$3000\mathrm{.}0$ mol pure nitrogen gas at $400$ K and $1$ atm is mixed with $500\mathrm{.}0$ mol pure

hydrogen gas at $200$ K and $1$ atm in a reactor. The gases mix and equilibrate to a

common temperature at $1$ atm. The $$p for each gas is $(7/2)$R$,$ no heat escapes the

reactor, and you may treat the gases as ideal. The standard molar entropy for nitrogen

gas and hydrogen gas are $191\mathrm{.}6$ J mol$-1$ K$-1$ and $130\mathrm{.}7$ J mol$-1$ K$-1,$ respectively, and are

constant over this temperature interval. Calculate $$H$,$S$,$ and $$G of the entire process.

Hint: note that at least two state changes occur here, so set a process path that best

simplifies your calculations