$2$: Upper Bound Materials $[20$ pt$]$

Polymer A has a nitrogen permeability coefficient of $0\mathrm{.}5$ Barrers at $25\backslash$deg C and is on the upper bound line for O$2/$N$2$ separation. It is being considered as a membrane material for a new separation, the removal of nitrogen from mixtures with CF$4,$ a commonly used cleaning gas in the microelectronics industry. If this polymer also exhibits upper bound behavior for the N$2/$CF$4$ separation, estimate the CF$4$ permeability and N$2/$CF$4$ separation factor from the upper bound model. Based on a feed containing $2500$ ppm CF$4$ in N$2,$ what is the maximum purity of N$2$ that can be produced in the permeate with this membrane at $25\backslash$deg C$?$ The kinetic diameter of CF$4$ is $4\mathrm{.}7,$ its Lennard$-$Jones force constant value is $134\mathrm{.}0$ K$,$ and its critical temperature is $227\mathrm{.}6$ K$.$ The feed pressure is $10$ bara, and the permeate pressure is $0\mathrm{.}1$ bara