Air can be separated into oxygen$-$enriched and

nitrogen$-$enriched streams by gas permeation through dense

membranes. A polyethylmethacrylate$($PEMA$)$ membrane in the form

of a thin film $(0\mathrm{.}2\backslash$mu m thick$)$ is being considered for this purpose. The

permeabilities of this membrane for oxygen $($A$)$ and nitrogen $($B$)$ at

$298$K are $3\mathrm{.}97\backslash$times $1013$ and $0\mathrm{.}76\backslash$times $1013$ mol$/($m$$s$$kPa$),$ respectively. An

air flow rate of $1\mathrm{.}0$ m$3/$s$($at STP$)$ is sent to the membrane separator at

$298$ K and a pressure of $1\mathrm{.}0$ MPa. The pressure on the permeate side

will be $0\mathrm{.}1$ MPa. Calculate the concentration of the permeate and

retentate, and the membrane area required for the separation if the

cut, $\backslash$theta is $0\mathrm{.}6,$ and the separation factor is $75\%$ of the ideal.