Determine enthalpy change for,
`D_(3)H_(8(g))+H_(2(g))rarr C_(2)H_(6(g))+CH_(4(g))`
at `25^(@)C` using heat of combustion values under standard condition.
`{:(Compounds,H_(2(g)),CH_(4(g)),C_(2)H_(6(g)),C_((Graph ite))),(DeltaH^(@)i n kJ//mol,-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

`H_(2(g))+(1)/(2)O_(2(g))rarrH_(2)O_((g)),DeltaH=-285.5kJ ...(1)`
`CH_(4(g))+2O_(2(g))rarr CO_(2(g))+2H_(2)O_((g)),DeltaH=-890kJ ...(2)`
`C_(2)H_(6(g))+(7)/(2)O_(2) rarr 2CO_(2(g))+3H_(2)O_((g)), DeltaH=-1560.0kJ ...(3)`
`3C_((s))+4H_(2(g))rarr C_(3)H_(8(g)),DeltaH=-103.8kJ ...(4)`
`C_((s))+O_(2(g)) rarr CO_(2(g)), DeltaH=-393.5kJ ...(5)`
Add `eqs. (2)` and `(3)`
`CH_(4(g))+C_(2)H_(6(g))+(11)/(2)O_(2(g))rarr 3CO_(2(g))+5H_(2)O_((g)),DeltaH=-2450kJ .....(6)`
Adding `eqs. (4)` and `(6)`
`CH_(4(g))+C_(2)H_(6(g))+3C_((s))+4H_(2(g))+(11)/(2)O_(2(g)) rarr 3CO_(2(g))+5H_(2)O_((g))+C_(3)H_(8(g)), DeltaH=-2553.8kJ ...(7)`
Multiply `eq.(1)` by 5 and `eq. (5)` by 3, then add them
`5H_(2(g))+3C_((s))+(11)/(2)O_(2(g))rarr 5H_(2)O_((g))+3CO_(2(g)),DeltaH=-2609.5kJ ...(8)`
Subtract `eq.(8)` from `eq. (7)` and on rearranging
`CH_(4(g))+C_(2)H_(6(g))+3C_((s))+4H_(2(g))+(11)/(2)O_(2(g))rarr 3CO_(2(g))+5H_(2)O_((g))+C_(2)H_(8(g)),DeltaH=-2553.8kJ`
`ul( {:(5H_(2(g)),+3C_((s)),+(11)/(2)O_(2(g)),rarr,5H_(2)O_((g)),+3CO_(2(g)),, DeltaH=-2609.5kJ),(-,-,-,,-,-," +"):} )`
`H_(2(g))+C_(3)H_(8(g))rarr CH_(4(g))+C_(2)H_(6(g)),DeltaH=-55.7kJ`