A saturated liquid solution of $40$mol$\%$ acetone and $60$mol$\%$ acetic acid is fed at a rate of $100$ lbmo$\frac{l}{?}$ hour to a distillation column. The desired separation of acetone is a $96$mol$\%$ distillate concentration and a $5$mol$\%$ bottoms concentration. The column is operated at $1\mathrm{.}6$ times the minimum reflux ratio, so $R_D=0\mathrm{.}44.$ The average column temperature is $95C$ and the average liquid density is $0\mathrm{.}95\frac{g}{c}{m}^3.$ The liquid depth on a tray is $1\mathrm{.}5cm,$ and the tower diameter is $30cm.$ The mass transfer coefficients are $k_{G}a=505se{c}^{-1}$ and $k_{L}a=1\mathrm{.}8se{c}^{-1}.$ Equilibrium data for acetone and acetic acid are

$\backslash$table$[[\backslash$table$[[x$