Question $2(30p)$ : The reaction occurring between $N_2$ and $O_2$ gases in internal combustion engines, leading to the formation of the environmentally hazardous product NO$,$ starts with $1$ mole of each reactant. Determine the equilibrium composition under conditions of $900K$ and $1$atm, with the given standard Gibbs free energy change of $G_{600K}=82820\mathrm{.}4\frac{J}{m}ol.$

$\frac{1}{2}{N}_{2()}+\frac{1}{2}{O}_{2(g)}>N{O}_{()}$