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$))$