Calculate the standard enthalpy of combustion of `CH_(4)`, it standard enthalpies of formation of `CH_(4(g)),H_(2)O_((l)),` and `CO_(2(g))` are `-74.81kJ mol^(-1), -285.83kJ mol^(-1)` and `-393.51kJ mol^(-1)` respectively.

Explanation

The desired equation is `:`
`CH_(4)+2O_(2)rarr CO_(2)+2H_(2)O, DeltaH_(1)^(@)=? …(1)`
Given that `:`
`C_((s))+2H_(2) rarr CH_(4(g)),`
`Delta_(2)^(@)=-74.81kJ …(2)`
`H_(2(g))+(1)/(2)O_(2(g))rarr H_(2)O_((l)),`
`DeltaH_(3)^(@)=-285.83kJ ...(3)`
`C_((s))+O_(2(g)) rarr CO_(2(g)),`
`DeltaH_(4)^(@)=-393.51kJ ....(4)`
The obtain `eq. (1)` following mathematical operation must be performed.
`2xx(3)+(4)-(1)`
`2H_(2(g))+O_(2(g))+C_((s))+O_(2(g))-C_((s))-2H_(2) rarr 2H_(2)O_((l))+CO_(2(g))-CH_(4(g))`
or `CH_(4(g))+2O_(2(g)) rarr CO_(2(g))+2H_(2)O_((l)) ...(i)`
Same mathematical treatment is done with `DeltaH` values
`DeltaH_(1)^(@)=[2xxDeltaH_(3)^(@)+DeltaH_(4)^(@)]-[DeltaH_(2)^(@)]`
`=[2xx(-285.83)+(-393.5)]-[-74.81]`
Thus, enthalpy of combustion of `CH_(4)`
`(i.e., DeltaH_(1)^(@)=-890.36kJ)`