A wetted$-$wall column is used to recover ammonia from flue$-$gas by absorption with water.

Unfortunately, the gas phase contains significant amount of $C{O}_2$ 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 $N{H}_3($component $A).$ The bulk gas and liquid phase

compositions are measured to be $6\mathrm{.}0(y_{A,b})$ and $0\mathrm{.}1(x_{A,b})mole\%N{H}_3,$ respectively. $(40$ points$)$

Let the mole fraction of $N{H}_3$ in solid polymer phase be $z_i$ akin to $x_i$ and $y_i$ 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:

$N=-P^{**}(d\frac{z}{d}l)$