A : `H_2O` liberate `O_2` an reaction with `KMnO_4` in acidic medium.
R : `KMnO_4` oxidises `H_2O_2" to " O_2`.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1)
B. If both Assertion & Reason are true but the reason is not the correct explanantion of the assertion, then mark (2)
C. If assertion is true statements but Reason is false, then mark (3)
D. If both Assertion and Reason are false statements, then mark (4)

Answer

To solve the question, we need to analyze the assertion (A) and the reason (R) provided:

**Assertion (A):** `H2O` liberates `O2` on reaction with `KMnO4` in acidic medium.
**Reason (R):** `KMnO4` oxidizes `H2O2` to `O2`.

### Step-by-Step Solution:

1. **Understanding the Reaction:**
- The assertion states that water (`H2O`) liberates oxygen gas (`O2`) when reacted with potassium permanganate (`KMnO4`) in an acidic medium.
- The reason states that potassium permanganate oxidizes hydrogen peroxide (`H2O2`) to oxygen gas.

2. **Analyzing the Assertion:**
- In acidic medium, potassium permanganate acts as a strong oxidizing agent.
- It is known that hydrogen peroxide can decompose to release oxygen gas, especially when oxidized by strong oxidizing agents like `KMnO4`.

3. **Analyzing the Reason:**
- The reaction between `KMnO4` and `H2O2` in acidic medium can be represented as:
\[ 2 KMnO_4 + 5 H_2O_2 + 6 H_2SO_4 \rightarrow 2 MnSO_4 + 5 O_2 + 8 H_2O + K_2SO_4 \]
- Here, `KMnO4` is reduced from Mn(VII) to Mn(II), indicating that it is indeed acting as an oxidizing agent, and `H2O2` is oxidized to `O2`.

4. **Conclusion:**
- Since `H2O` does not directly liberate `O2` in this reaction; rather, it is `H2O2` that is oxidized to produce `O2`, the assertion is not entirely accurate.
- However, the reason correctly explains the process occurring in the reaction.

5. **Final Evaluation:**
- Assertion (A) is **false** because `H2O` does not liberate `O2`; it is `H2O2` that does.
- Reason (R) is **true** as `KMnO4` does oxidize `H2O2` to `O2`.
- Therefore, the correct conclusion is that the assertion is false, but the reason is true.

### Summary:
- Assertion (A) is false.
- Reason (R) is true.
- Therefore, the assertion does not correctly explain the reason.