Ozone gas (O₃, solute A) dissolved in high-purity water is commonly used in wet cleaning processes associated with semiconductor device fabrication. It is desired to produce a liquid water stream containing 3.0 gmole O₃/m³(238 mg/L) by a process that does not create any gas bubbles. One engineer€™s idea is shown in the figure below. Liquid water containing 1.0 gmole O₃/m³enters a well-mixed tank at a volumetric flow rate 0.050 m³/h. A pressurized gas mixture of O₃diluted in inert N₂is continuously added the head space of the tank at a total pressure of 1.5 atm. Both the liquid and gas inside the tank are assumed to be well mixed. The gas€”liquid surface area inside the tank is 4.0 m². The process is maintained at 20°C. At 20°C, the solution density is 992.3 kg/m³. For a well-mixed, non-bubbled ozonation tank, the appropriate film mass-transfer coefficients for the liquid and gas films are k_L= 3.0 · 10^-6m/s and k_c= 5.0 · 10^-3m/s, respectively. Equilibrium distribution data for O₃gas dissolved in water at 20°C follows Henry€™s law, with H = 68.2 m³atm/kgmole based on the definition p_A,i= H · c_AL,i.

a. What are m, and the Henry€™s law constant H in units of atm? Is O₃ very soluble in water?
b. What is the overall mass-transfer coefficient K_G, based on the overall gas-phase driving force?
c. What is the overall mass-transfer coefficient K_L based on the overall liquid-phase driving force?
d. For the process to operate as intended, what are the required partial pressure (p_A) and mole fraction (y_A) of ozone (O₃) in the gas phase inside the tank? As part of your solution,

develop a material balance model in algebraic form for solute A that contains the following terms: v₀, volumetric flow rate of liquid (m³/hr); c_AL,₀, inlet concentration of solute A in liquid (gmole A/m³); c_AL, outlet concentration of solute A in liquid (gmole O₃/m³); K_G, overall mass-transfer coefficient based on gas-phase driving force (gmole/m² · s · atm), p_A partial pressure of O₃ in bulk gas phase (atm); H, Henry€™s law constant for O₃ between gas and liquid (m³ · atm/gmole); S, surface area for inter phase mass-transfer (m²). 

e. What is the total transfer rate of O₃, W_A? 

f. Is the mass-transfer process is gas film controlling, liquid film controlling, or neither? Comment on the relative contributions of the film mass-transfer coefficients and the equilibrium distribution relationship on the controlling mass-transfer resistance.

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P. Closed Tank N2+O3 | GAS N2+O3 gas OUT P = 1.5 atm gas IN well-mixed PA = ? Water + Water + NA dissolved O, IN dissolved O, OUT Absorption CAL LIQUID V= 0.05 m³/h CAL = 3.0 gmole/m3 Vo = 0.05 m³/h CALO= 1.0 gmole/m3