The product `A` in the following reaction is :
`2KMnO_4 rarr A + MnO_2 + O_2`

Options

A. `K_2 Mn_2 O_7`
B. `K_2 MnO_4`
C. `K_2 O`
D. `K_2 O_2`

Explanation

To determine the product \( A \) in the reaction \( 2KMnO_4 \rightarrow A + MnO_2 + O_2 \), we can follow these steps:

### Step 1: Identify the Reactant
The reactant in this reaction is potassium permanganate, represented as \( KMnO_4 \).

### Step 2: Understand the Reaction Type
This reaction is a thermal decomposition reaction. In thermal decomposition, a single compound breaks down into two or more products when heated.

### Step 3: Write the Balanced Equation
The balanced equation for the thermal decomposition of potassium permanganate is:
\[ 2KMnO_4 \rightarrow K_2Mn_2O_7 + MnO_2 + O_2 \]

### Step 4: Identify the Products
From the balanced equation, we can see that the products formed are:
- Manganese dioxide (\( MnO_2 \))
- Oxygen gas (\( O_2 \))
- Potassium manganate (\( K_2MnO_4 \))

### Step 5: Determine the Product \( A \)
In the reaction, the product \( A \) corresponds to the compound formed alongside \( MnO_2 \) and \( O_2 \). From our balanced equation, we see that \( A \) is \( K_2MnO_4 \).

### Conclusion
Thus, the product \( A \) in the reaction \( 2KMnO_4 \rightarrow A + MnO_2 + O_2 \) is \( K_2MnO_4 \).

### Final Answer
The product \( A \) is \( K_2MnO_4 \).

---