Thermal decomposition of a Mn compound (X) at `513 K` results in compound `Y, MnO_(2)` and a gaseous product. `MnO_(2)` reacts with `NaCl` and concentrated `H_(2)SO_(4)` to give a pungent gas `Z,X,Y` and `Z` respectively are :

Options

A. `K_(3)MnO_(4),K_(2)MnO_(4)` and `Cl_(2)`
B. `K_(2)MnO_(4),KMnO_(4)` and `SO_(2)`
C. `KMnO_(4),K_(2)MnO_(4)` and `Cl_(2)`
D. `K_(2)MnO_(4),KMnO_(4)` and `Cl_(2)`

Answer

To solve the problem, we need to identify the manganese compound (X), the product (Y) formed during thermal decomposition, and the pungent gas (Z) produced in the subsequent reaction.

### Step-by-Step Solution:

1. **Identify the Thermal Decomposition Reaction:**
The problem states that a manganese compound (X) undergoes thermal decomposition at 513 K to yield compound Y (MnO2) and a gaseous product. A common manganese compound that decomposes upon heating is potassium permanganate (KMnO4).

**Reaction:**
\[ 2 KMnO_4 \xrightarrow{513 K} K_2MnO_4 + MnO_2 + O_2 \]

Here, KMnO4 decomposes to form K2MnO4 (Y), MnO2, and O2 (the gaseous product).

2. **Identify Compound Y:**
From the decomposition reaction, we see that Y is K2MnO4.

3. **Identify the Gaseous Product:**
The gaseous product from the decomposition is O2 (oxygen).

4. **Identify the Reaction of MnO2 with NaCl and H2SO4:**
The next part of the problem states that MnO2 reacts with NaCl and concentrated H2SO4 to produce a pungent gas (Z). The reaction can be written as follows:

**Reaction:**
\[ MnO_2 + 4 H_2SO_4 + 2 NaCl \rightarrow MnSO_4 + Na_2SO_4 + 2 H_2O + Cl_2 \]

Here, Cl2 (chlorine gas) is produced, which is known for its pungent smell.

5. **Identify Compound Z:**
From the reaction, we see that Z is Cl2 (chlorine gas).

### Summary of Results:
- **X (Manganese Compound):** KMnO4
- **Y (Product from Decomposition):** K2MnO4
- **Z (Pungent Gas):** Cl2

Thus, the final answer is:
- X = KMnO4
- Y = K2MnO4
- Z = Cl2