Please design a production scale packed column to reduce the composition of pollutant in an effluent gas by absorption into water. The Henry's law constant for the gas is known to be 75 atm/mol fraction at ambient temperature, and the column will be operated at 5 atm. pressure. The production column needs to reduce the composition of a pollutant in an effluent gas from 500 ppm to 150 ppm, with a molar flow rate of the gas of 20 mol/s. For the given molar flow rate of the gas and packing material used, vendors suggest that a molar liquid flow rate of 500 mol/s in a column that is 80 cm in diameter will lead to excellent distribution of gas/liquid. Mass transfer coefficient (K) is unknown. However, we have a bench scale (pilot) column that is 1.5 m tall and 20 cm wide in which to perform a preliminary study. The pumping system can handle a wide range of gas and liquid flows, so is not anticipated to be limiting. A large supply of the same effluent gas that will ultimately be treated in the production column is available for pilot experimentation. The pilot column can be run at the same temperature and pressure as in the production column. The liquid flow rate is maintained at 31.25 mol/s and the gas flow rate is maintained at 1.25 mol/s in the pilot plant for the linear speed of gas remains the same as the production scale. a) Once the liquid and gas flow rates are chosen, the pilot column is run, and the measured pollutant composition in the pilot column effluent gas is 400 ppm. Determine the mass transfer coefficient (K) in the pilot column. The answer is 6.3 x10^-6 mol/cm3 *s. Please show work. b) Determine the height of the production scale column. Answer is 10.3 m. Please show work