Consider an inter phase mass-transfer process for the chlorine dioxide (C1O₂)-air-water system at 20°C, where ClO₂, gas (solute A) is sparingly soluble in water. At the current conditions of operation, the mole fraction of ClO₂, in the bulk gas phase is y_A= 0.040 and the mole fraction of C1O₂in the bulk liquid phase is x_A= 0.00040. The mass density of the liquid phase is 992.3 kg/m³and is not dependent on the very small amount of C1O₂dissolved in it. The molecular weight of water is 18 g/gmole, and the molecular weight of C1O₂is 67.5 g/gmole. The total system pressure is 1.5 atm. The liquid film mass transfer coefficient for C1O₂in water is k_x= 1.0 gmole/m²· s, and the gas film mass-transfer coefficient C1O₂in air is k_G= 0.010 gmole/m²· s atm. The equilibrium distribution data for the C1O₂-water-air system at 20°C are provided below:

a. Plot out the equilibrium line in p_A €“ c_AL coordinates, and the operating point (p_A, c_AL). Is the process gas absorption or liquid stripping? 

b. What is the equilibrium relationship as m equal to? 

c. What is k_L for the liquid film? 

d. If the C1O₂ mole fraction in the bulk gas phase is maintained at 0.040 under 1.5 atm total system pressure, what is the maximum possible dissolved C1O₂ concentration (gmole A/m³) in the liquid phase that could possibly exit the process€”i.e., c^*_AL? 

e. What are the compositions at the gas€“liquid interface, p_A,i and c_AL,i? 

f. What is K_y the overall mass-transfer coefficient based upon the overall gas phase mole fraction driving force? There are several valid approaches for calculating K_y, based on the information provided. Show at least two approaches that lead to the same result. 

g. What is the mass-transfer flux N_A for C1O₂ in units of gmo1e/m² · s?

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1.00E-02 PA 3.00E-02 5.00E-02 7.00E-02 1.00E-01 7.19E-04 1.30E-01 1.10E-01 1.15E-03 2.40E-04 XA 1.64E-03 2.34E-03 2.58E-03 1.50E-01 1.60E-01 1.20E-01 1.40E-01 PA 3.06E-03 3.28E-03 3.52E-03 3.78E-03 2.81E-03 XẠ