Step 1: Understanding the Concept:
Potassium permanganate (\( KMnO_4 \)) is a very strong oxidizing agent.
When it reacts with concentrated sulfuric acid (\( H_2SO_4 \)), a dehydration reaction occurs.
The reaction produces Manganese heptoxide (\( Mn_2O_7 \)), which is a unique and dangerous oxide of manganese.
Step 2: Key Formula or Approach:
The chemical reaction proceeds in two steps:
1. Formation of permanganic acid:
\[ KMnO_4 + H_2SO_4 (\text{conc.}) \rightarrow HMnO_4 + KHSO_4 \]
2. Dehydration of the acid to form the anhydride:
\[ 2HMnO_4 \xrightarrow{H_2SO_4} Mn_2O_7 + H_2O \]
Concentrated sulfuric acid acts as the dehydrating agent that pulls water out of the permanganic acid molecules.
Step 3: Detailed Explanation:
The product, \( Mn_2O_7 \), has very specific properties that match the description in the question:
- Physical State: It is a dark green oily liquid.
- Stability: It is highly unstable and extremely explosive. It can detonate upon contact with organic matter, friction, or heat.
- Oxidation State: In this oxide, Manganese is in its maximum oxidation state of +7.
Let's look at the other options:
- (B) \( MnO_2 \) (Pyrolusite) is a stable black solid. It is not an oily liquid and is not explosive.
- (C) \( MnSO_4 \) is a common pink salt. It is stable and non-oily.
- (D) \( Mn_2O_3 \) is a stable brownish-black solid oxide.
Since only Manganese heptoxide fits the "green oily explosive" description, it is the correct compound.
Step 4: Final Answer:
Based on the specific reaction between concentrated sulfuric acid and permanganate crystals, the product is Manganese heptoxide (\( Mn_2O_7 \)).
Therefore, the correct option is (A).