A $1-$mol mixture of N$2$ and O$2$ where the mol fraction of N$2$ is x is separated

such that there are two products: i$)$ pure N$2,$ and ii$)$ a mixture of N$2$ and O$2$ where the mol fraction of N$2$

is y$,$ and y $<$ x$.($In the example done in class, x $=80\%$ and y $=20\%).$ Everything is at $300$ K and $1$ atm.

Determine the number of moles of i$)$ and ii$).$

b$)$ Determine the minimum work of separation of the process described above, if we assume ideal gas.

c$)$ Determine the the minimum work of separation of the same initial mixture $($mol fraction of N$2=$ x$)$ into

pure N$2$ and pure O$2.$

d$)$ Determine the ratio of the answer in b$)$ to the answer in c$)$a$)$