The unit has two inlet streams: one gas stream consisting of $97$ mol.$\%$ air and $3$ mol.$\%$ acetone, and one liquid stream consisting of pure water. The acetone and air is premixed before entering the unit. The acetone from the air is continuously absorbed with water at $15$ and $1$ atm. At the aforementioned conditions, the following information is given:

$-$ The gas flow rate is $20$ft$^3/$min$.$

$-$ A $97\%$ of acetone recovery is desired.

$-$ The density of gas is assumed to $1\mathrm{.}259$kg$/$m$^3.$

$-$ There is no absorption of air and no stripping of water.

$-$ The cross$-$sectional area of the column is approximately $0\mathrm{.}0119$ m$^2.$

$-$ The overall volumetric mass transfer coefficient in gas phase Kya$=320\mathrm{.}36$ kmol$/($m$^3).$

$-$ The equilibrium relation is y$=1\mathrm{.}294$x where y and x are the mole fractions of acetone in the gas and liquid phases, respectively.

$1)$ Make a schematic drawing of the setup.

$2)$ Calculate the following variables:

$-$The minimum liquid molar flow rate in kmo$\frac{l}{h}.$

$-$The number of theoretical stages for a liquid molar flow ratio $1\mathrm{.}5$ times the minimum.

$-$The number of overall gas transfer units $($NTU$).$

$-$ he overall height of the gas transfer unit $($HTU$)$ in meters.

$-$The height of the column in meters

$3)$ Quantitatively and qualitatively discuss how the height of the column varies as a function of the liquid$-$to$-$vapor molar flow rate ratio $($e$.$g$.,1\mathrm{.}0,1\mathrm{.}5,2,10),$ assuming that the gas flow rate and HTU remain constant.

$4)$ Quantitatively and qualitatively discuss how the recovery of acetone is affected by the liquid$-$to$-$vapor molar flow rate ratio $($e$.$g$.,1\mathrm{.}0,1\mathrm{.}5,2,10),$ assuming that the number of theoretical stages remains constant at $6\mathrm{.}42.$

$5)$ Compare the results from questions $3)$ and $4).$ What can you conclude? What would you recommend to obtain a high recovery of acetone?