Consider the waste treatment process shown in the figure below. In this process, wastewater containing a dissolved TCE concentration of 50 gmole/m³enters a clarifier, which is essentially a shallow, well-mixed tank with an exposed liquid surface. The overall diameter of the tank is 20.0 m, and the maximum depth of the liquid in the tank is 4.0 m. The clarifier is enclosed to contain the gases that are emitted from the wastewater. Fresh air is blown into this enclosure to sweep away the gases emitted from the clarifier, which are sent to an incinerator. Samples of effluent gas phase and effluent liquid phase were measured for TCE content. The TCE composition in the effluent gas is 4.0 mole%, whereas the TCE concentration dissolved in the effluent liquid phase is 10 gmole TCE/m³liquid. The clarifier operates at 1.0 atm and constant temperature of 20°C. In independent pilot plant studies, for the transferring species TCE, the liquid film mass-transfer coefficient for the clarifier was k_x= 200 gmole/ m²· s, whereas the gas film mass-transfer coefficient for the clarifier was k_y= 0.1 gmole/m²· s. Equilibrium data for the air-TCE-water system at 20°C is represented by Henry€™s law of the form p_A,i= H · x_A,i, with H = 550 atm.

a. What is the overall mass-transfer coefficient based on the liquid phase, as K_L?
b. What is the flux of TCE from the clarifier liquid surface?
c. Develop a well-mixed, steady material balance model for the process. What is the inlet volumetric flow rate of wastewater, v_o (in units of m³/hr) needed to ensure that the liquid effluent TCE concentration is c_AL = 10 gmole TCE/m³?

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D = 20 m Effluent air + 4.0 mole% TCE Fresh air - CALO = 50 gmole/m3 Vo = ? m3/h 4.0 mole% TCE in air CAL = 10 gmole TCE/m³ Effluent liquid CAL = 10 gmole TCE/m³