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

Step (a) suggests that (X) is a reducing agent.
Step (c) suggests, (X) is `SO_(2)` gas
`SO_(2) + 2 H_(2) rarr underset ("Turbidity") (3 S darr + 2 H_(2) O)`
`SO_(2) + K_(2) Cr_(2) O_(7) + H_(2) SO_(4) rarr K_(2) SO_(4) + Cr_(2) (SO_(4))_(3) + H_(2) O`
Colour of acidified `K_(2) Cr_(2) O_(7)` i.e. orange changes to light green as `Cr_(2) O_(7)^(2-)` is reduced to `Cr^(3-)` (green)
`{:([SO_(2)+2H_(2)OtoSO_(4)^(2-)+4H^(o+)+2e^(Ө)]xx3),(Cr_(2)O_(7)^(2-)+14H^(o+)+6e^(Ө)to2Cr^(3)+7H_(2)O),(ulbar(2SO_(2)+2H^(o+)+Cr_(2)O_(7)^(2-)to2Cr^(3+)+3SO_(4)^(2-)+H_(2)O)):}`
`H_(2)O_(2) +SO_(2) rarr H_(2) SO_(4)`
`H_(2) SO_(4) + BaCl_(2) rarr underset("White ppt.") (BaSO_(4) + 2 HCl`
`BaSO_(4)` is insoluble in conc, HCl.