A perfectly mixed gas permeation module is separating carbon dioxide from nitrogen using a poly $(2,6-$ dimethylphenylene oxide$)$ membrane. The feed is $20\mathrm{.}0$mol$\%$ carbon dioxide and is at $25C.$ The module has $50\mathrm{.}0m^2$ of membrane. The module is operated with a retentate pressure of $5\mathrm{.}5$atm and a permeate pressure of $1\mathrm{.}01$atm. We desire a permeate that is $40\mathrm{.}0$ mol$\%$ carbon dioxide. The membrane thickness is $t_{ms}=1\mathrm{.}0{10}^{-4}cm.$ Find $y_{r,CO2}=y_{\text{o}\text{u}\text{t}},CO2,$ widehat$(F_P)($in $mo\frac{l}{m}in),$ cut $$ and $($in $mo\frac{l}{m}in),$ and widehat$(F_{in})($in $mo\frac{l}{m}in).$

Table $1$: Permeabilities of gases in various membranes; $cm3(STP)c\frac{m}{c{m}^2.s.cmHg}{10}^{10}$

Reference Code: N $=$ Nakagawa, $1992$; DR $=$ Drioli and Romano, $2001$; G$=$ Geankoplis, $2003$

$\backslash$table$[[$Membrane$,\backslash$table$[[$Temp$.],[("$C$)]],$He$,$H$\_(2),$CO$\_(2),$O$\_(2),$CH$\_(4),$N$\_(2),$Ref$],[\backslash$table$[[$Poly$[1-],[($trimethylsilyl$)],[-1-$propyne$]]],,,,28,000,7730,,4970,$DR$],[\backslash$table$[[$Poly$],[($dimethylsiloxane$)]],25,230,,3240,605,,300,$N$],[\backslash$table$[[$Poly$],[($dimethylsiloxane$)]],)^(35),,,4550,781,,351,$DR$],[\backslash$table$[[$Poly$],[(4-$methyl pentene$)]],25,100,,93,32,,8\mathrm{.}0,$N$],[$Natural rubber,$25,23\mathrm{.}7,90\mathrm{.}8,99\mathrm{.}6,17\mathrm{.}7,,6\mathrm{.}12,$N$],[$Natural rubber,$25,,,153\mathrm{.}0,,,9\mathrm{.}43,$DR$],[$Natural rubber,$25,31,49,131,24,30,8\mathrm{.}1,$G$],[$Silicone rubber,$25,300,550,2700,500,800,250,$G$],[$Ethyl cellulose,$25,53\mathrm{.}4,,113,15,,3\mathrm{.}0,$N$],[$Ethyl cellulose,$35,,,5\mathrm{.}0,12\mathrm{.}4,,3\mathrm{.}4,$DR$],[$Ethyl cellulose,$30,35\mathrm{.}7,49\mathrm{.}2,47\mathrm{.}5,11\mathrm{.}2,7\mathrm{.}47,3\mathrm{.}29,$G$],[\backslash$table$[[$Poly$(2\mathrm{.}6-],[$dimethylphenylene$],[$oxide$)]],$c$^(25),,,75,15,,4\mathrm{.}43,$N$],[$Polystyrene$,20,16\mathrm{.}7,,10\mathrm{.}0,2\mathrm{.}01,,0\mathrm{.}32,$N$],[$Polystyrene$,35,,,12\mathrm{.}4,2\mathrm{.}9,,0\mathrm{.}52,$DR$],[$Polystyrene$,30,40\mathrm{.}8,56\mathrm{.}0,23\mathrm{.}3,7\mathrm{.}47,2\mathrm{.}72,2\mathrm{.}55,$G$],[$Polycarbonate$,25,19,,8\mathrm{.}0,1\mathrm{.}4,,0\mathrm{.}30,$N$],[$Butyl rubber,$25,8\mathrm{.}42,,5\mathrm{.}2,1\mathrm{.}30,,0\mathrm{.}33,$N$],[$Butyl rubber,$35,,,5\mathrm{.}18,,,0\mathrm{.}324,$DR$],[$Acetyl cellulose,$22,13\mathrm{.}6,,,0\mathrm{.}43,,0\mathrm{.}14,$N$],[$Cellulose acetate,$35,,,4\mathrm{.}75,0\mathrm{.}82,,0\mathrm{.}15,$DR$],[$Nylon $6,30,0\mathrm{.}53,,0\mathrm{.}16,0\mathrm{.}038,,,$N$],[$Nylon $66,25,1\mathrm{.}0,,0\mathrm{.}17,0\mathrm{.}034,,0\mathrm{.}008,$G$]]$