$29\mathrm{.}25$ Ammonia, $N{H}_3,$ in air is being absorbed into water within the enclosed tank shown in the figure below. The liquid and gas phases are both well mixed, and mass transfer occurs only at the exposed gas$-$liquid interface. The diameter of the cylindrical tank is $4m,$ total liquid volume inside the tank is

constant. The bulk gas pressure of ammonia is maintained at $0\mathrm{.}02$atm, and the total gas pressure is constant at $1\mathrm{.}0$atm. The system is isothermal at $20C.$ The inlet volumetric flow rate of water is $200\frac{L}{h}$ and enters $N{H}_3$ free. You may assume that Henry's law, $p_{Ai}=H{c}_{Ai}$ describes the equilibrium distribution of $N{H}_3$ between the gas and the liquid phases where $H=0\mathrm{.}02at\frac{m}{\text{k}\text{g}\text{m}\text{o}\frac{l}{m^3}}.$ The film mass$-$transfer coefficients are $k_G=1\mathrm{.}25$kgmo$\frac{l}{m^2}*h*$ atm and $k_L=0\mathrm{.}05$kgmo$\frac{l}{m^2}*h.(kgmo\frac{l}{m^3}).$

a$.$ Determine the overall mass transfer coefficient, $K_G.$

b$.$ Determine the partial pressure of $N{H}_3$ at the gas$-$liquid interface, $p_{Ai}.$

c$.$ Determine $W_A$ the total molar rate of ammonia transfer.

d$.$ Develop a material balance for $N{H}_3$; then determine $c_{Ai}$ the concentration of $N{H}_3$ in the outlet liquid stream.