A membrane system is used to separate a gas mixture of $50/50$ mol. CO$2/$CH$4$ at $50$ bars, the permeate side is at $1$ bar without purging. Given the membrane have permeance of $10-6$ mol$/$m$2$Pa$$s and CO$2/$CH$4$ permselectivity of $200.$ Calculate the molar composition of the retentate, permeate and$/$or molar fraction of gas coming out as permeate $($R$/$F$).$ MWCO$2=44$ g$/$mol$,$ MWCH$4=16$ g$/$mol$.$ For:

$($a$)40\%$ molar fraction of gas coming out in the permeate stream.

$($b$)$ Given $100$ tons$/$hr of gas needs to be handled through the process, what will be the required membrane area?