A packed-bed liquid stripping process will be designed to remove benzene from contaminated wastewater. A liquid wastewater stream containing dissolved benzene of concentration 693 mg benzene/L (mole fraction 1.6 × 10^-4) is sent to the top of a packed tower at a flow rate of 100 lbmole/ft² · h. Air containing no benzene vapor is sent to the bottom of the tower. The tower is maintained at 1.20 atm total system pressure and 20°C. It is desired to reduce the mole fraction of dissolved benzene in the water to only 86 mg/L (mole fraction 2.0 × 10^-5), and to increase the composition of benzene vapor in the air stream exiting the top of the tower to a mole fraction of 0.01 (1.0 mole% benzene vapor in air). At these flow conditions, the film mass-transfer coefficients for the packing are k_Lα = 17.4 h^-1 and k_Gα = 7.4 lbmole/ft³ · h · atm, for the liquid and gas films, respectively. At 20°C, the equilibrium distribution curve for benzene-water air system is linear with Henry’s law constant H = 150 atm based on the definition p_A = H ·x^*_A. At 20°C, water is nonvolatile relative to benzene, the maximum soluble concentration of volatile benzene in dissolved in liquid water is 780 mg/L, and the density of liquid water is 62.4 lb_m/ft³. The molecular weight of benzene is 78 g/gmole. For a liquid stripping process, by convention the interphase mass-transfer process is based on the overall liquid-phase mass-transfer driving force. 

a. Plot out the equilibrium and operating lines for the process in mole fraction (y_A vs. x_A) coordinates. Do the desired terminal stream compositions allow for mass-transfer to occur between phases? Explain why. 

b. Determine the overall mass-transfer driving force (x^*_A - x_A) at the top and bottom of the tower, and the log-mean driving force. Indicate these driving forces on the y_A vs. x_A plot from part (a). 

c. Estimate the height of packing required to achieve the separation.