Gas absorption is used in the field of purification by allowing the transfer of pollutants from the gas phase to the liquid phase, and it helps in meeting the regulatory requirements for the release of gases into the environment. Assume that you are a newly employed Chemical Engineer and your supervisor wants to test how best you understand mass transfer concepts through the following question that deals with the separation of component A$.$ A gas stream contains $4\mathrm{.}0$ mol$\%A,$ and its content must be reduced to $0\mathrm{.}5$mol$\%$ in a packed absorption tower that operates at $101\mathrm{.}325$kPa and $293K.$ The inlet pure solvent B flow is $68\mathrm{.}0$kmo$\frac{l}{h}$ and the total inlet gas flow is $57\mathrm{.}8$kmo$\frac{l}{h}.$ The tower diameter is $747mm.$ The gas$-$liquid equilibrium data is listed in the Table $1,$ and the local film mass$-$transfer coefficients are as follows:

$k_{y}a=0\mathrm{.}0739$kmo$\frac{l}{m^3}.s.$ mol fraction; $k_{x}a=0\mathrm{.}169$kmo$\frac{l}{m^3}.s.$ mol fraction

If the system obeys Henry's law and$/$or using the design methods for dilute gas mixtures, determine the height of the absorption tower in $cm.$

Table $1.$ The gas$-$liquid equilibrium data at $1$atm

$\backslash$table$[[$Mole fraction of $A$ in$,$Partial pressure of $A$ in gas $(mmHg)$