You are asked to design a packed column to recover acetone from air continuously by absorption with pure water at \(289 \mathrm{~K}\). The air contains \(3.0 \mathrm{~mol} \%\) acetone, and a \(97 \%\) recovery is desired. The gas flow rate is \(1.42 \mathrm{~m}^{3} / \mathrm{min}\) at \(289 \mathrm{~K}\) and \(1 \mathrm{~atm}\). The maximum-allowable gas superficial velocity is \(0.73 \mathrm{~m} / \mathrm{s}\). It may be assumed that in the range of operation, \(Y_{i}=1.75 X_{i}\), where \(Y_{i}\) and \(X_{i}\) are mol ratios for acetone. Calculate

(a) The minimum water-to-air molar flow rate ratio.

(b) The maximum acetone concentration possible in the aqueous solution.

Answer: \(1.74 \mathrm{~mol} \%\)

(c) The overall number of gas-phase transfer units for a molar flow rate ratio of 1.4 times the minimum.

(d) The packing height, assuming that \(K_{y} a_{h}=3.2 \mathrm{kmol} /\left(\mathrm{m}^{3} \cdot \mathrm{min}\right)\).

(e) The packing height as a function of the molar flow rate ratio, assuming that \(V\) and \(H_{t O G}\) remain constant.