A wetted$-$wall column is used to recover ammonia from flue$-$gas by absorption with water. Unfortunately, the gas phase contains significant amount of CO$2$ and other gases which can also dissolve in water. Thus, a solid polymer membrane $(3-$mm thick$)$ is used in between the liquid and gas phase to selectively permeate only NH$3($component A$).$ The bulk gas and liquid phase compositions are measured to be $6\mathrm{.}0($yA$,$b$)$ and $0\mathrm{.}1($xA$,$b$)$ mole$\%$ NH$3,$ respectively. $(40$ points$)$ Let the mole fraction of NH$3$ in solid polymer phase be zi akin to xi and yi in liquid and gas phase respectively. The equilibrium relation between gas and polymer phase is given by z $=0\mathrm{.}8*$y and between liquid and polymer phase by z $=2*$x$.$ Mass transfer through a membrane is given by the permeability equation: N $=-$P$*($dz$/$dl$)2$ where, N is the molar flux of the diffusing species, P is the permeability $(=3*10-6$ kmol$/$m$.$s$),$ and l is the thickness of the membrane. The temperature is $300$K and the total pressure is $1$ atm. $80\%$ of the total resistance to mass transfer is found to be in the solid polymer phase while resistance to mass transfer is negligible in the gas phase. Calculate a$)$ steady$-$state flux of ammonia in the column $($NA$)$ b$)$ overall mass transfer coefficient based on gas phase $($KY$),$ c$)$ individual film coefficients $($kx$,$ ky$,$ kz$)$ and d$)$ interfacial concentrations $($xA$,$i$,$ yA$,$i$,$ zAG,i$,$ zAL,i$).$ zAG,i and zAL,i refer to the interfacial concentrations of ammonia between the polymer and the gas, and the polymer and water respectively. Interfacial concentrations lie on the equilibrium lines. $($Hint: the film coefficient for the solid polymer phase is defined as follows, kz $=$ NA$/($zAG$,$i $$ zAL,i$))$