An aqueous solution of a gas `(X)` gives the following reactions :
(a) It decolourises an acidified `K_2 Cr_2 O_7` solution.
(b) On boiling with `H_2 O_2`, cooling it and then adding an aqueous solution of `BaCl_2`, a precipitate insoluble in `conc. HCl` is obtained.
(c) On passing `H_2 S` in the solution, white turbidity is obtained.
Identify `(X)` and give equations for steps `(a), (b)` and `(c)`.

Explanation

To identify the gas (X) and provide the equations for the reactions described, we will analyze each step systematically.

### Step 1: Analyzing Reaction (a)
The first reaction states that the gas (X) decolorizes an acidified K₂Cr₂O₇ solution.

- **Understanding the Reaction**: K₂Cr₂O₇ (potassium dichromate) is orange in color and acts as an oxidizing agent. If it is decolorized, it indicates that a reducing agent is present in the solution. The acidified solution typically involves sulfuric acid (H₂SO₄).

- **Identifying the Reducing Agent**: The gas (X) must be a reducing agent that can reduce Cr(VI) to Cr(III). A common reducing agent that fits this description is sulfur dioxide (SO₂).
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