We are separating \(1.0 \mathrm{kmol} / \mathrm{min}\) of a mixture that is \(25 \mathrm{~mol} \% \mathrm{CO}_{2}\) and \(75 \mathrm{~mol} \% \mathrm{~N}_{2}\) at \(25^{\circ} \mathrm{C}\) on a silicone rubber membrane. The permeator is perfectly mixed. The permeate mole fraction of \(\mathrm{CO}_{2}\) is \(\mathrm{y}_{\mathrm{p}}=0.46\). The inlet pressure is \(7.2 \mathrm{bar}\), and the outlet pressure is \(1.2 \mathrm{bar}\). Assume ideal gas. Find the membrane area required in \(\mathrm{m}^{2}\). Data are in Table \(19-2\).