$2{\mathrm{NO}}_2\left(g\right)⟶{\mathrm{N}}_2{\mathrm{O}}_4\left(g\right)$

${\mathrm{\Delta U}}_{\mathrm{f}}^{\circ }\left[{\mathrm{N}}_2{\mathrm{O}}_4\left(\mathrm{g}\right)\right]=2 \mathrm{kcal}/\mathrm{mole}$ and $\mathrm{\Delta }{U}^{\circ }\text{ reaction }=-16$ $\mathrm{Kcal}/\mathrm{mol}$, then calculate $\mathrm{\Delta }{H}_{\text{formation }}^{\circ }$ of ${\mathrm{NO}}_2$ ate ${727}^{0}C$:

$\begin{array}{l}2{\mathrm{NO}}_2\left(\mathrm{g}\right)⟶{\mathrm{N}}_2{\mathrm{O}}_4\left(\mathrm{g}\right)\\ -16=2-2{\mathrm{\Delta U}}_{\mathrm{f}}^{\circ }\left[{\mathrm{NO}}_2\left(\mathrm{g}\right)\right]\\ {\mathrm{\Delta U}}_{\mathrm{f}}^{\circ }\left[{\mathrm{NO}}_2\left(\mathrm{g}\right)\right]=9 \mathrm{Kcal}/\mathrm{mol}\\ \frac{1}{2}{\mathrm{N}}_2\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)⟶{\mathrm{NO}}_2\left(\mathrm{g}\right)\\ {\mathrm{\Delta H}}_{\mathrm{f}}^{\circ }\left[{\mathrm{NO}}_2\left(\mathrm{g}\right)\right]=9-\frac{1}{2}\left(\frac{2}{1000}\right)\left(1000\right)\\ {\mathrm{\Delta H}}_{\mathrm{f}}^{\circ }\left[{\mathrm{NO}}_2\left(\mathrm{g}\right)\right]=8\mathrm{Kcal}/\mathrm{mol}\end{array}$