The standared heat of formation listed for gaseous `NH_(3)` is `-11.0kcal mol^(-1)` at `298K`. Given that at `298k`, the constant pressure heat capacities of gaseous `N_(2),H_(2)`, and `NH_(3)` are, respectively, `7.0, 6.0` and `8.0 cal mol^(-1)`. Determine `DeltaH^(Theta)underset(298K)` and `DeltaH_(773K)` for the reactions:
`(1)/(2)N_(2)(g) +(3)/(2)H_(2)(g) rarr NH_(3)(g)`
`(1)/(2)N_(2)(g) +(3)/(2)H_(2)(g) rarr NH_(3)(g)`
`(1)/(2)N_(2)(g) +(3)/(2)H_(2)(g) rarr NH_(3)(g)`
`DeltaH_(298K)=sumunderset(f(P))H^(Theta)-sumunderset(f(R))H^(Theta) =(-11.0-0) =- 11.0 kcal mol^(-1)`
`(DeltaH_(2)-DeltaH_(1))/(T_(2)-T_(1)) = DeltaC_(P)`
`(DeltaH_(2)-(-11.0))/(773-298) = (8.0-(1)/(2)xx7.0-(3)/(2)xx6.0) xx 10^(-3)`
`DeltaH^(Theta)_(2) =- 13.137k cal mol^(-1)`