$29\mathrm{.}19$ Wastewater containing the dissolved contaminant naphthalene is sent to a well$-$mixed open pond maintained at $20C,$ as shown in the figure $($next column$).$ The pond allows the naphthalene to transfer from the water to the air. The pond is $10\mathrm{.}0m$ per side and $1\mathrm{.}0m$ deep. Naphthalene is volatile and slightly

soluble in water, and the equilibrium portioning of naphthalene vapor $($solute $A)$ and water at $20C$ follows Henry's Law with $H=36\mathrm{.}6Pa*\frac{m^3}{g}$mole. The concentration of dissolved naphthalene in the inlet waste water is $c_{AL,o}=0\mathrm{.}25$gmol$\frac{e}{m^3},$ and the outlet concentration of the exiting waste water is $c_{AL}=0\mathrm{.}15$ gmol$\frac{e}{m^3}.$ Air blows over the entire flat liquid surface of the pond, and it has been determined that the convective mass transfer coefficient for naphthalene across the gas film is $k_c=0\mathrm{.}50c\frac{m}{s}(3\mathrm{.}0{10}^{-3}\frac{m}{s}).$ It has also been determined that the liquid film mass transfer coefficient for naphthalene is $k_L=4\mathrm{.}0{10}^{-5}\frac{m}{s}.$ Assume that naphthalene vapor concentration in the bulk air is zero $($e$.$g$.,y_A=0,p_A=0).$ The process is at $1\mathrm{.}0$atm total system pressure and temperature of $20C.$ At these process conditions, the gas$-$phase diffusion coefficient of naphthalene in air is $0\mathrm{.}065c\frac{m^2}{s}.$ The molecular weight of naphthalene $(M_A)$ is $128\frac{g}{g}$mole.

a$.$ Plot out the operating point $(p_A,c_{AL})$ on the $p_{A^{-}}{c}_{AL}$ diagram. What is the Henry's Law constant, $H,$ as defined by $p_{A,i}=H{c}_{AL,i}?$ What are $p_A^{**}$ and $c_{AL}^{**}?$ Plot out $p_A^{**},c_{AL}^{**},p_{A,i},$ and $c_{AL,i}.$

b$.$ What is the overall mass transfer coefficient based on the liquid phase driving force, $K_L?$

c$.$ What is the velocity of air flowing over the pond $(v_{}),$ in units of $\frac{m}{s}$ to achieve $k_c=0\mathrm{.}50c\frac{m}{s},$ and its Reynolds and Schmidt numbers, $Re$ and $Sc?$

d$.$ What is the inlet volumetric flowrate of wastewater into the pond $(v_o),$ in units of $\frac{m^3}{h}?$