Consider a gas$-$phase reaction $2$SO$2+$ O$22$SO$3.$ It was obtained that mole fractions for a certain equilibrium mixture at $1000$ K and $1767$ torr are $2=0\mathrm{.}310,2=0\mathrm{.}250,$ and $3=0\mathrm{.}440.($a$)$ Find $$ and $$G$$ at $1000$ K$,$ assuming ideal gases.