$(40$ points$)$ Pure water at $26\mathrm{.}1C$ is flowing past a single sphere of solid benzoic$(50$ points$)$ A gas mixture containing A and $B$ at $101\mathrm{.}32$kPa is brought into contact in a

countercurrent stage tower with pure water at $298K.$ The total inlet gas flow rate to the tower

is $40$kgmo$\frac{l}{h},$ and the total inlet pure water flow rate to be used to absorb $A$ is $100$kgmol

$H_2\frac{O}{h}.$ The gas $B$ is insoluble in water. Water does not vaporize to the gas phase. The

equilibrium relation for $A$ in the gas$-$liquid is $y_A=1\mathrm{.}8x_A.$ The inlet gas to the tower contains

$1\mathrm{.}0$mol$\%$A and the balance B$.90\%$ of $A$ in the inlet gas to the tower is absorbed by water.

a$.$ Draw and label the process flow diagram.

b$.$ Calculate mole fractions of $A$ in the gas and liquid streams leaving the tower.

c$.$ Calculate absorption factors at the top and at the bottom stages of the tower, $A_1$ and $A_N.$

d$.$ Using the Kremser analytical equation calculate the number of theoretical stages required

for this separation.

acid. Diameter of the sphere is $28mm.$ Velocity of water is $0\mathrm{.}25\frac{m}{s}.$ Viscosity

and density of water at $26\mathrm{.}1C$ are $=8\mathrm{.}71{10}^{-4}Pa.s,$ and $=996k\frac{g}{m^3},$

respectively. Diffusivity of benzoic acid in water is $1\mathrm{.}245{10}^{-9}\frac{m^2}{s}$ at $26\mathrm{.}1C$

and $101\mathrm{.}32$kPa. Solubility of benzoic acid in water is $0\mathrm{.}02948$kgmo$\frac{l}{m^3}.$

Calculate the mass$-$transfer coefficient $k_L$ in $\frac{?}{s},$ and the molar flux of benzoic

acid in kgmo$\frac{l}{h*m^2}.$