In a packed column with a cross$-$sectional area of $0\mathrm{.}2$ m$2,$ acetone will be adsorbed with pure water at $25$oC and $1$ atm. There is $2$ mol$\%$ acetone in the feed gas and $0\mathrm{.}4$ mol$\%$ acetone in the outlet gas. The equilibrium relation can be taken as y $=1\mathrm{.}2$x$.$ Gas flow is $15$ kmol inert air$/$hour$,$ pure water inlet flow is $55$ kmol water$/$hour$.$ It is given as the fraction K in the column $=2,25\mathrm{.}10-2$ kmol$/$s$.$m$3.$mol. Calculate the column length $($hint: Vort$/$S $($y$1-$y$2)=$ K to z $($y$-$y$*)$M$).$