Calculate the equilibrium constant at (25^{circ} mathrm{C}) for the following reaction: [ mathrm{N}_{2} mathrm{O}_{4}(mathrm{~g}) ightarrow 2

Calculate the equilibrium constant at \(25^{\circ} \mathrm{C}\) for the following reaction:

\[ \mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{~g}) \rightarrow 2 \mathrm{NO}_{2}(\mathrm{~g}) \]

Given that \(\Delta G_{f, \mathrm{NO}_{2}}^{0}=51.31 \mathrm{~kJ} / \mathrm{mol}\) and \(\Delta G_{f, \mathrm{~N}_{2} \mathrm{O}_{4}}^{0}=97.54 \mathrm{~kJ} / \mathrm{mol}\).