In the interest of $CO2$ capture, the exit gas $(100$kmo$\frac{l}{h})$ from an alcohol fermenter consists of an

air$-$CO$2$ mixture containing $10$mol$\%CO2$ that is to be absorbed in a recycled $5\mathrm{.}0-$N solution of

triethanolamine, containing $0\mathrm{.}03$molCO$2$ per mol of amine solution. Assume that the column operates

isothermally at $25C,$ and we desire to absorb $78\%$ of the $CO2$ in the feed gas to the absorber$.$ Assume

that the gas carrier rate is constant through the absorber$,$ and that negligible water and amine are

stripped. VLE data for $CO2$ at $25C$ with this amine solution are tabulated below in mole ratio

coordinates.

$($a$)$ Convert the equilibrium data to mole fractions and calculate the VLE K$-$ratio. Would an assumption of

constant K$-$ratio be a good idea for this system?

$($b$)$ Calculate the mole fraction $y$ and mole ratio $Y$ of $CO2$ in the exiting gas.

$($c$)$ Determine the minimum amount of amine solution using a graphical method and the exiting liquid

mole ratio composition $x$ if the minimum solvent was used.

$($d$)$ Using $1\mathrm{.}2x$ the minimum solvent rate, determine the exiting liquid composition $x$ and the number of

stages needed.