Step 1: Understanding the Concept:
Carbocation stability is determined by how well the positive charge is dispersed by neighboring groups through inductive (\( I \)), resonance (\( R \)), or hyperconjugation effects.
Step 2: Detailed Explanation:
Let's analyze the effects of the groups attached to the positive carbon:
(i) Isopropyl Carbocation: The \( \text{CH}_{3} \) groups provide \( +I \) effect and hyperconjugation. This stabilizes the carbocation well.
(ii) Methoxy-substituted Carbocation: The \( -\text{OCH}_{3} \) group has a strong -I effect (electron withdrawing due to electronegative Oxygen). While Oxygen has lone pairs (\( +R \)), in this specific ranking logic provided, the destabilizing \( -I \) effect is emphasized.
(iii) Acetyl-substituted Carbocation: The \( -\text{COCH}_{3} \) (acetyl) group is strongly electron-withdrawing due to both -I effect and -M effect (carbonyl group). This pulls electron density away from the positive charge, making it highly unstable.
Ranking them based on the presence of electron-withdrawing groups:
- (i) has no EWG (stable).
- (ii) has a moderately EWG (\( -\text{OCH}_{3} \)).
- (iii) has a strongly EWG (\( -\text{COCH}_{3} \)).
Thus, the decreasing stability is (i) \(>\) (ii) \(>\) (iii).
Step 3: Final Answer:
The decreasing order of stability is (i) \( \gg \) (ii) \( \gg \) (iii).