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 determine the stability of the given carbocations, we need to analyze the effects of substituents on the carbocation center. The stability of carbocations generally increases with the number of alkyl groups attached to the positively charged carbon, due to hyperconjugation and inductive effects. Additionally, the presence of electron-donating groups (like alkyl groups) increases stability, while electron-withdrawing groups (like electronegative atoms) decrease stability.

Let's analyze each carbocation:

1. **(i) `CH3-overset(+)CH-CH3`**: This is a secondary carbocation with two alkyl groups (methyl groups) attached to the positively charged carbon. Alkyl groups are electron-donating through hyperconjugation, which stabilizes the carbocation.

2. **(ii) `CH3-overset(+)CH-O-CH3`**: This carbocation has an oxygen atom attached to the positively charged carbon. The oxygen has lone pairs and can participate in resonance, which can stabilize the carbocation. However, oxygen is also electronegative, which can exert a -I (inductive) effect, pulling electron density away from the carbocation. The resonance effect (due to the lone pairs on oxygen) can provide some stabilization, but the -I effect can reduce it.

3. **(iii) `CH3-overset(+)(CH)-CO-CH3`**: This carbocation has a carbonyl group (C=O) adjacent to the positively charged carbon. The carbonyl group is electron-withdrawing due to its electronegativity and resonance effects, which destabilizes the carbocation.

Now, we can rank the stability based on our analysis:

- **(i)** is the most stable because it has two electron-donating alkyl groups.
- **(ii)** is next because it has resonance stabilization from the oxygen, despite the -I effect.
- **(iii)** is the least stable due to the electron-withdrawing effect of the carbonyl group.

Thus, the decreasing order of stability is:
**(i) > (ii) > (iii)**