Air, containing $3\%$ acetone vapor by volume is to be washed with water in a packed column, operating countercurrently at $1$ bar and $25C.$ Permissible acetone in the exit gas is $0\mathrm{.}5\%$ by volume, and the flow rate of the gas to the column is $300$kmo$\frac{l}{h}.$ Water, which is acetone$-$free, will be supplied at a rate of $1\mathrm{.}25$ times the minimum water flow rate. The column is to be packed with $321\mathrm{.}6mm$ metal Raschig rings.

a$)$ Calculate the flow rate of the water as $k\frac{g}{h}.$

b$)$ Write the operating line equation.

c$)$ Calculate the concentration of liquid solution leaving the column as the mass percent.

d$)$ Calculate the percentage recovery of acetone.

e$)$ Calculate the diameter of the column, for a gas side pressure drop of $400\frac{N}{m^2}$ per meter height of packing.

f$)$ Find out with what percent of the flooding gas velocity the operation is carried out.

g$)$ Calculate the height of packing required.

At the operating pressure and temperature and within the concentration range involved, the equilibrium distribution of acetone between air$-$water is given as $y^{**}=2\mathrm{.}2x,$ where $y$ and $x$ are mole fractions of acetone in gas and liquid respectively.

Height of transfer units for acetone absorption into the water in a column packed with $321\mathrm{.}6mm$ Raschig rings were found experimentally and given as:

$,][H_L=0,395L^{,0\mathrm{.}22}$ where, $H_G$ and $H_L$ in $m,G^{\text{'}}$ and $L^{\text{'}}$ are in $k\frac{g}{m^2}.s.$

Data: ${}_L=997k\frac{g}{m^3},{}_L=0\mathrm{.}894cP.$