An amorphous solid (X) burns in air to form a gas ( Y) which turns lime water milky. This gas decolourises aqueous solution of acidified `KMnO_(4).` Gas (Y) reacts with oxygen to give another gas (Z) which is responsible for acid rain. X, Y and Z are

Options

A. `{:("X","Y","Z"),(C, CO,CO_(2)):}`
B. `{:("X","Y","Z"),(S, SO_(2),SO_(3)):}`
C. `{:("X","Y","Z"),(P, P_(2)O_(3),P_(2)O_(5)):}`
D. `{:("X","Y","Z"),(S, SO_(3),H_(2)SO_(4)):}`

Explanation

To solve the problem step by step, we will identify the substances X, Y, and Z based on the given clues.

### Step 1: Identify the Amorphous Solid (X)
The question states that an amorphous solid (X) burns in air to form a gas (Y). The most common amorphous solid that fits this description is **sulfur (S)**.

**Hint:** Think about common amorphous solids that can combust in air.

### Step 2: Determine the Gas Produced (Y)
When sulfur burns in air (which contains oxygen), it reacts to form **sulfur dioxide (SO₂)**.

**Hint:** Consider the combustion reactions of common elements.

### Step 3: Verify the Properties of Gas (Y)
The next clue states that gas Y (sulfur dioxide) turns lime water milky. This occurs because sulfur dioxide reacts with lime water (calcium hydroxide) to form calcium sulfite, which is a precipitate.

The reaction is:
\[ \text{SO}_2 + \text{Ca(OH)}_2 \rightarrow \text{CaSO}_3 \downarrow + \text{H}_2\text{O} \]

**Hint:** Recall the reaction of carbon dioxide with lime water and apply similar reasoning.

### Step 4: Check the Reaction with Acidified KMnO₄
The question also mentions that gas Y decolorizes an acidified KMnO₄ solution. This is because sulfur dioxide can reduce potassium permanganate (KMnO₄) to manganese(II) sulfate (MnSO₄), turning the purple solution colorless.

The reaction is:
\[ \text{SO}_2 + \text{KMnO}_4 \rightarrow \text{K}_2\text{SO}_4 + \text{MnSO}_4 \]

**Hint:** Think about the reducing properties of sulfur dioxide.

### Step 5: Identify the Second Gas (Z)
The next part of the question states that gas Y reacts with oxygen to form another gas (Z). When sulfur dioxide reacts with oxygen, it forms **sulfur trioxide (SO₃)**.

The reaction is:
\[ \text{SO}_2 + \text{O}_2 \rightarrow \text{SO}_3 \]

**Hint:** Consider the oxidation reactions of sulfur compounds.

### Step 6: Link Gas (Z) to Acid Rain
Finally, the question states that gas Z is responsible for acid rain. Sulfur trioxide reacts with water vapor in the atmosphere to form **sulfuric acid (H₂SO₄)**, which is a major component of acid rain.

The reaction is:
\[ \text{SO}_3 + \text{H}_2\text{O} \rightarrow \text{H}_2\text{SO}_4 \]

**Hint:** Think about the formation of acids from oxides in the atmosphere.

### Conclusion
Based on the above steps, we can conclude:
- **X** is sulfur (S)
- **Y** is sulfur dioxide (SO₂)
- **Z** is sulfur trioxide (SO₃)

Thus, the correct answer is:
- **X = Sulfur (S)**
- **Y = Sulfur Dioxide (SO₂)**
- **Z = Sulfur Trioxide (SO₃)**

### Final Answer
X, Y, and Z are:
- X = Sulfur (S)
- Y = Sulfur Dioxide (SO₂)
- Z = Sulfur Trioxide (SO₃)