Given the following reactions and their values of $\Delta G^{\circ},$ calculate the value of $\Delta G_{\mathrm{f}}^{\circ}$ for $\mathrm{N}_{2} \mathrm{O}_{5}(g)$.
$$
\begin{aligned}
2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow & 2 \mathrm{H}_{2} \mathrm{O}(l) \\
& \Delta G^{\circ}=-474.4 \mathrm{~kJ} \\
\mathrm{~N}_{2} \mathrm{O}_{5}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow & 2 \mathrm{HNO}_{3}(l) \\
& \Delta G^{\circ}=-37.6 \mathrm{~kJ}
\end{aligned}
$$
$\begin{aligned} \frac{1}{2} \mathrm{~N}_{2}(g)+\frac{3}{2} \mathrm{O}_{2}(g)+2 \mathrm{H}_{2}(g) \longrightarrow & \mathrm{HNO}_{3}(l) \\ \Delta G^{\circ}=-79.91 \mathrm{~kJ} \end{aligned}$