Step 1: Understanding the Concept:
This question involves the oxidative cleavage of an alkene using acidic potassium permanganate (KMnO\(_4\)). This strong oxidizing agent breaks the carbon-carbon double bond of the alkene, and the nature of the products (ketones, carboxylic acids, or CO\(_2\)) depends on the substitution pattern of the double bond.
Step 2: Key Formula or Approach:
- The reaction is oxidative cleavage. The C=C double bond is broken completely.
- Each carbon atom of the original double bond becomes the carbonyl carbon of a new molecule.
- If a carbon of the double bond is bonded to at least one hydrogen (\(=CHR\)), it is oxidized to a carboxylic acid (\(-COOH\)).
- If a carbon of the double bond is bonded to two alkyl groups (\(=CR_2\)), it is oxidized to a ketone (\(C=O\)).
- If a carbon of the double bond is bonded to two hydrogens (\(=CH_2\)), it is oxidized to carbon dioxide (CO\(_2\)) and water.
The problem states that the product is two moles of ethanoic acid (CH\(_3\)COOH). To find the original alkene, we can work backward from the products.
Step 3: Detailed Explanation:
The product is two molecules of ethanoic acid:
\[ \text{CH}_3\text{COOH} \quad + \quad \text{HOOCCH}_3 \]
To reconstruct the alkene, we remove the two oxygen atoms from the carboxyl groups and join the two carbonyl carbons with a double bond.
\[ \text{CH}_3-\text{C}(=\text{O})\text{OH} \quad + \quad \text{HO}(\text{O}=)\text{C}-\text{CH}_3 \]
Removing the oxygens and joining the carbons gives:
\[ \text{CH}_3-\text{CH}=\text{CH}-\text{CH}_3 \]
This molecule is but-2-ene (or 2-Butene).
Let's verify this by writing the forward reaction:
\[ \underset{\text{2-Butene}}{\text{CH}_3-\text{CH}=\text{CH}-\text{CH}_3} \xrightarrow{\text{acidic KMnO}_4, \Delta} \underset{\text{Ethanoic acid}}{2\text{CH}_3\text{COOH}} \]
Each of the double-bonded carbons (=CH-CH\(_3\)) has one hydrogen and one methyl group attached. Therefore, upon oxidative cleavage, each part becomes a carboxylic acid with two carbons, which is ethanoic acid. Since the alkene is symmetric, we get two identical molecules.
Step 4: Final Answer:
The alkene is 2-Butene.