A process is being developed to produce carbonated beverages. As part of this process, a wetted-wall absorption column 2.0 m long will be used to dissolve carbon dioxide (CO₂) gas into water. The process is shown in the figure (next page). In this process, pure mountain spring water containing no dissolved CO₂ enters the top of the column at a flow rate of 2.0 gmole/s (36.0 g/s). Pure, 100% CO₂ gas at 2.54 atm is also fed to the bottom of the column at a flow rate of 0.5 gmole/s. As the liquid flows down the wetted-wall column, CO₂ gas dissolves into the water. The carbonated water exits the bottom of the column, and the unused CO₂ gas exits the top of the column. The inner column diameter is 6.0 cm. The temperature is aintained 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 density of liquid water is 55.5 kgmole/m³ at 20 C, the mass density of liquid water is 998.2 kg/m³ at 20 C, the viscosity of liquid water is 993 X 10^–6 kg/m s at 20 C. Water has a vapor pressure at 20 C. However, for this problem you may assume that the water solvent is essentially nonvolatile, so that 100% CO₂ gas composition is always maintained down the length of the column.
a. What is the maximum possible concentration of dissolved CO₂ in water at 2.54 atm CO₂ partial pressure?
b. What is the liquid-phase mass-transfer coefficient for this process?
c. What is the exit concentration of dissolved CO₂ in the carbonated water if the wetted-wall column is 2.0 m in length?

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Liquid water flow in 2.0 gmole/s (36 g/s) L = 2.0 m D NA D = 6 cm -Liquid film Liquid out (water + dissolved CO₂) 100% CO₂ flow in 2.54 atm, 20 C 0.5 gmole/s