Water soluble mixture `underset((ii)." dil ."HCl)overset((i)." "BaCl_(2))to`White ppt.
Filtrate+(Hot and conc.)`HNO_(3)+BaCl_(2) to `White ppt.
The mixture contains:

Options

A. `SO_(4)^(2-)`
B. `SO_(3)^(2-)`
C. both (a) and (b)
D. none of these

Answer

To solve the problem, we need to analyze the reactions step by step to determine the components of the water-soluble mixture.

### Step 1: Identify the Initial Reaction
The mixture is treated with dilute hydrochloric acid (HCl) and barium chloride (BaCl₂), which produces a white precipitate.

**Hint:** Consider the common anions that form white precipitates with Ba²⁺ ions.

### Step 2: Possible Anions
The two common anions that can react with Ba²⁺ to form a white precipitate are:
- Sulfate ions (SO₄²⁻), which form barium sulfate (BaSO₄).
- Sulfite ions (SO₃²⁻), which form barium sulfite (BaSO₃).

Both BaSO₄ and BaSO₃ are white precipitates.

**Hint:** Think about the solubility rules and the color of the precipitates formed.

### Step 3: Analyze the Filtrate Reaction
The filtrate obtained from the first reaction is then treated with hot and concentrated nitric acid (HNO₃) followed by BaCl₂, which again leads to the formation of a white precipitate.

**Hint:** Consider the properties of HNO₃ as a strong oxidizing agent and how it might affect the anions present.

### Step 4: Oxidation of Anions
HNO₃ can oxidize sulfite ions (SO₃²⁻) to sulfate ions (SO₄²⁻). In this case:
- If SO₄²⁻ is present, it remains unchanged as it is already in the highest oxidation state (+6).
- If SO₃²⁻ is present, it will be oxidized to SO₄²⁻.

Thus, the reaction will still produce BaSO₄ as a white precipitate.

**Hint:** Remember that oxidation states can help determine the behavior of the ions in the presence of strong oxidizing agents.

### Step 5: Conclusion
Since both sulfate and sulfite ions can lead to the formation of white precipitates with Ba²⁺, and the sulfite ions can be oxidized to sulfate ions, the mixture can contain both SO₄²⁻ and SO₃²⁻.

**Final Answer:** The mixture contains both sulfate ions (SO₄²⁻) and sulfite ions (SO₃²⁻).

### Summary of Steps:
1. Identify the initial reaction with BaCl₂ and HCl.
2. Recognize the possible anions forming white precipitates.
3. Analyze the subsequent reaction with HNO₃ and BaCl₂.
4. Understand the oxidation of sulfite ions to sulfate ions.
5. Conclude that both anions can be present in the mixture.