It is desired to absorb $89\%$ of the ammonia in a gas containing $4\mathrm{.}0$mol$\%$ in air in a

countercurrent stage tower. The total inlet gas flow to the tower is $20\mathrm{.}0$kgmo$\frac{l}{h},$ and the total

inlet pure water flow to be used to absorb the ammonia is $75kgmol{H}_2\frac{O}{h}.$ The process is to

operate isothermally at $310K$ and a total pressure of $101\mathrm{.}3$kPa. The equilibrium relation for the

ammonia in the gas$-$liquid is $y_A=2\mathrm{.}53x_A.$ Determine the number of theoretical stages required for

this separation $($a$)$ graphically and $($b$)$ using the analytical Kremser equation.