At `25^(@)C`, the following heat of formations are given:
`{:("Compound",SO_(2)(g),H_(2)O(l),,),(Delta_(f)H^(Theta)kJmol^(-1),-296.0,-285.0,,):}`
For the reactions at `25^(@)C`,
`2H_(2)S(g) +Fe(s) rarr FeS_(2)(s) +2H_(2)(g), DeltaH^(Theta) =- 137 kJ mool^(-1)`
`H_(2)S(g) +(3)/(2)O_(2)(g) rarr H_(2)O(l) +So_(2)(g),DeltaH^(Theta) =- 562kJ mol^(-1)`
Calculate the heat of formation of `H_(2)S(g)` and `FeS_(2)(g)` at `25^(@)C`.

Explanation

heat of formation of `H_(2)S=x" "kJ//mol`
Heat of formation of `FeS_(2)=y" "kJ//mol`
`2H_(2)S(g)+Fe(s)toFeS_(2)+2H_(2)(g),DeltaH^(@)=-137kJ//mol`
`-137=y-2x` . . . (i)
`H_(2)S(g)+(3)/(2)O_(2)(g)toH_(2)O(l)+SO_(2)(g),DeltaH^(@)=-562kJ//mol`
`-562=-285.83-296.81-x` . . .(ii)
From eq. (ii), `x=-20.64kJ" "mol^(-1)`
From eq. (i), we get
`y=2x-137=2(-20.64)-137=-178.28kJ" "mol^(-1)`
`DeltaH_(fH_(2)S)=-20.64kJ//mol`
`DeltaH_(fFeS_(2))=-178kJ//mol`