Step 1: Understanding the Concept:
Alkenes undergo oxidative cleavage when treated with hot acidic \(KMnO_4\) or ozonolysis (\(O_3/Zn, H_2O\)). Oxidative cleavage of the \(C=C\) bond results in the formation of ketones or carboxylic acids (with \(KMnO_4/H^+\)) and ketones or aldehydes (with reductive ozonolysis).
Step 2: Key Formula or Approach:
1. Molecular formula \(C_4H_8\) indicates a degree of unsaturation (DU) of 1. It can be an alkene or a cycloalkane.
2. Since it reacts with \(KMnO_4/H^+\), it must be an alkene.
3. Compound 'B' (\(C_3H_6O\)) has DU = 1, suggesting it is a ketone (acetone) or an aldehyde (propanal).
Step 3: Detailed Explanation:
Let's analyze the options:
- But-2-ene (\(CH_3CH=CHCH_3\)): Oxidative cleavage would yield two molecules of ethanoic acid (\(C_2H_4O_2\)) or acetaldehyde (\(C_2H_4O\)). This does not match 'B'.
- 2-Methylpropene (\((CH_3)_2C=CH_2\)):
- Ozonolysis: Reductive ozonolysis cleaves the double bond to give Acetone (\(CH_3COCH_3\), \(C_3H_6O\)) and Formaldehyde (\(HCHO\)).
- Oxidative cleavage (\(KMnO_4/H^+\)): Cleavage gives Acetone (\(C_3H_6O\)) and Formic acid, which further oxidizes to \(CO_2\) and \(H_2O\).
This matches both experimental results described in the question.
Step 4: Final Answer:
Compound 'A' is 2-methylpropene because its cleavage consistently yields the \(C_3\) compound acetone (\(C_3H_6O\)).