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)`

Explanation

To solve the problem, we need to determine the standard enthalpy change (\( \Delta H^\Theta \)) at 298 K and at 773 K for the reaction:

\[ \frac{1}{2} N_2(g) + \frac{3}{2} H_2(g) \rightarrow NH_3(g) \]

### Step 1: Identify the given data
- Standard heat of formation of \( NH_3(g) \) at 298 K: \( \Delta H_f^\Theta = -11.0 \, \text{kcal/mol} \)
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