Calculate the standard Gibbs free energy change and the equilibrium constant at \(1 \mathrm{bar}\) and \(298 \mathrm{~K}\) for the ammonia synthesis reaction

\[ \mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{NH}_{3}(\mathrm{~g}) \]

given that the standard free energies of formation at \(298 \mathrm{~K}\) for \(\mathrm{NH}_{3}\) are \(-16.750 \mathrm{~kJ} / \mathrm{mol}\).