Given the following standard free energies at \(25^{\circ} \mathrm{C}\), $$ \begin{array}{ll} \mathrm{N}_{2} \mathrm{O}_{5}(g) \longrightarrow 2 \mathrm{NO}(g)+\frac{3}{2} \mathrm{O}_{2}(g) & \Delta G^{\circ}=-59.2 \mathrm{~kJ} \\ \mathrm{NO}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{NO}_{2}(g) & \Delta G^{\circ}=-35.6 \mathrm{~kJ} \end{array} $$ calculate \(\Delta G^{\circ}\) at \(25^{\circ} \mathrm{C}\) for the reaction $$ 2 \mathrm{NO}_{2}(g)+{ }_{2}^{1} \mathrm{O}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{5}(g) $$

Question: Calculate the standard free energy change for the following reaction using the given data: Reaction: \(2\, \mathrm{NO}_2(g) + \frac{1}{2}\, \mathrm{O}_2(g) \longrightarrow \mathrm{N}_2\mathrm{O}_5(g)\) Given Data: 1. \(\mathrm{N}_{2} \mathrm{O}_{5}(g) \longrightarrow 2 \mathrm{NO}(g) + \frac{3}{2} \mathrm{O}_{2}(g)\) ; \(\Delta G^{\circ} = -59.2 \, \mathrm{kJ}\) 2. \(\mathrm{NO}(g) + \frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{NO}_{2}(g)\) ; \(\Delta G^{\circ} = -35.6\, \mathrm{kJ}\) Answer: The standard free energy change (\(\Delta G^{\circ}\)) of the reaction \(2\, \mathrm{NO}_2(g) + \frac{1}{2}\, \mathrm{O}_2(g) \longrightarrow \mathrm{N}_2\mathrm{O}_5(g)\) at \(25^{\circ} \mathrm{C}\) is \(-12.0\) kJ.