$29\mathrm{.}20$ Consider the waste treatment operation proposed in the figure below. In this process, wastewater conraining a TCE concentration of $50$gmo$\frac{l}{m^3}$ enters a clarifier, which is essentially a shallow, well$-$mixed tank with an exposed liquid surface. The overall diameter is $20\mathrm{.}0m$ and the maximum depth of the liquid in the tank is $4\mathrm{.}0m.$ The clarifier is enclosed to contain the gases $($often quite odorous$)$ that are emitted from the wastewater. Fresh air is blown into this enclosure to sweep away the gases emitted from the clarifier and is then sent to an incinerator. The TCE content in the effluent gas is $4\mathrm{.}0$mol$\%,$ whereas the TCE content in the effluent liquid phase is $10g$ mol TCE $\frac{?}{m^3}$ liquid. The clarifier operates at $1\mathrm{.}0$atm and a constant temperature of $20C.$ In independent pilot

plant studies for TCE, the liquid film mass$-$transfer coefficient for the clarifier was, $k_x=200$gmo$\frac{l}{m^2}*s,$ whereas the gas film mass$-$transfer coefficient for the clarifier was $k_y=0\mathrm{.}1$gmo$\frac{l}{?}{m}^2.$ s$.$ Equilibrium data for the air$-$TCE$-$water system at $20C$ are represented by Henry's law in the form $p_A=H^{\text{'}}{x}_A$ with $H^{\text{'}}=550$atm. The molar density of the effluent liquid is $66$gmo$\frac{l}{m^3}.$

a$.$ What is the overall mass$-$transfer coefficient based on the liquid phase, $K_L?$

b$.$ What is the flux of TCE from the clarifier liquid surface?

c$.$ What is the inlet volumetric flow rate of wastewater, in units of $\frac{m^3}{h},$ needed to ensure that the liquid effluent TCE concentration is $10$gmolTC$\frac{E}{m^3}?$