Assuming that the standard enthalpy changes of the reaction are constant in the temperature range of \(298 \mathrm{~K}\) to \(700 \mathrm{~K}\), estimate the equilibrium constant at \(700 \mathrm{~K}\) 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

\[ \begin{aligned} \Delta H_{f, \mathrm{NH}_{3}}^{0} & =-46.1 \mathrm{~kJ} \\ \Delta G_{f, \mathrm{NH}}^{0} & =-16.747 \mathrm{~kJ} \end{aligned} \]