$(40$ points$)$ A feed solution containing $5$gNaC$\frac{l}{L}(=1001\frac{kg}{m^3})$ is purified using a reverse osmosis system. Water permeability constant $(A_w)$ and a solute $(NaCl)$ permeability constant $(A_s)$ are $5{10}^{-4}k\frac{g}{m^2}*s*atm,$ and $4{10}^{-7}\frac{m}{s},$ respectively, and $P=30$atm. Assume that the fraction recovered of the solvent water is $0\mathrm{.}15.$ The flow rate $q_2$ of the permeate water solution is $50\frac{L}{m}in($see Figure $1).$ You may assume complete mixing model applies. Calculate $c_1$ and $c_2$ in kgNaC$\frac{l}{m^3}$ and the membrane area in $m^2.$ Calculate R$.$