Assuming that the standard enthalpy changes of the reaction are constant in the temperature range \(298 \mathrm{~K}\) to \(800 \mathrm{~K}\), estimate the equilibrium constant at \(800 \mathrm{~K}\) 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 \(\Delta H_{f, \mathrm{NH}_{3}}^{0}=-46.1 \mathrm{~kJ}\) and \(\Delta G_{f, \mathrm{NH}_{3}}^{0}=-16.747 \mathrm{~kJ}\).