Which is the decreasing order of stability
(a). `CH_(3)-overset(+)(C)H-CH_(3)`
(b). `CH_(3)-overset(+)(C)H-O-CH_(3)`
(c). `CH_(3)_overset(+)(C)H-CO-CH_(3)`

Options

A. agtcgtb
B. agtbgtc
C. cgtbgta
D. bgtagtc

Answer

To determine the decreasing order of stability for the given carbocations, we need to analyze the effects of substituents on the stability of the carbocation in each case.

### Step-by-step Solution:

1. **Identify the Structures**:
- (a) `CH3-CH^+(C)-CH3` (Carbocation with two methyl groups)
- (b) `CH3-CH^+(C)-O-CH3` (Carbocation with a methoxy group)
- (c) `CH3-CH^+(C)-CO-CH3` (Carbocation with a carbonyl group)

2. **Analyze Stability Factors**:
- **Carbocation Stability**: The stability of carbocations is influenced by the ability of substituents to donate electron density to the positively charged carbon.
- **Inductive Effect**: Alkyl groups (like methyl) have a +I (inductive) effect, which helps to stabilize the positive charge.
- **Resonance Effect**: Groups like -O (methoxy) can stabilize the carbocation through resonance, which is a significant stabilizing factor.

3. **Evaluate Each Carbocation**:
- **For (a)**: The carbocation is stabilized by the +I effect from the two methyl groups. However, there is no resonance stabilization.
- **For (b)**: The positive charge is adjacent to an oxygen atom with a lone pair. This allows for resonance stabilization, where the lone pair can delocalize the positive charge, making this carbocation the most stable.
- **For (c)**: The carbonyl group (C=O) has a strong electronegative oxygen that pulls electron density away from the carbocation, increasing the positive charge density and thus destabilizing it. Therefore, this is the least stable carbocation.

4. **Rank the Stability**:
- Based on the analysis:
- (b) `CH3-CH^+(C)-O-CH3` is the most stable due to resonance stabilization.
- (a) `CH3-CH^+(C)-CH3` is next, stabilized by the +I effect from the methyl groups.
- (c) `CH3-CH^+(C)-CO-CH3` is the least stable due to the electron-withdrawing effect of the carbonyl group.

### Final Order of Stability:
(b) > (a) > (c)