A membrane module performs air separation to obtain higher purity oxygen

permeate product. For simplicity, assume that the air is made of $35$ vol$\%$ O$2$ and $65$ vol$\%$ N$2.$ The air feed

flow rate is $8,000$ cm$3($STP$)/$hr$.$ For this membrane module, which is $0\mathrm{.}0004$ cm in thickness, the

permeability of O$2$ and N$2$ are determined to be $65\backslash$times $10-10[$cm$3($STP$)$cm$/($cm$2$s$$cmHg$)]$ and $5\backslash$times $10-10[$cm$3$

$($STP$)$cm$/($cm$2$s$$cmHg$)],$ respectively. The retentate side has a uniform pressure of $10\mathrm{.}5$ bar, the permeate

side has a uniform pressure of $1\mathrm{.}1$ bar. Our goal is to produce a permeate stream containing $70$ vol$\%$ O$2.$

Conversion factor that might be useful: $1$ mol of ideal gas has $22\mathrm{.}4$ L at STP$.$

$($a$)$ Calculate the O $2$ selectivity of this membrane over N $2$ AND the N$2$ permeance of the membrane

$($b$)$ For the retentate stream, determine its oxygen composition $($in vol$\%)$

$($c$)$ What is the volumetric flow rate?

$($d$)$ Calculate the cut fraction.

$($e$)$ Determine the area of the membrane module