A packed tower, 2.0 ft in diameter and 4.0 ft in packed height, is used to produce a solution of dissolved oxygen in water for a biochemical process. The tower will be pressured to 5.0 atm with pure oxygen (O₂) gas. There is no gas outlet, and pure oxygen gas will enter the tower only to maintain the gas-phase pressure at 5.0 atm. Pure water containing no dissolved O₂ enters the top of the column and flows down the packing at a rate of 200 lb_m/min. The process temperature is 25°C, and at this temperature the equilibrium distribution of oxygen between the gas and liquid phase follows Henry’s law of the form p_A = H · x^*_A with H = 4.38 × 10⁴ atm. The vaporization of water can be ignored so that no water vapor exists in the gas phase. At the column flow conditions, the liquid film capacity coefficient is k_xα = 194 lbmole/ft³ · h. Although this is a gas absorption process, since  100% O₂ 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. Provide a plot of the operating and equilibrium lines in mole fraction coordinates. 

b. What is the mole fraction of dissolved O₂ in the outlet liquid for a packing height of 4.0 ft?