An air stream contains $12\%$ of a volatile organic component $($VOC$)$ that is to be absorbed by countercurrent

contact with pure water in a valve$-$tray column. The final concentration in the exiting air is not to exceed

$1\%.$ The column will operate at $20C$ and $101$kPa.

Equilibrium data for the VOC at these conditions within the range of compositions of interest $($up to $15\%$

mol fraction$)$ can be approximated using: $,Y=-2\mathrm{.}86x^2+1\mathrm{.}35x$

where $x$ and $Y$ are solute$-$free mol fraction of VOC in water and air, respectively.

a$)$ Determine the minimum amount of water to be used per mol of air to achieve the absorption$.$

b$)$ Determine the number of equilibrium stages if we use $1\mathrm{.}5$ times the minimum flow of water.

c$)$ Let $N$ be your answer in part $c,$ rounded up to an integer. Suppose we are to use exactly $N+3$ equilibrium

stages $($three more stages than $N$ stages$)$ to achieve the absorption as described above. Determine the

amount of water to be used per mol of air. Hint: For this part, some iterations may be needed; therefore,

it may be easier to implement the graphical method on Matlab or Excel.