Use the standard enthalpies of formation and calculation the enthalpy changes accompanying the following reaction:
a. `CH_(4)(g)+2O_(2)(g) rarr CO_(2)(g)+2H_(2)O(l)`
b. `4Al(s)+3O_(2)(g) rarr 2Al_(2)O_(3)(s)`

Explanation

Given `Delta_(f)HCO_(2)(g)=-393.51 kJ mol^(-1)`
`Delta_(f)HCH_(4)(g)=-74.81 kJ mol^(-1)`
`Delta_(f)HH_(2)O(l)=-285.83 kJ mol^(-1)`
`CH_(4)(g)+2O_(2)(g) rarr CO_(2)(g)+2H_(2)O(l)`
`Delta_(R)H=Sigma(Delta_(f)H "Products")-Sigma(Delta_(f)H "Reactants")`
`=(Delta_(f)H CO_(2)+2Delta_(f)HH_(2)O)-(Delta_(f)HCH_(4)+2Delta_(f)HO_(2))`
`=(-393.51-2xx285.83)-(-74.81+2xx0)`
`=-890.36 kJ mol^(-1)`
b. Given `Delta_(f)H` of `Al_(2)O_(3)(s)=-1675.7 kJ mol^(-1)`
`4 Al(s)+3O_(2)(g) rarr 2Al_(2)O_(3)(s)`
`DeltaH_(R)=Sigma(Delta_(f)H "Products")-Sigma(Delta_(f)H "Reactants")`
`=(2 Delta_(f)HAl_(2)O_(3))-(4 Delta_(f)HAl+3Delta_(f)HO_(2))`
`=2xx-1675.7-(4xx0+3xx0)`
`=-3351.4 kJ mol^(-1)`