gt(ii) gt(i)`
B. `(i) gt(ii) gt(iii)`
C. `(i) gt(ii) gt(iii)`
D. `(i) lt(ii) lt(iii)`

Answer

To arrange the given carbocations in decreasing order of stability, we need to analyze the structure and the effects of the substituents on the stability of each carbocation.

### Step 1: Identify the carbocations
The given carbocations are:
1. (i) `CH3-CH^+-CH3` (Carbocation 1)
2. (ii) `CH3-CH^+-O-CH3` (Carbocation 2)
3. (iii) `CH3-CH^+-C(=O)-CH3` (Carbocation 3)

### Step 2: Analyze Carbocation 1
For Carbocation 1 (`CH3-CH^+-CH3`):
- This carbocation is a secondary carbocation.
- It is stabilized by the +I (inductive) effect of the two methyl (CH3) groups.
- The positive charge on the carbon is somewhat stabilized by the electron-donating effect of the adjacent carbon atoms.

### Step 3: Analyze Carbocation 2
For Carbocation 2 (`CH3-CH^+-O-CH3`):
- This carbocation is also a secondary carbocation.
- The oxygen atom has a lone pair that can participate in resonance (mesomeric effect) with the carbocation.
- This resonance stabilization makes this carbocation more stable than Carbocation 1.

### Step 4: Analyze Carbocation 3
For Carbocation 3 (`CH3-CH^+-C(=O)-CH3`):
- This carbocation is also a secondary carbocation.
- However, the carbonyl group (C=O) is an electron-withdrawing group due to its -I (inductive) effect and -M (mesomeric) effect.
- This means that it destabilizes the carbocation by pulling electron density away from the positively charged carbon, making it the least stable of the three.

### Step 5: Arrange in Decreasing Order of Stability
Based on the analysis:
- Carbocation 2 (`CH3-CH^+-O-CH3`) is the most stable due to resonance stabilization.
- Carbocation 1 (`CH3-CH^+-CH3`) is next, stabilized by the +I effect of the methyl groups.
- Carbocation 3 (`CH3-CH^+-C(=O)-CH3`) is the least stable due to the electron-withdrawing effect of the carbonyl group.

### Final Order
The decreasing order of stability is:
**(ii) > (i) > (iii)**