Estimate the standard free energy change and equilibrium constant at \(700 \mathrm{~K}\) for the reaction

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

given that the standard heat of formation and standard free energy of formation of \(\mathrm{NH}_{3}\) at \(298 \mathrm{~K}\) is \(-46,100 \mathrm{~J} / \mathrm{mol}\) and \(-16,500 \mathrm{~J} / \mathrm{mol}\) respectively. The specific heats (in \(\mathrm{J} / \mathrm{mol}-\mathrm{K}\) ) as functions of temperature \((\mathrm{K})\) are as follows:

\[ \begin{array}{ll} C_{P}=27.27+4.93 \times 10^{-3} T & \text { for } \mathrm{N}_{2} \\ C_{P}=27.01+3.51 \times 10^{-3} T & \text { for } \mathrm{H}_{2} \\ C_{P}=29.75+25.11 \times 10^{-3} T & \text { for } \mathrm{NH}_{3} \end{array} \]