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From the following data , C("s , graphit...

From the following data , `C_("s , graphite") + O_(2(g)) to CO_(2 (g)) Delta H^(@) = - 393 . 5 kJ` /mole `H_(2) (g) + 1//2 O_(2) (g) to H_(2)O (l) Delta H^(@) = -286` kJ/mole `2C_(2) H_(6) (g) + 7O_(2) (g) to 4 CO_(2 (g)) + 6H_(2)O (l) Delta H^(@) = - 3120` kJ/mole
Calculate the standard enthalpy of formation of `C_(2) H_(6) (g)` (in kJ/mole)

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From `eq^(n) (1) Delta H_(f)^(@) (CO_(2)) = -393.5 ` kJ/mole
From `eq^(n) (2) DeltaH_(f)^(@) (H_(2)O) = -286 ` kJ/mole
From `eq^(n) (3) Delta_(r) H^(@) = 4 Delta H_(f)^(@) (CO_(2)) + 6 Delta H_(f)^(@) (H_(2)O) - 2 xx Delta H_(f)^(@) (C_(2) H_(6)) - 7 xx DeltaH_(f)^(@) O_(2) (g) - 3120 = 4 xx (-393. 5) + 6 xx (-286) - 2 xx Delta H_(f)^(@) (C_(2)H_(6))` (As `Delta H_(f)^(@) O_(2) (g) = 0)`
`implies -3120 = -1574 - 1716 - 2 xx Delta H_(f)^(@) (C_(2) H_(6))`
`implies - 3120 + 3290 = -2 xx Delta H_(f)^(@) (C_(2) H_(6))`
`implies 170 = - 2 xx Delta H_(f)^(@) (C_(2) H_(6))`
`implies Delta H_(f)^(@) = - 85 ` kJ/mole
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