Beaver Brewing Corporation has received a contract to produce carbonated beverages. A packed-bed absorption tower will be used for dissolving carbon dioxide (CO₂) gas into water. In the present process, pure CO₂ gas at 2.0 atm constant total system pressure is fed into the tower at a flow rate of 1.0 kgmole/min. Pure mountain spring water containing no dissolved CO₂ enters the top of the tower at a flow rate of 4.0 kgmole/min. The desired outlet mole fraction of dissolved CO₂ is 0.1 mole% dissolved in the liquid, which is below the concentration in equilibrium with the CO₂ gas. The tower is packed with 1.0-inch ceramic Intalox saddles. The temperature is maintained at 20°C. At 20°C, the Henry’s law constant for the dissolution of CO₂ gas in water is 25.4 atm · m³/kgmole, the molar concentration of liquid water is 55.5 kgmole/m³ at 20°C, the mass density of liquid water is 998.2 kg/m³, the viscosity of liquid water is 993 · 10^-6 kg/m · s at 20°C. Although this is a gas absorption process, since 100% CO₂ is present in the gas phase, all mass-transfer will occur within the liquid film, and so it will be appropriate to base the calculations on the liquid-phase mole fraction, x_A. 

a. What is the required tower diameter if the pressure drop per unit volume of packing can be no greater than 200 Pa/m? 

b. Based on the result for part (a), what is the liquid film mass transfer coefficient, k_Lα, as estimated by the Sherwood & Holloway correlation provided in Chapter 30? 

c. Based on the result for part (b), what is the volume of packing required to perform the absorption process?