Predict `Delta_(f) H^(@)` for the reaction
`n - C_(6) H_(14) (1) + CH_(4) (g) rarr n- C_(7) H_(16) (1) + H_(2) (g)`
if the standard enthalpies of combustion are `- 981.8 - 210.8,- 1149.4`, and `68.38 kcal mol^(-1)` for `n - C_(6) H_(14), CH_(4), n - C_(7) H_(16)`, and `H_(2)`, respectively, at `298 K`.
Strategy : Use Hess's law in the form of Eq.

Explanation

Applying Eq. to the desired reaction, we get
`Delta_(f) H^(@) = - [(1) Delta_(c ) H^(@) (n - C_(7) H_(16), 1) + (1) Delta_(c ) H^(@) (H_(2), g)] + [(1) Delta_(C ) H^(@) (n - C_(6) H_(14),1) + (1) Delta_(C ) H^(@) (CH_(4) g]`
`= -[(1) (-1149.4) + (1) (-68.38)] + [(1) (-989.8) + (1) (-210.8)]`
`= (17.7 kcal) (4.184 kJ kcal^(-1))`
`= 74.1 kJ`