An unknown inorganic compound (X) loses its water of crystallisation. On heating and its aqueous solution gives the following reactions `:`
(i) It gives a white turbidity with dilute HCl solution.
(ii) It decolourises a solution of iodide in KI.
(iii) It gives a white precipitate with `AgNO_(3)` solution which turns black on standing.
Identify compound (X) and give chemical equation for the reactions at step (i), (ii) & (iii).

Explanation

(I) Step (ii) suggest that X amy be hypo as it decolorizes solution of `I_(2)` and also loses water of crystallization.
(II) X is `Na_(2)S_(2)O_(3).5H_(2)O` i.e. `:` hypo
`Na_(2)S_(2)O_(3).5H_(2)O rarr Na_(2)S_(2)O_(3)+5H_(2)O`
`Na_(2)S_(2)O_(3)+2HCl overset(Delta)(rarr)2NaCl + underset("Turbidity")(SO_(2)+S+H_(2)O)`
`underset((X))(2Na_(2)S_(2)O_(3))+I_(2)rarr Na_(2)S_(4)O_(6)+2NaI`
`underset((X)"white ppt.")(Na_(2)S_(2)O_(3))+2AgNO_(3)rarrAg_(2)S_(2)O_(3)+2NaNO_(3)`
`Ag_(2)S_(2)O_(3) +H_(2)O rarr underset("Black on standing ")(Ag_(2)S) +H_(2)SO_(4)`