Determine the enthalpy of the reaction `C_(3)H_(8)(g)+H_(2)(g) rarr C_(2)H_(6)(g)+CH_(4)(g) at 25^(@)C` using the given heat of combustion alues under standard conditions.
`|{:("Compound":,H_(2)(g),CH_(4)(g),C_(2)H_(6)(g),C("graphite")),(DeltaH^(Theta)(kJmol^(-1)):,-285.8,-890.0,-1560.0,-393.5):}|`
The standard heat of formation of `C_(3)H_(8)(g)` is `-103.8 kJ mol^(-1)`.

Explanation

First we need to determine heat of combustion of `C_(3)H_(8)`
`3C(gr) + 4H_(2)(g) rarr C_(3)H_(8)(g) " "Delta H_(f)^(@) = -103 kJ`
`implies -103 kJ = -3 xx 393 - 4 xx 285.80 - Delta_("comb")^(@) (C_3H_8)`
`implies Delta H_("comb")^(@) (C_(3)H_(8)) = -2219.20 kJ`
`implies Delta H_(r )^(@) = sum Delta H_("comb")^(@) ("reactants") - sum DeltaH_("comb")^(@) ("products")`
`= -2219.20 - 285.80 + 1560 + 890 = -55 kJ`.