An acetone$/$air mixture containing $0\mathrm{.}015$mol fraction of acetone has the mol fraction reduced to $0\mathrm{.}0015$ by countercurrent absorption with pure water in a packed tower. The gas flowrate entering the column is $35mo\frac{l}{s}$ while the water entering is at $89mo\frac{l}{s}.$ The column pressure is $200$kPa, the temperature is $60C$ and the diameter is $90cm.$

You may assume all solutions are dilute. For this system, Henry's Law holds with a Henry's Law constant of $H=350$kPa.

$($a$)$ If the total height of packing in the tower is $10m,$ and the interfacial area for mass transfer, $a=37\mathrm{.}4\frac{m^2}{m^3},$ what is the overall mass transfer coefficient based on the gas phase, $K_{0y}?$