Water is being used to absorb acetone in a packed tower whose cross-sectional area is \(0.2 \mathrm{~m}^{2}\). The inlet air contains 3 mole \% acetone and the outlet contains \(0.6 \%\). The gas flow is \(14.0 \mathrm{~kg} \mathrm{~mol} / \mathrm{hr}\) and the pure water inlet flow is \(45.3 \mathrm{~kg}-\mathrm{mole} / \mathrm{hr}\). The local mass transfer coefficients have been measured to be

\[k_{c l}=0.04 \mathrm{~m} / \mathrm{s} \quad k_{c g}=0.0625 \mathrm{~m} / \mathrm{s}\]

The equilibrium relationship for acetone/water is: \(y_{a}=1.186 x_{a}\)

Determine the overall mass transfer coefficient and the tower height required.