A process is being developed to produce carbonated beverages. As part of this process, a wetted-wall absorption column of 2.0 m length will be used to dissolve carbon dioxide, CO 2 , gas into water....

A process is being developed to produce carbonated beverages. As part of this process, a wetted-wall absorption column of 2.0 m length will be used to dissolve carbon dioxide, CO₂, gas into water. Pure mountain spring water, containing no dissolved CO₂
enters the top of the column at a flow rate of 2.0 g mol/s. Pure 100% CO₂
gas at 2.54 atm is fed to the bottom of the column at a flow rate of 0.5 g mol/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 leaves the top of the column. The inner column diameter is 6.0 cm. The temperature is maintained at 20C. At this temperature, the Henry’s law constant for the dissolution of CO₂
gas in water is 25.4 atm/(kg mol/m³). At 20C, the molar density of liquid water is 55.5 kg mol/m³, the mass density of liquid water is 998.2 kg/m³, and the viscosity of liquid water is 993
kg/ms.

Water has a finite vapor pressure at 20C. 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?